Light directional angle control for light-emitting device and light-emitting apparatus

Abstract

A light-emitting device includes a photoluminescent layer that emits light containing first light, a light-transmissive layer located on or near the photoluminescent layer, a low-refractive-index layer and a high-refractive-index layer. A submicron structure is defined on the photoluminescent layer and/or the light-transmissive layer. The low-refractive-index layer is located on or near the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and light-transmissive layer. The high-refractive-index layer is located on or near the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer. The submicron structure includes at least projections or recesses and satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light.

Claims

1. A light-emitting device comprising: a photoluminescent layer that has a first surface perpendicular to a thickness direction thereof and emits light containing first light, an area of the first surface being larger than a sectional area of the photoluminescent layer perpendicular to the first surface; a light-transmissive layer located on the photoluminescent layer; and a low-refractive-index layer located on the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and the light-transmissive layer, the low-refractive-index layer having a lower refractive index than the photoluminescent layer, wherein at least one of the photoluminescent layer and the light-transmissive layer has a first submicron structure comprising at least projections or recesses arranged perpendicular to the thickness direction of the photoluminescent layer, at least one of the photoluminescent layer and the light-transmissive layer has a light emitting surface perpendicular to the thickness direction of the photoluminescent layer, the first light being emitted from the light emitting surface, the first submicron structure satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a where D.sub.int is a center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light, and a thickness of the photoluminescent layer, the refractive index of the photoluminescent layer, and the center-to-center distance are set to limit a directional angle of the first light emitted from the light emitting surface, the light-emitting device further comprises a high-refractive-index layer located on the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer, wherein the first submicron structure comprises the projections and recesses, the high-refractive-index layer has a lower refractive index than the photoluminescent layer, and the light-emitting device satisfies the following relationship:
(4m1).sub.a/8<h.sub.pn.sub.pf+n.sub.Wt.sub.W<(4m+1).sub.a/8 where m is a natural number, h.sub.p is the height of the first submicron structure, n.sub.p is the refractive index of the first submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the first submicron structure, n.sub.W is the refractive index of the photoluminescent layer, and t.sub.W is the thickness of the photoluminescent layer.

2. The light-emitting device according to claim 1, wherein the low-refractive-index layer has a thickness of .sub.a/6 or more.

3. The light-emitting device according to claim 1, wherein a second submicron structure is defined on an interface between the photoluminescent layer and the low-refractive-index layer.

4. The light-emitting device according to claim 3, wherein the second submicron structure has a same period as the first submicron structure.

5. The light-emitting device according to claim 3, further comprising a high-refractive-index layer located on the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer, wherein a third submicron structure is defined on an interface between the low-refractive-index layer and the high-refractive-index layer.

6. The light-emitting device according to claim 5, wherein the third submicron structure has a same period as the first and second submicron structures.

7. A light-emitting apparatus comprising: the light-emitting device according to claim 1; and a light source that directs excitation light into the light-emitting device.

8. A light-emitting device according to claim 1, wherein the photoluminescent layer includes a phosphor.

9. The light-emitting device according to claim 1, wherein 380 nm.sub.a780 nm is satisfied.

10. The light-emitting device according to claim 1, wherein the thickness of the photoluminescent layer, the refractive index of the photoluminescent layer and the center-to-center distance are set to allow an electric field to be formed in the photoluminescent layer, in which antinodes of the electric field are located in areas, the areas each corresponding to respective one of the projections and/or recesses.

11. The light-emitting device according to claim 1, wherein the light-transmissive layer is located indirectly on the photoluminescent layer.

12. The light-emitting device according to claim 1, wherein the directional angle is limited less than 15 degrees.

13. The light-emitting device according to claim 1, wherein the thickness of the photoluminescent layer, the refractive index of the photoluminescent layer and the center-to-center distance are set to allow an electric field to be formed in the photoluminescent layer, in which antinodes of the electric field are located at, or adjacent to, at least the projections or recesses.

14. A light-emitting device comprising: a photoluminescent layer that has a first surface perpendicular to a thickness direction thereof and emits light containing first light, an area of the first surface being larger than a sectional area of the photoluminescent layer perpendicular to the first surface; a light-transmissive layer located on the photoluminescent layer; and a low-refractive-index layer located on the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and the light-transmissive layer, the low-refractive-index layer having a lower refractive index than the photoluminescent layer, wherein at least one of the photoluminescent layer and the light-transmissive layer has a first submicron structure comprising at least projections or recesses arranged perpendicular to the thickness direction of the photoluminescent layer, at least one of the photoluminescent layer and the light-transmissive layer has a light emitting surface perpendicular to the thickness direction of the photoluminescent layer, the first light being emitted from the light emitting surface, the first submicron structure satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a where D.sub.int is a center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light, and a thickness of the photoluminescent layer, the refractive index of the photoluminescent layer, and the center-to-center distance are set to limit a directional angle of the first light emitted from the light emitting surface, the light-emitting device further comprises a high-refractive-index layer located on the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer, wherein the first submicron structure comprises the projections and recesses, the high-refractive-index layer has a higher refractive index than the photoluminescent layer, and the light-emitting device satisfies the following relationship:
(4m3).sub.a/8<h.sub.pn.sub.pf+n.sub.Lt.sub.L+n.sub.Wt.sub.W<(4m1).sub.a/8 where m is a natural number, h.sub.p is the height of the first submicron structure, n.sub.p is the refractive index of the first submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the first submicron structure, n.sub.W is the refractive index of the photoluminescent layer, t.sub.W is the thickness of the photoluminescent layer, n.sub.L is the refractive index of the low-refractive-index layer, and t.sub.L is the thickness of the low-refractive-index layer.

15. A light-emitting device comprising: a photoluminescent layer that has a first surface perpendicular to a thickness direction thereof and emits light containing first light, an area of the first surface being larger than a sectional area of the photoluminescent layer perpendicular to the first surface; a light-transmissive layer having a higher refractive index than the photoluminescent layer; a low-refractive-index layer located on the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and the light-transmissive layer, the low-refractive-index layer having a lower refractive index than the photoluminescent layer; and a high-refractive-index layer located on the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer, wherein the light-transmissive layer has a submicron structure comprising a periodic structure having at least projections or recesses arranged perpendicular to the thickness direction of the photoluminescent layer, at least one of the photoluminescent layer and the light-transmissive layer has a light emitting surface perpendicular to the thickness direction of the photoluminescent layer, the first light being emitted from the light emitting surface, the periodic structure satisfies the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a where p.sub.a is the period of the periodic structure, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light, and a thickness of the photoluminescent layer, the refractive index of the photoluminescent layer, and the period of the periodic structure are set to limit a directional angle of the first light emitted from the light emitting surface, the high-refractive-index layer has a lower refractive index than the photoluminescent layer, and the light-emitting device satisfies the following relationship:
(4m-1) .sub.a/8<h.sub.pn.sub.pf +n.sub.wt.sub.w<(4m+1).sub.a/8 where m is a natural number, h.sub.p is the height of the first submicron structure, n.sub.p is the refractive index of the first submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the first submicron structure, n.sub.w is the refractive index of the photoluminescent layer and t.sub.w is the thickness of the photoluminescent layer.

16. The light-emitting device according to claim 15, wherein a distance between the submicron structure and the photoluminescent layer is more than .sub.a/2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a perspective view showing the structure of a light-emitting device according to an embodiment;

(2) FIG. 1B is a partial sectional view of the light-emitting device shown in FIG. 1A;

(3) FIG. 1C is a perspective view showing the structure of a light-emitting device according to another embodiment;

(4) FIG. 1D is a partial sectional view of the light-emitting device shown in FIG. 1C;

(5) FIG. 2 is a graph showing the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying periods of a periodic structure;

(6) FIG. 3 is a graph illustrating the conditions for m=1 and m=3 in inequality (10);

(7) FIG. 4 is a graph showing the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying thicknesses t of a photoluminescent layer;

(8) FIG. 5A is a graph showing the results of calculations of the electric field distribution of a mode to guide light in the x direction for a thickness t of 238 nm;

(9) FIG. 5B is a graph showing the results of calculations of the electric field distribution of a mode to guide light in the x direction for a thickness t of 539 nm;

(10) FIG. 5C is a graph showing the results of calculations of the electric field distribution of a mode to guide light in the x direction for a thickness t of 300 nm;

(11) FIG. 6 is a graph showing the results of calculations of the enhancement of light performed under the same conditions as in FIG. 2 except that the polarization of the light was assumed to be the TE mode, which has an electric field component perpendicular to the y direction;

(12) FIG. 7A is a plan view of an example two-dimensional periodic structure;

(13) FIG. 7B is a graph showing the results of calculations performed as in FIG. 2 for the two-dimensional periodic structure;

(14) FIG. 8 is a graph showing the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying refractive indices of the periodic structure;

(15) FIG. 9 is a graph showing the results obtained under the same conditions as in FIG. 8 except that the photoluminescent layer was assumed to have a thickness of 1,000 nm;

(16) FIG. 10 is a graph showing the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying heights of the periodic structure;

(17) FIG. 11 is a graph showing the results of calculations performed under the same conditions as in FIG. 10 except that the periodic structure was assumed to have a refractive index n.sub.p of 2.0;

(18) FIG. 12 is a graph showing the results of calculations performed under the same conditions as in FIG. 9 except that the polarization of the light was assumed to be the TE mode, which has an electric field component perpendicular to the y direction;

(19) FIG. 13 is a graph showing the results of calculations performed under the same conditions as in FIG. 9 except that the photoluminescent layer was assumed to have a refractive index n.sub.wav of 1.5;

(20) FIG. 14 is a graph showing the results of calculations performed under the same conditions as in FIG. 2 except that the photoluminescent layer and the periodic structure were assumed to be located on a transparent substrate having a refractive index of 1.5;

(21) FIG. 15 is a graph illustrating the conditions represented by inequality (15);

(22) FIG. 16 is a schematic view of an example light-emitting apparatus including the light-emitting device shown in FIGS. 1A and 1B and a light source that directs excitation light into the photoluminescent layer;

(23) FIGS. 17A to 17D illustrate structures in which excitation light is coupled into a quasi-guided mode to efficiently output light: FIG. 17A shows a one-dimensional periodic structure having a period p.sub.x in the x direction, FIG. 17B shows a two-dimensional periodic structure having a period p.sub.x in the x direction and a period p.sub.y in the y direction, FIG. 17C shows the wavelength dependence of light absorptivity in the structure in FIG. 17A, and FIG. 17D shows the wavelength dependence of light absorptivity in the structure in FIG. 17B;

(24) FIG. 18A is a schematic view of an example two-dimensional periodic structure;

(25) FIG. 18B is a schematic view of another example two-dimensional periodic structure;

(26) FIG. 19A is a schematic view of a modification in which the periodic structure is formed on the transparent substrate;

(27) FIG. 19B is a schematic view of another modification in which the periodic structure is formed on the transparent substrate;

(28) FIG. 19C is a graph showing the results of calculations of the enhancement of light output from the structure in FIG. 19A in the front direction with varying emission wavelengths and varying periods of the periodic structure;

(29) FIG. 20 is a schematic view of a mixture of light-emitting devices in powder form;

(30) FIG. 21 is a plan view of an example two-dimensional array of periodic structures having different periods on the photoluminescent layer;

(31) FIG. 22 is a graph showing an example light-emitting device having a layered structure including photoluminescent layers having a texture formed thereon;

(32) FIG. 23 is a sectional view of an example structure including a protective layer between the photoluminescent layer and the periodic structure;

(33) FIG. 24 is an example where the periodic structure is formed by partially processing the photoluminescent layer;

(34) FIG. 25 is a cross-sectional transmission electron microscopy (TEM) image of a photoluminescent layer formed on a glass substrate having a periodic structure;

(35) FIG. 26 is a graph showing the results of measurements of the spectrum of light output from a sample light-emitting device in the front direction;

(36) FIGS. 27A and 27B are graphs showing the results of measurements (top) and calculations (bottom) of the angular dependence of light output from the sample light-emitting device;

(37) FIGS. 28A and 28B are graphs showing the results of measurements (top) and calculations (bottom) of the angular dependence of the light output from the sample light-emitting device;

(38) FIG. 29 is a graph showing the results of measurements of the angular dependence of light (wavelength: 610 nm) output from the sample light-emitting device;

(39) FIG. 30 is a schematic perspective view of an example slab waveguide;

(40) FIG. 31 is a schematic sectional view of an example where a photoluminescent layer (waveguide) having a periodic structure thereon is formed on a low-refractive-index layer;

(41) FIG. 32 is a graph showing the results of calculations of the intensity of output light for each wavelength with varying thicknesses t.sub.W of the photoluminescent layer in the structure shown in FIG. 31;

(42) FIG. 33 is a graph showing the dependence of light transmittance on the wavelength and the thickness t.sub.W in the structure shown in FIG. 31;

(43) FIG. 34 is a schematic view illustrating the interference of light in the structure shown in FIG. 31;

(44) FIG. 35 is a partial sectional view of an example light-emitting device including, in sequence, a high-refractive-index layer, a low-refractive-index layer, a photoluminescent layer, and a periodic structure;

(45) FIG. 36 is a graph showing the results of calculations of the intensity of output light for each wavelength with varying thicknesses t.sub.W of the photoluminescent layer in the structure shown in FIG. 35;

(46) FIG. 37 is a graph showing the dependence of light transmittance on the wavelength and the thickness t.sub.W in the structure shown in FIG. 35;

(47) FIG. 38 is a graph showing the results of calculations of the intensity of output light for each wavelength with varying thicknesses t.sub.L of the low-refractive-index layer in the structure shown in FIG. 35;

(48) FIG. 39 is a graph showing the dependence of light transmittance on the wavelength and the thickness t.sub.L in the structure shown in FIG. 35;

(49) FIG. 40 is a schematic view illustrating the interference of light in the structure shown in FIG. 35;

(50) FIG. 41 is a graph showing the results of calculations of transmittance with varying thicknesses t.sub.L of the low-refractive-index layer and varying thicknesses t.sub.W of the photoluminescent layer in the structure shown in FIG. 35;

(51) FIG. 42 is a schematic partial sectional view of a light-emitting device according to a first modification;

(52) FIG. 43 is a schematic partial sectional view of a light-emitting device according to a second modification; and

(53) FIG. 44 is a schematic partial sectional view of a light-emitting device according to a third modification.

DETAILED DESCRIPTION

(54) Optical devices including optical elements such as reflectors and lenses need to be larger to ensure sufficient space for these optical elements. Accordingly, it is desirable to eliminate or reduce the size of these optical elements.

(55) The present disclosure includes the following light-emitting devices and light-emitting apparatus:

(56) 1. A light-emitting device includes a photoluminescent layer that emits light containing first light, and a light-transmissive layer located on or near the photoluminescent layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. The submicron structure includes at least projections or recesses and satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light. The wavelength .sub.a is, for example, within the visible wavelength range (e.g., 380 to 780 nm).

(57) In general, the light emitted from the photoluminescent layer is light in a wavelength range including the peak wavelength. The wavelength .sub.a of the first light need not be the peak wavelength, but may be any wavelength within the emission wavelength range. If the first light is light of a wavelength other than the peak wavelength, light weaker than light of the peak wavelength can be enhanced. Thus, the emission spectrum of the light-emitting device can be changed to output the desired light without changing the material for the photoluminescent layer.

(58) 2. In Item 1, the submicron structure may include at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure may include a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure.

(59) 3. In Item 1 or 2, the refractive index n.sub.t-a of the light-transmissive layer for the first light may be lower than the refractive index n.sub.wav-a of the photoluminescent layer for the first light.

(60) 4. In any one of Items 1 to 3, the first light may have the maximum intensity in a first direction determined in advance by the submicron structure.

(61) 5. In Item 4, the first direction may be normal to the photoluminescent layer.

(62) 6. In Item 4 or 5, the first light output in the first direction may be linearly polarized light.

(63) 7. In any one of Items 4 to 6, the angle of directionality of the first light with respect to the first direction may be less than 15.

(64) 8. In any one of Items 4 to 7, second light having a wavelength .sub.b different from the wavelength .sub.a of the first light may have the maximum intensity in a second direction different from the first direction.

(65) 9. In any one of Items 1 to 8, the light-transmissive layer may have the submicron structure.

(66) 10. In any one of Items 1 to 9, the photoluminescent layer may have the submicron structure.

(67) 11. In any one of Items 1 to 8, the photoluminescent layer may have a flat main surface, and the light-transmissive layer may be located on the flat main surface of the photoluminescent layer and may have the submicron structure.

(68) 12. In Item 11, the light-emitting device may further include a transparent substrate that supports the photoluminescent layer.

(69) 13. In any one of Items 1 to 8, the light-transmissive layer may be a transparent substrate having the submicron structure on a main surface thereof, and the photoluminescent layer may be located on the submicron structure.

(70) 14. In Item 1 or 2, the refractive index n.sub.t-a of the light-transmissive layer for the first light may be higher than or equal to the refractive index n.sub.wav-a of the photoluminescent layer for the first light, and each of the projections or recesses in the submicron structure may have a height or depth of 150 nm or less.

(71) 15. In any one of Items 1 and 3 to 14, the submicron structure may include at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure may include a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure. The first periodic structure may be a one-dimensional periodic structure.

(72) 16. In Item 15, the light emitted from the photoluminescent layer may contain second light having a wavelength .sub.b different from the wavelength .sub.a in air, and the at least one periodic structure may further include a second periodic structure satisfying the following relationship:
.sub.b/n.sub.wav-b<p.sub.b<.sub.b
where n.sub.wav-b is the refractive index of the photoluminescent layer for the second light, and p.sub.b is the period of the second periodic structure. The second periodic structure may be a one-dimensional periodic structure.

(73) 17. In any one of Items 1 and 3 to 14, the submicron structure may include at least two periodic structures defined by at least the projections or recesses, and the at least two periodic structures may include a two-dimensional periodic structure having periodicity in different directions.

(74) 18. In any one of Items 1 and 3 to 14, the submicron structure may include periodic structures defined by at least the projections or recesses, and the periodic structures may include periodic structures arranged in a matrix.

(75) 19. In any one of Items 1 and 3 to 14, the submicron structure may include periodic structures defined by at least the projections or recesses, and the periodic structures may include a periodic structure satisfying the following relationship:
.sub.ex/n.sub.wav-ex<p.sub.ex<.sub.ex
where p.sub.ex is the period of the periodic structure, .sub.ex is the wavelength, in air, of excitation light for a photoluminescent material contained in the photoluminescent layer, and n.sub.wav-ex is the refractive index of the photoluminescent layer for the excitation light.

(76) 20. A light-emitting device includes photoluminescent layers and light-transmissive layers. At least two of the photoluminescent layers are each independently the photoluminescent layer according to any one of Items 1 to 19, and at least two of the light-transmissive layers are each independently the light-transmissive layer according to any one of Items 1 to 19.

(77) 21. In Item 20, the photoluminescent layers and the light-transmissive layers may be stacked on top of each other.

(78) 22. A light-emitting device includes a photoluminescent layer, and a light-transmissive layer located on or near the photoluminescent layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. Light is directed into the photoluminescent layer and the light-transmissive layer to form a quasi-guided mode.

(79) 23. A light-emitting device includes a waveguide layer capable of guiding light and a periodic structure located on or near the waveguide layer. The waveguide layer contains a photoluminescent material. The waveguide layer forms a quasi-guided mode in which light emitted from the photoluminescent material is guided while interacting with the periodic structure.

(80) 24. A light-emitting apparatus includes the light-emitting device according to any one of Items 1 to 23 and an excitation light source that irradiates the photoluminescent layer with excitation light.

(81) 25. A light-emitting device includes a photoluminescent layer, and a light-transmissive layer located on or near the photoluminescent layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. The submicron structure includes at least projections or recesses and satisfies the following relationship:
.sub.ex/n.sub.wav-ex<D.sub.int<.sub.ex
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.ex is the wavelength, in air, of excitation light for a photoluminescent material contained in the photoluminescent layer, and n.sub.wav-ex is the refractive index, for the excitation light, of a medium having the highest refractive index of media present in an optical path to the photoluminescent layer or the light-transmissive layer.

(82) 26. In Item 25, the submicron structure may include at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure may include a first periodic structure satisfying the following relationship:
.sub.ex/n.sub.wav-ex<p.sub.ex<.sub.ex
where p.sub.ex is the period of the first periodic structure.

(83) 27. A light-emitting device includes a photoluminescent layer that emits light containing first light, a light-transmissive layer located on or near the photoluminescent layer, a low-refractive-index layer and a high-refractive-index layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. The low-refractive-index layer is located on or near the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and light-transmissive layer. The low-refractive-index layer has a lower refractive index than the photoluminescent layer. The high-refractive-index layer is located on or near the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer. The high-refractive-index layer has a higher refractive index than the low-refractive-index layer. The submicron structure includes at least projections or recesses and satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light.

(84) 28. In Item 27, the submicron structure may include the projections and recesses. The high-refractive-index layer may have a lower refractive index than the photoluminescent layer. The light-emitting device may satisfy the following relationship:
(4m1).sub.a/8<h.sub.pn.sub.pf+n.sub.Wt.sub.W<(4m+1).sub.a/8
where m is a natural number, h.sub.p is the height of the submicron structure, n.sub.p is the refractive index of the submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the submicron structure, n.sub.W is the refractive index of the photoluminescent layer, and t.sub.W is the thickness of the photoluminescent layer.

(85) 29. In Item 27, the submicron structure may include the projections and recesses. The high-refractive-index layer may have a higher refractive index than the photoluminescent layer. The light-emitting device may satisfy the following relationship:
(4m3).sub.a/8<h.sub.pn.sub.pf+n.sub.Lt.sub.L+n.sub.Wt.sub.W<(4m1).sub.a/8(where m is a natural number)
where h.sub.p is the height of the submicron structure, n.sub.p is the refractive index of the submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the submicron structure, n.sub.W is the refractive index of the photoluminescent layer, t.sub.W is the thickness of the photoluminescent layer, n.sub.L is the refractive index of the low-refractive-index layer, and t.sub.L is the thickness of the low-refractive-index layer.

(86) 30. In any one of Items 27 to 29, the low-refractive-index layer may have a thickness of .sub.a/6 or more.

(87) 31. In any one of Items 27 to 30, if the submicron structure is referred to as first submicron structure, a second submicron structure may be defined on an interface between the photoluminescent layer and the low-refractive-index layer.

(88) 32. In Item 31, the second submicron structure may have a same period as the first submicron structure.

(89) 33. In Item 31 or 32, a third submicron structure may be defined on an interface between the low-refractive-index layer and the high-refractive-index layer.

(90) 34. In Item 33, the third submicron structure may have a same period as the first and second submicron structures.

(91) 35. A light-emitting device includes a photoluminescent layer that emits light containing first light, a light-transmissive layer located on or near the photoluminescent layer, and a low-refractive-index layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. The low-refractive-index layer is located on or near the photoluminescent layer so that the photoluminescent is located between the low-refractive-index layer and the light-transmissive layer. The low-refractive-index layer has a lower refractive index than the photoluminescent layer. The submicron structure includes at least projections or recesses and satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light. The light-emitting device satisfies the following relationship:
(4m1).sub.a/8<h.sub.ph.sub.pf+h.sub.Wt.sub.W<(4m+1).sub.a/8
where m is a natural number, h.sub.p is the height of the submicron structure, n.sub.p is the refractive index of the submicron structure, f is the ratio of the volume of the projections to the sum of the volumes of the projections and the recesses in the submicron structure, n.sub.W is the refractive index of the photoluminescent layer, and t.sub.W is the thickness of the photoluminescent layer.

(92) 36. A light-emitting apparatus includes the light-emitting device according to any one of Items 27 to 35; and a light source that directs excitation light into the light-emitting device.

(93) 37. In Item 1, the first submicron structure comprises the projections. The high-refractive-index layer may have a lower refractive index than the photoluminescent layer. The light-emitting device may satisfy the following relationship:
(4m1).sub.a/8<h.sub.ph.sub.pf+n.sub.Wt.sub.W<(4m+1).sub.a/8
where m is a natural number, h.sub.p is the height of the first submicron structure, n.sub.p is the refractive index of the first submicron structure, f is the ratio of the volume of the first submicron structure, n.sub.W is the refractive index of the photoluminescent layer, and t.sub.W is the thickness of the photoluminescent layer.

(94) 38. A light-emitting device includes a photoluminescent layer that emits light containing first light, a light-transmissive layer having a higher refractive index than the photoluminescent layer, a low-refractive-index layer located on or near the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and the light-transmissive layer, the low-refractive-index layer having a lower refractive index than the photoluminescent layer; and a high-refractive-index layer located on or near the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer. A submicron structure is defined on the light-transmissive layer, the submicron structure comprising at least projections or recesses. The submicron structure includes at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure includes a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light.

(95) 39. In Item 38, a distance between the submicron structure and the photoluminescent layer may be more than .sub.a/2.

(96) 40. A light-emitting device includes a light-transmissive layer on which a submicron structure is defined, a photoluminescent layer that is located on or near the submicron structure and emits light containing first light, a low-refractive-index layer located on or near the photoluminescent layer so that the photoluminescent layer is located between the low-refractive-index layer and the light-transmissive layer, the low-refractive-index layer having a lower refractive index than the photoluminescent layer; and a high-refractive-index layer located on or near the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer. The submicron structure comprises at least projections or recesses, and the submicron structure includes at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure includes a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light.

(97) 41. A light-emitting device includes a photoluminescent layer that emits light containing first light, a low-refractive-index layer located on or near the photoluminescent layer having a lower refractive index than the photoluminescent layer, and a high-refractive-index layer located on or near the low-refractive-index layer so that the low-refractive-index layer is located between the high-refractive-index layer and the photoluminescent layer, the high-refractive-index layer having a higher refractive index than the low-refractive-index layer. A submicron structure is defined on the photoluminescent, the submicron structure comprising at least projections or recesses. The submicron structure includes at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure includes a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light.

(98) A light-emitting device according to an embodiment of the present disclosure includes a photoluminescent layer that emits light containing first light, and a light-transmissive layer located on or near the photoluminescent layer. A submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. The submicron structure may extend in a plane of the photoluminescent layer or the light-transmissive layer. The submicron structure includes at least projections or recesses. The submicron structure satisfies the following relationship:
.sub.a/n.sub.wav-a<D.sub.int<.sub.a
where D.sub.int is the center-to-center distance between adjacent projections or recesses, .sub.a is the wavelength of the first light in air, and n.sub.wav-a is the refractive index of the photoluminescent layer for the first light. The wavelength .sub.a is, for example, within the visible wavelength range (e.g., 380 to 780 nm).

(99) The photoluminescent layer contains a photoluminescent material. The term photoluminescent material refers to a material that emits light in response to excitation light. This term encompasses fluorescent materials and phosphorescent materials in a narrow sense, encompasses inorganic materials and organic materials (e.g., dyes), and encompasses quantum dots (i.e., tiny semiconductor particles). The photoluminescent layer may contain a matrix material (host material) in addition to the photoluminescent material. Examples of matrix materials include resins and inorganic materials such as glasses and oxides.

(100) The light-transmissive layer located on or near the photoluminescent layer is made of a material with high transmittance to the light emitted from the photoluminescent layer. Examples of such materials include inorganic materials and resins. For example, the light-transmissive layer is desirably made of a dielectric (particularly, an insulator with low light absorption). For example, the light-transmissive layer may be a substrate that supports the photoluminescent layer. Alternatively, if the surface of the photoluminescent layer facing air has the submicron structure, the air layer can serve as the light-transmissive layer.

(101) In the light-emitting device according to the embodiment of the present disclosure, the submicron structure (e.g., a periodic structure) defined on at least one of the photoluminescent layer and the light-transmissive layer forms a unique electric field distribution inside the photoluminescent layer and the light-transmissive layer, as described in detail later with reference to the results of calculations and experiments. This electric field distribution, also termed quasi-guided mode, is due to the interaction of guided light with the submicron structure. The quasi-guided mode can be utilized to improve the luminous efficiency, directionality, and polarization selectivity of photoluminescence, as described later. Although the term quasi-guided mode is used in the following description to describe novel structures and/or mechanisms contemplated by the inventors, this description is for illustrative purposes only and is not intended to limit the present disclosure in any way.

(102) For example, the submicron structure includes projections and satisfies the relationship .sub.a/n.sub.wav-a<D.sub.int<.sub.a, where D.sub.int is the center-to-center distance between adjacent projections. Instead of the projections, the submicron structure may include recesses. For simplicity, the following description will be directed to a submicron structure including projections. The symbol is the wavelength of light, and the symbol .sub.a is the wavelength of light in air. The symbol n.sub.wav is the refractive index of the photoluminescent layer. If the photoluminescent layer is a medium containing materials, the refractive index n.sub.wav is the average refractive index of the materials weighted by their respective volume fractions. Although it is preferable to use the symbol n.sub.wav-a to refer to the refractive index of the photoluminescent layer for light of the wavelength .sub.a because the refractive index n generally depends on the wavelength, it may be abbreviated for simplicity. The symbol n.sub.wav is basically the refractive index of the photoluminescent layer; however, if a layer having a higher refractive index than the photoluminescent layer is adjacent to the photoluminescent layer, the refractive index n.sub.wav is the average refractive index of the layer having a higher refractive index and the photoluminescent layer weighted by their respective volume fractions. This is optically equivalent to a photoluminescent layer composed of layers of different materials.

(103) The effective refractive index n.sub.eff of the medium for light in the quasi-guided mode satisfies n.sub.a<n.sub.eff<n.sub.wav, where n.sub.a is the refractive index of air. If light in the quasi-guided mode is assumed to be light propagating through the photoluminescent layer while being totally reflected at an angle of incidence , the effective refractive index n.sub.eff can be written as n.sub.eff=n.sub.wav sin . The effective refractive index n.sub.eff is determined by the refractive index of the medium present in the region where the electric field of the quasi-guided mode is distributed. For example, if the submicron structure is defined by the light-transmissive layer, the effective refractive index n.sub.eff depends not only on the refractive index of the photoluminescent layer, but also on the refractive index of the light-transmissive layer. Because the electric field distribution also varies depending on the polarization direction of the quasi-guided mode (i.e., the TE mode or the TM mode), the effective refractive index n.sub.eff can differ between the TE mode and the TM mode.

(104) The submicron structure is defined on at least one of the photoluminescent layer and the light-transmissive layer. If the photoluminescent layer and the light-transmissive layer are in contact with each other, the submicron structure may be defined on the interface between the photoluminescent layer and the light-transmissive layer. In this case, the photoluminescent layer and the light-transmissive layer have the submicron structure. Alternatively, the light-transmissive layer located on or near the photoluminescent layer may have the submicron structure without the photoluminescent layer having the submicron structure. When the submicron structure of the light-transmissive layer is said to be near the photoluminescent layer, or one layer is said to be near another layer, the distance therebetween is typically half the wavelength .sub.a or less. This allows the electric field of a guided mode to reach the submicron structure, thus forming a quasi-guided mode. However, the distance between the submicron structure of the light-transmissive layer and the photoluminescent layer may exceed half the wavelength .sub.a if the light-transmissive layer has a higher refractive index than the photoluminescent layer. If the light-transmissive layer has a higher refractive index than the photoluminescent layer, light reaches the light-transmissive layer even if the above relationship is not satisfied.

(105) The submicron structure, which satisfies the relationship .sub.a/n.sub.wav-a<D.sub.int<.sub.a, as described above, is characterized by a submicron size. The submicron structure includes, for example, at least one periodic structure, as in the light-emitting devices according to the embodiments described in detail later. The at least one periodic structure satisfies the relationship .sub.a/n.sub.wav-a<p.sub.a<.sub.a, where p.sub.a is the period of the at least one periodic structure. That is, the submicron structure includes a periodic structure in which the center-to-center distance D.sub.int between adjacent projections is constant at p.sub.a. If the submicron structure includes such a periodic structure, light in the quasi-guided mode propagates while repeatedly interacting with the periodic structure so that the light is diffracted by the submicron structure. Unlike the phenomenon in which light propagating through free space is diffracted by a periodic structure, this is the phenomenon in which light is guided (i.e., repeatedly totally reflected) while interacting with the periodic structure. This efficiently diffracts the light even if the periodic structure causes a small phase shift (i.e., even if the periodic structure has a small height).

(106) The above mechanism can be utilized to improve the luminous efficiency of photoluminescence by the enhancement of the electric field due to the quasi-guided mode and also to couple the emitted light into the quasi-guided mode. The angle of travel of the light in the quasi-guided mode is varied by the angle of diffraction determined by the periodic structure. This can be utilized to output light of a particular wavelength in a particular direction (i.e., significantly improve the directionality). Furthermore, high polarization selectivity can be simultaneously achieved because the effective refractive index n.sub.eff (=n.sub.wav sin ) differs between the TE mode and the TM mode. For example, as demonstrated by the experimental examples below, a light-emitting device can be provided that outputs intense linearly polarized light (e.g., the TM mode) of a particular wavelength (e.g., 610 nm) in the front direction. The angle of directionality of the light output in the front direction is, for example, less than 15. The term angle of directionality refers to the angle of one side with respect to the front direction, which is assumed to be 0.

(107) Conversely, a submicron structure having a lower periodicity results in a lower directionality, luminous efficiency, polarization, and wavelength selectivity. The periodicity of the submicron structure may be adjusted depending on the need. The periodic structure may be a one-dimensional periodic structure, which has a higher polarization selectivity, or a two-dimensional periodic structure, which allows for a lower polarization.

(108) The submicron structure may include periodic structures. For example, these periodic structures may have different periods or different periodic directions (axes). The periodic structures may be defined on the same plane or may be stacked on top of each other. The light-emitting device may include photoluminescent layers and light-transmissive layers, and they may have submicron structures.

(109) The submicron structure can be used not only to control the light emitted from the photoluminescent layer, but also to efficiently guide excitation light into the photoluminescent layer. That is, the excitation light can be diffracted and coupled into the quasi-guided mode to guide light in the photoluminescent layer and the light-transmissive layer by the submicron structure to efficiently excite the photoluminescent layer. A submicron structure may be used that satisfies the relationship .sub.ex/n.sub.wav-ex<D.sub.int<.sub.ex, where .sub.ex is the wavelength, in air, of the light that excites the photoluminescent material, and n.sub.wav-ex is the refractive index of the photoluminescent layer for the excitation light. The symbol n.sub.wav-ex is the refractive index of the photoluminescent layer for the emission wavelength of the photoluminescent material. Alternatively, a submicron structure may be used that includes a periodic structure satisfying the relationship .sub.ex/n.sub.wav-ex<p.sub.ex<.sub.ex, where P.sub.ex is the period of the periodic structure. The excitation light has a wavelength .sub.ex of, for example, 450 nm, although it may have a shorter wavelength than visible light. If the excitation light has a wavelength within the visible range, it may be output together with the light emitted from the photoluminescent layer.

(110) 1. Underlying Knowledge Forming Basis of the Present Disclosure

(111) The underlying knowledge forming the basis for the present disclosure will be described before describing specific embodiments of the present disclosure. As described above, photoluminescent materials such as those used for fluorescent lamps and white LEDs emit light in all directions and thus require optical elements such as reflectors and lenses to emit light in a particular direction. These optical elements, however, can be eliminated (or the size thereof can be reduced) if the photoluminescent layer itself emits directional light. This results in a significant reduction in the size of optical devices and equipment. With this idea in mind, the inventors have conducted a detailed study on the photoluminescent layer to achieve directional light emission.

(112) The inventors have investigated the possibility of inducing light emission with particular directionality so that the light emitted from the photoluminescent layer is localized in a particular direction. Based on Fermi's golden rule, the emission rate , which is a measure characterizing light emission, is represented by equation (1):

(113) $\begin{array}{cc}\left(r\right)=\frac{2}{}{.Math.\left(d.Math.E\left(r\right)\right).Math.}^2\left(\right)& \left(1\right)\end{array}$

(114) In equation (1), r is the vector indicating the position, is the wavelength of light, d is the dipole vector, E is the electric field vector, and is the density of states. For many substances other than some crystalline substances, the dipole vector d is randomly oriented. The magnitude of the electric field E is substantially constant irrespective of the direction if the size and thickness of the photoluminescent layer are sufficiently larger than the wavelength of light. Hence, in most cases, the value of <(d.Math.E(r))>.sup.2 does not depend on the direction. Accordingly, the emission rate is constant irrespective of the direction. Thus, in most cases, the photoluminescent layer emits light in all directions.

(115) As can be seen from equation (1), to achieve anisotropic light emission, it is necessary to align the dipole vector d in a particular direction or to enhance the component of the electric field vector in a particular direction. One of these approaches can be employed to achieve directional light emission. In the present disclosure, the results of a detailed study and analysis on structures for utilizing a quasi-guided mode in which the electric field component in a particular direction is enhanced by the confinement of light in the photoluminescent layer will be described below.

(116) 2. Structure for Enhancing Only Electric Field in Particular Direction

(117) The inventors have investigated the possibility of controlling light emission using a guided mode with an intense electric field. Light can be coupled into a guided mode using a waveguide structure that itself contains a photoluminescent material. However, a waveguide structure simply formed using a photoluminescent material outputs little or no light in the front direction because the emitted light is coupled into a guided mode. Accordingly, the inventors have investigated the possibility of combining a waveguide containing a photoluminescent material with a periodic structure (including at least projections or recesses). When the electric field of light is guided in a waveguide while overlapping with a periodic structure located on or near the waveguide, a quasi-guided mode is formed by the effect of the periodic structure. That is, the quasi-guided mode is a guided mode restricted by the periodic structure and is characterized in that the antinodes of the amplitude of the electric field have the same period as the periodic structure. Light in this mode is confined in the waveguide structure to enhance the electric field in a particular direction. This mode also interacts with the periodic structure to undergo diffraction so that the light in this mode is converted into light propagating in a particular direction and can thus be output from the waveguide. The electric field of light other than the quasi-guided mode is not enhanced because little or no such light is confined in the waveguide. Thus, most light is coupled into a quasi-guided mode with a large electric field component.

(118) That is, the inventors have investigated the possibility of using a photoluminescent layer containing a photoluminescent material as a waveguide (or a waveguide layer including a photoluminescent layer) in combination with a periodic structure located on or near the waveguide to couple light into a quasi-guided mode in which the light is converted into light propagating in a particular direction, thereby providing a directional light source.

(119) As a simple waveguide structure, the inventors have studied slab waveguides. A slab waveguide has a planar structure in which light is guided. FIG. 30 is a schematic perspective view of an example slab waveguide 110S. There is a mode of light propagating through the waveguide 110S if the waveguide 110S has a higher refractive index than a transparent substrate 140 that supports the waveguide 110S. If such a slab waveguide includes a photoluminescent layer, the electric field of light emitted from an emission point overlaps largely with the electric field of a guided mode. This allows most of the light emitted from the photoluminescent layer to be coupled into the guided mode. If the photoluminescent layer has a thickness close to the wavelength of the light, a situation can be created where there is only a guided mode with a large electric field amplitude.

(120) If a periodic structure is located on or near the photoluminescent layer, the electric field of the guided mode interacts with the periodic structure to form a quasi-guided mode. Even if the photoluminescent layer is composed of layers, a quasi-guided mode is formed as long as the electric field of the guided mode reaches the periodic structure. Not all of the photoluminescent layer needs to be made of a photoluminescent material; it may be a layer including at least a region that functions to emit light.

(121) If the periodic structure is made of a metal, a mode due to the guided mode and plasmon resonance is formed. This mode has different properties from the quasi-guided mode described above and is less effective in enhancing emission because a large loss occurs due to high absorption by the metal. Thus, it is desirable to form the periodic structure using a dielectric with low absorption.

(122) The inventors have studied the coupling of light into a quasi-guided mode that can be output as light propagating in a particular angular direction using a periodic structure formed on a waveguide (e.g. photoluminescent layer). FIG. 1A is a schematic perspective view of an example light-emitting device 100 including a waveguide (e.g. photoluminescent layer) 110 and a periodic structure (e.g. light-transmissive layer) 120. The light-transmissive layer 120 may be hereinafter referred to as periodic structure 120 if the light-transmissive layer 120 forms a periodic structure. In other words, a submicron structure is defined on the light-transmissive layer 120. In this example, the periodic structure 120 is a one-dimensional periodic structure in which stripe-shaped projections extending in the y direction are arranged at regular intervals in the x direction. FIG. 1B is a sectional view of the light-emitting device 100 taken along a plane parallel to the xz plane. If a periodic structure 120 having a period p is provided in contact with the waveguide 110, a quasi-guided mode having a wave number k.sub.wav in the in-plane direction is converted into light propagating outside the waveguide 110. The wave number k.sub.out of the light can be represented by equation (2):

(123) $\begin{array}{cc}{k}_{\mathrm{out}}=k_{\mathrm{wav}}-m\frac{2}{p}& \left(2\right)\end{array}$

(124) In equation (2), m is an integer indicating the diffraction order.

(125) For simplicity, the light guided in the waveguide 110 is assumed to be a ray of light propagating at an angle .sub.wav. This approximation gives equations (3) and (4):

(126) $\begin{array}{cc}\frac{k_{\mathrm{wav}}{}_0}{2}=n_{\mathrm{wav}}\sin {}_{\mathrm{wav}}& \left(3\right)\\ \frac{k_{\mathrm{out}}{}_0}{2}=n_{\mathrm{out}}\sin {}_{\mathrm{out}}& \left(4\right)\end{array}$

(127) In these equations, .sub.0 is the wavelength of the light in air, n.sub.wav is the refractive index of the waveguide 110, n.sub.out is the refractive index of the medium from which the light is output, and .sub.out is the angle at which the light is output from the waveguide 110 to a substrate or air. From equations (2) to (4), the output angle .sub.out can be represented by equation (5):
n.sub.out sin .sub.out=n.sub.wav sin .sub.wavm.sub.0/p(5)

(128) If n.sub.wav sin .sub.wav=m.sub.0/p in equation (5), .sub.out=0, meaning that the light can be output in the direction perpendicular to the plane of the waveguide 110 (i.e., in the front direction).

(129) Based on this principle, light can be coupled into a particular quasi-guided mode and be converted into light having a particular output angle using the periodic structure to output intense light in that direction.

(130) There are some constraints to achieving the above situation. To form a quasi-guided mode, the light propagating through the waveguide 110 has to be totally reflected. The conditions therefor are represented by inequality (6):
n.sub.out<n.sub.wav sin .sub.wav(6)

(131) To diffract the quasi-guided mode using the periodic structure and thereby output the light from the waveguide 110, 1<sin .sub.out<1 has to be satisfied in equation (5). Hence, inequality (7) has to be satisfied:

(132) $\begin{array}{cc}-1<\frac{n_{\mathrm{wav}}}{n_{\mathrm{out}}}\sin {}_{\mathrm{wav}}-\frac{m{}_0}{n_{\mathrm{out}}p}<1& \left(7\right)\end{array}$

(133) Taking into account inequality (6), inequality (8) may be satisfied:

(134) $\begin{array}{cc}\frac{m{}_0}{2n_{\mathrm{out}}}<p& \left(8\right)\end{array}$

(135) To output the light from the waveguide 110 in the front direction (i.e., .sub.out=0), as can be seen from equation (5), equation (9) has to be satisfied:
p=m.sub.0/(n.sub.wav sin .sub.wav)(9)

(136) As can be seen from equation (9) and inequality (6), the required conditions are represented by inequality (10):

(137) $\begin{array}{cc}\frac{m{}_0}{n_{\mathrm{wav}}}<p<\frac{m{}_0}{n_{\mathrm{out}}}& \left(10\right)\end{array}$

(138) If the periodic structure 120 as shown in FIGS. 1A and 1B is provided, it may be designed based on first-order diffracted light (i.e., m=1) because higher-order diffracted light (i.e., m2) has low diffraction efficiency. In this embodiment, the period p of the periodic structure 120 is determined so as to satisfy inequality (11), which is given by substituting m=1 into inequality (10):

(139) $\begin{array}{cc}\frac{{}_0}{n_{\mathrm{wav}}}<p<\frac{{}_0}{n_{\mathrm{out}}}& \left(11\right)\end{array}$

(140) If the waveguide (photoluminescent layer) 110 is not in contact with a transparent substrate, as shown in FIGS. 1A and 1B, n.sub.out is equal to the refractive index of air (i.e., about 1.0). Thus, the period p may be determined so as to satisfy inequality (12):

(141) $\begin{array}{cc}\frac{{}_0}{n_{\mathrm{wav}}}<p<{}_0& \left(12\right)\end{array}$

(142) Alternatively, a structure as illustrated in FIGS. 1C and 1D may be employed in which the photoluminescent layer 110 and the periodic structure 120 are formed on a transparent substrate 140. The refractive index n.sub.s of the transparent substrate 140 is higher than the refractive index of air. Thus, the period p may be determined so as to satisfy inequality (13), which is given by substituting n.sub.out=n.sub.s into inequality (11):

(143) $\begin{array}{cc}\frac{{}_0}{n_{\mathrm{wav}}}<p<\frac{{}_0}{n_s}& \left(13\right)\end{array}$

(144) Although m=1 is assumed in inequality (10) to give inequalities (12) and (13), m2 may be assumed. That is, if both surfaces of the light-emitting device 100 are in contact with air layers, as shown in FIGS. 1A and 1B, the period p may be determined so as to satisfy inequality (14):

(145) 0$\begin{array}{cc}\frac{m{}_0}{n_{\mathrm{wav}}}<p<m{}_0& \left(14\right)\end{array}$
where m is an integer of 1 or more.

(146) Similarly, if the photoluminescent layer 110 is formed on the transparent substrate 140, as in the light-emitting device 100a shown in FIGS. 1C and 1D, the period p may be determined so as to satisfy inequality (15):

(147) $\begin{array}{cc}\frac{m{}_0}{n_{\mathrm{wav}}}<p<\frac{m{}_0}{n_s}& \left(15\right)\end{array}$

(148) By determining the period p of the periodic structure so as to satisfy the above inequalities, the light emitted from the photoluminescent layer 110 can be output in the front direction, thus providing a directional light-emitting device.

(149) 3. Verification by Calculations

(150) 3-1. Period and Wavelength Dependence

(151) The inventors verified, by optical analysis, whether the output of light in a particular direction as described above is actually possible. The optical analysis was performed by calculations using DiffractMOD available from Cybernet Systems Co., Ltd. In these calculations, the change in the absorption of external light incident perpendicular to a light-emitting device by a photoluminescent layer was calculated to determine the enhancement of light output perpendicular to the light-emitting device. The calculation of the process by which external incident light is coupled into a quasi-guided mode and is absorbed by the photoluminescent layer corresponds to the calculation of a process opposite to the process by which light emitted from the photoluminescent layer is coupled into a quasi-guided mode and is converted into propagating light output perpendicular to the light-emitting device. Similarly, the electric field distribution of a quasi-guided mode was calculated from the electric field of external incident light.

(152) FIG. 2 shows the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying periods of the periodic structure, where the photoluminescent layer was assumed to have a thickness of 1 m and a refractive index n.sub.wav of 1.8, and the periodic structure was assumed to have a height of 50 nm and a refractive index of 1.5. In these calculations, the periodic structure was assumed to be a one-dimensional periodic structure uniform in the y direction, as shown in FIG. 1A, and the polarization of the light was assumed to be the TM mode, which has an electric field component parallel to the y direction. The results in FIG. 2 show that there are enhancement peaks at certain combinations of wavelength and period. In FIG. 2, the magnitude of the enhancement is expressed by different shades of color; a darker color (black) indicates a higher enhancement, whereas a lighter color (white) indicates a lower enhancement.

(153) In the above calculations, the periodic structure was assumed to have a rectangular cross section as shown in FIG. 1B. FIG. 3 is a graph illustrating the conditions for m=1 and m=3 in inequality (10). A comparison between FIGS. 2 and 3 shows that the peaks in FIG. 2 are located within the regions corresponding to m=1 and m=3. The intensity is higher for m=1 because first-order diffracted light has a higher diffraction efficiency than third- or higher-order diffracted light. There is no peak for m=2 because of low diffraction efficiency in the periodic structure.

(154) In FIG. 2, lines are observed in each of the regions corresponding to m=1 and m=3 in FIG. 3. This indicates the presence of quasi-guided modes.

(155) 3-2. Thickness Dependence

(156) FIG. 4 is a graph showing the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying thicknesses t of the photoluminescent layer, where the photoluminescent layer was assumed to have a refractive index n.sub.wav of 1.8, and the periodic structure was assumed to have a period of 400 nm, a height of 50 nm, and a refractive index of 1.5. FIG. 4 shows that the enhancement of the light peaks at a particular thickness t the photoluminescent layer.

(157) FIGS. 5A and 5B show the results of calculations of the electric field distributions of a mode to guide light in the x direction for a wavelength of 600 nm and thicknesses t of 238 nm and 539 nm, respectively, at which there are peaks in FIG. 4. For comparison, FIG. 5C shows the results of similar calculations for a thickness t of 300 nm, at which there is no peak. In these calculations, as in the above calculations, the periodic structure was a one-dimensional periodic structure uniform in the y direction. In each figure, a black region indicates a higher electric field intensity, whereas a white region indicates a lower electric field intensity. Whereas the results for t=238 nm and t=539 nm show high electric field intensity, the results for t=300 nm shows low electric field intensity as a whole. This is because there are guided modes for t=238 nm and t=539 nm so that light is strongly confined. Furthermore, regions with the highest electric field intensity (i.e., antinodes) are necessarily present in or directly below the projections, indicating the correlation between the electric field and the periodic structure 120. Thus, the resulting guided mode depends on the arrangement of the periodic structure 120. A comparison between the results for t=238 nm and t=539 nm shows that these modes differ in the number of nodes (white regions) of the electric field in the z direction by one.

(158) 3-3. Polarization Dependence

(159) To examine the polarization dependence, the enhancement of light was calculated under the same conditions as in FIG. 2 except that the polarization of the light was assumed to be the TE mode, which has an electric field component perpendicular to the y direction. FIG. 6 shows the results of these calculations. Although the peaks in FIG. 6 differ slightly in position from the peaks for the TM mode (FIG. 2), they are located within the regions shown in FIG. 3. This demonstrates that the structure according to this embodiment is effective for both of the TM mode and the TE mode.

(160) 3-4. Two-Dimensional Periodic Structure

(161) The effect of a two-dimensional periodic structure was also studied. FIG. 7A is a partial plan view of a two-dimensional periodic structure 120 including recesses and projections arranged in both of the x direction and the y direction. In FIG. 7A, the black regions indicate the projections, and the white regions indicate the recesses. For a two-dimensional periodic structure, both of the diffraction in the x direction and the diffraction in the y direction have to be taken into account. Although the diffraction in only the x direction or the y direction is similar to that in a one-dimensional periodic structure, a two-dimensional periodic structure can be expected to give different results from a one-dimensional periodic structure because diffraction also occurs in a direction containing both of an x component and a y component (e.g., a direction inclined at 45). FIG. 7B shows the results of calculations of the enhancement of light for the two-dimensional periodic structure. The calculations were performed under the same conditions as in FIG. 2 except for the type of periodic structure. As shown in FIG. 7B, peaks matching the peaks for the TE mode in FIG. 6 were observed in addition to peaks matching the peaks for the TM mode in FIG. 2. These results demonstrate that the two-dimensional periodic structure also converts and outputs the TE mode by diffraction. For a two-dimensional periodic structure, the diffraction that simultaneously satisfies the first-order diffraction conditions in both of the x direction and the y direction also has to be taken into account. Such diffracted light is output in the direction at the angle corresponding to 2 times (i.e., 2.sup.1/2 times) the period p. Thus, peaks will occur at 2 times the period p in addition to peaks that occur in a one-dimensional periodic structure. Such peaks are observed in FIG. 7B.

(162) The two-dimensional periodic structure does not have to be a square grid structure having equal periods in the x direction and the y direction, as shown in FIG. 7A, but may be a hexagonal grid structure, as shown in FIG. 18A, or a triangular grid structure, as shown in FIG. 18B. The two-dimensional periodic structure may have different periods in different directions (e.g., in the x direction and the y direction for a square grid structure).

(163) In this embodiment, as demonstrated above, light in a characteristic quasi-guided mode formed by the periodic structure and the photoluminescent layer can be selectively output only in the front direction through diffraction by the periodic structure. With this structure, the photoluminescent layer can be excited with excitation light such as ultraviolet light or blue light to output directional light.

(164) 4. Study on Constructions of Periodic Structure and Photoluminescent Layer

(165) The effects of changes in various conditions such as the constructions and refractive indices of the periodic structure and the photoluminescent layer will now be described.

(166) 4-1. Refractive Index of Periodic Structure

(167) The refractive index of the periodic structure was studied. In the calculations performed herein, the photoluminescent layer was assumed to have a thickness of 200 nm and a refractive index n.sub.wav of 1.8, the periodic structure was assumed to be a one-dimensional periodic structure uniform in the y direction, as shown in FIG. 1A, having a height of 50 nm and a period of 400 nm, and the polarization of the light was assumed to be the TM mode, which has an electric field component parallel to the y direction. FIG. 8 shows the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying refractive indices of the periodic structure. FIG. 9 shows the results obtained under the same conditions except that the photoluminescent layer was assumed to have a thickness of 1,000 nm.

(168) The results show that a photoluminescent layer with a thickness of 1,000 nm (FIG. 9) results in a smaller shift in the wavelength at which the light intensity peaks (i.e., peak wavelength) with the change in the refractive index of the periodic structure than a photoluminescent layer with a thickness of 200 nm (FIG. 8). This is because the quasi-guided mode is more affected by the refractive index of the periodic structure as the photoluminescent layer is thinner. Specifically, a periodic structure with a higher refractive index increases the effective refractive index and thus shifts the peak wavelength toward longer wavelengths, and this effect is more noticeable as the photoluminescent layer is thinner. The effective refractive index is determined by the refractive index of the medium present in the region where the electric field of the quasi-guided mode is distributed.

(169) The results also show that a periodic structure with a higher refractive index results in a broader peak and a lower intensity. This is because a periodic structure with a higher refractive index outputs light in the quasi-guided mode at a higher rate and is therefore less effective in confining the light, i.e., has a lower Q value. To maintain a high peak intensity, a structure may be employed in which light is moderately output using a quasi-guided mode that is effective in confining the light (i.e., has a high Q value). This means that it is undesirable to use a periodic structure made of a material having a much higher refractive index than the photoluminescent layer. Thus, to achieve a high peak intensity and Q value, the periodic structure (i.e., the light-transmissive layer) may be made of a dielectric having a refractive index lower than or similar to that of the photoluminescent layer. This is also true if the photoluminescent layer contains materials other than photoluminescent materials.

(170) 4-2. Height of Periodic Structure

(171) The height of the periodic structure was then studied. In the calculations performed herein, the photoluminescent layer was assumed to have a thickness of 1,000 nm and a refractive index n.sub.wav of 1.8, the periodic structure was assumed to be a one-dimensional periodic structure uniform in the y direction, as shown in FIG. 1A, having a refractive index n.sub.p of 1.5 and a period of 400 nm, and the polarization of the light was assumed to be the TM mode, which has an electric field component parallel to the y direction. FIG. 10 shows the results of calculations of the enhancement of light output in the front direction with varying emission wavelengths and varying heights of the periodic structure. FIG. 11 shows the results of calculations performed under the same conditions except that the periodic structure was assumed to have a refractive index n.sub.p of 2.0. Whereas the results in FIG. 10 show that the peak intensity and the Q value (i.e., the peak line width) do not change above a certain height of the periodic structure, the results in FIG. 11 show that the peak intensity and the Q value decrease with increasing height of the periodic structure. If the refractive index n.sub.wav of the photoluminescent layer is higher than the refractive index n.sub.p of the periodic structure (FIG. 10), the light is totally reflected, and only a leaking (i.e., evanescent) portion of the electric field of the quasi-guided mode interacts with the periodic structure. If the periodic structure has a sufficiently large height, the influence of the interaction between the evanescent portion of the electric field and the periodic structure remains constant irrespective of the height. In contrast, if the refractive index n.sub.wav of the photoluminescent layer is lower than the refractive index n.sub.p of the periodic structure (FIG. 11), the light reaches the surface of the periodic structure without being totally reflected and is therefore more influenced by a periodic structure with a larger height. As shown in FIG. 11, a height of about 100 nm is sufficient, and the peak intensity and the Q value decrease above a height of 150 nm. Thus, if the refractive index n.sub.wav of the photoluminescent layer is lower than the refractive index n.sub.p of the periodic structure, the periodic structure may have a height of 150 nm or less to achieve a high peak intensity and Q value.

(172) 4-3. Polarization Direction

(173) The polarization direction was then studied. FIG. 12 shows the results of calculations performed under the same conditions as in FIG. 9 except that the polarization of the light was assumed to be the TE mode, which has an electric field component perpendicular to the y direction. The TE mode is more influenced by the periodic structure than the TM mode because the electric field of the quasi-guided mode leaks more largely for the TE mode than for the TM mode. Thus, the peak intensity and the Q value decrease more significantly for the TE mode than for the TM mode if the refractive index n.sub.p of the periodic structure is higher than the refractive index n.sub.wav of the photoluminescent layer.

(174) 4-4. Refractive Index of Photoluminescent Layer

(175) The refractive index of the photoluminescent layer was then studied. FIG. 13 shows the results of calculations performed under the same conditions as in FIG. 9 except that the photoluminescent layer was assumed to have a refractive index n.sub.wav of 1.5. The results for the photoluminescent layer having a refractive index n.sub.wav of 1.5 are similar to the results in FIG. 9. However, light of a wavelength of 600 nm or more was not output in the front direction. This is because, from inequality (10), .sub.0<n.sub.wavp/m=1.5400 nm/1=600 nm.

(176) The above analysis demonstrates that a high peak intensity and Q value can be achieved if the periodic structure has a refractive index lower than or similar to the refractive index of the photoluminescent layer or if the periodic structure has a higher refractive index than the photoluminescent layer and a height of 150 nm or less.

(177) 5. Modifications

(178) Modifications of this embodiment will now be described.

(179) 5-1. Structure Including Substrate

(180) As described above, the light-emitting device may have a structure in which the photoluminescent layer 110 and the periodic structure 120 are formed on the transparent substrate 140, as shown in FIGS. 1C and 1D. Such a light-emitting device 100a may be fabricated by forming a thin film of the photoluminescent material for the photoluminescent layer 110 (optionally containing a matrix material; the same applies hereinafter) on the transparent substrate 140 and then forming the periodic structure 120 thereon. In this structure, the refractive index n.sub.s of the transparent substrate 140 has to be lower than or equal to the refractive index n.sub.wav of the photoluminescent layer 110 so that the photoluminescent layer 110 and the periodic structure 120 function to output light in a particular direction. If the transparent substrate 140 is provided in contact with the photoluminescent layer 110, the period p has to be set so as to satisfy inequality (15), which is given by replacing the refractive index n.sub.out of the output medium in inequality (10) by n.sub.s.

(181) To demonstrate this, calculations were performed under the same conditions as in FIG. 2 except that the photoluminescent layer 110 and the periodic structure 120 were assumed to be located on a transparent substrate 140 having a refractive index of 1.5. FIG. 14 shows the results of these calculations. As in the results in FIG. 2, light intensity peaks are observed at particular periods for each wavelength, although the ranges of periods where peaks appear differ from those in FIG. 2. FIG. 15 is a graph illustrating the conditions represented by inequality (15), which is given by substituting n.sub.out=n.sub.s into inequality (10). In FIG. 14, light intensity peaks are observed in the regions corresponding to the ranges shown in FIG. 15.

(182) Thus, for the light-emitting device 100a, in which the photoluminescent layer 110 and the periodic structure 120 are located on the transparent substrate 140, a period p that satisfies inequality (15) is effective, and a period p that satisfies inequality (13) is significantly effective.

(183) 5-2. Light-Emitting Apparatus Including Excitation Light Source

(184) FIG. 16 is a schematic view of an example light-emitting apparatus 200 including the light-emitting device 100 shown in FIGS. 1A and 1B and a light source 180 that directs excitation light into the photoluminescent layer 110. In this embodiment, as described above, the photoluminescent layer can be excited with excitation light such as ultraviolet light or blue light to output directional light. The light source 180 can be configured to emit such excitation light to provide a directional light-emitting apparatus 200. Although the wavelength of the excitation light emitted from the light source 180 is typically within the ultraviolet or blue range, it is not necessarily within these ranges, but may be determined depending on the photoluminescent material for the photoluminescent layer 110. Although the light source 180 illustrated in FIG. 16 is configured to direct excitation light into the bottom surface of the photoluminescent layer 110, it may be configured otherwise, for example, to direct excitation light into the top surface of the photoluminescent layer 110.

(185) The excitation light may be coupled into a quasi-guided mode to efficiently output light. This method is illustrated in FIGS. 17A to 17D. In this example, as in the structure shown in FIGS. 1C and 1D, the photoluminescent layer 110 and the periodic structure 120 are formed on the transparent substrate 140. As shown in FIG. 17A, the period p.sub.x in the x direction is first determined so as to enhance light emission. As shown in FIG. 17B, the period p.sub.y in the y direction is then determined so as to couple the excitation light into a quasi-guided mode. The period p.sub.x is determined so as to satisfy the conditions given by replacing p in inequality (10) by p.sub.x. The period p.sub.y is determined so as to satisfy inequality (16):

(186) $\begin{array}{cc}\frac{m{}_{\mathrm{ex}}}{n_{\mathrm{wav}}}<p_y<\frac{m{}_{\mathrm{ex}}}{n_{\mathrm{out}}}& \left(16\right)\end{array}$
where m is an integer of 1 or more, .sub.ex is the wavelength of the excitation light, and n.sub.out is the refractive index of the medium having the highest refractive index of the media in contact with the photoluminescent layer 110 except the periodic structure 120.

(187) In the example in FIGS. 17A and 17B, n.sub.out is the refractive index n.sub.s of the transparent substrate 140. For a structure including no transparent substrate 140, as illustrated in FIG. 16, n.sub.out is the refractive index of air (i.e., about 1.0).

(188) In particular, the excitation light can be more effectively converted into a quasi-guided mode if m=1, i.e., if the period p.sub.y is determined so as to satisfy inequality (17):

(189) $\begin{array}{cc}\frac{{}_{\mathrm{ex}}}{n_{\mathrm{wav}}}<p_y<\frac{{}_{\mathrm{ex}}}{n_{\mathrm{out}}}& \left(17\right)\end{array}$

(190) Thus, the excitation light can be converted into a quasi-guided mode if the period p.sub.y is set so as to satisfy the conditions represented by inequality (16) (particularly, the conditions represented by inequality (17)). As a result, the photoluminescent layer 110 can efficiently absorb the excitation light of the wavelength .sub.ex.

(191) FIGS. 17C and 17D are the results of calculations of the proportion of absorbed light to light incident on the structures shown in FIGS. 17A and 17B, respectively, for each wavelength. In these calculations, p.sub.x=365 nm, p.sub.y=265 nm, the photoluminescent layer 110 was assumed to have an emission wavelength of about 600 nm, the excitation light was assumed to have a wavelength .sub.ex of about 450 nm, and the photoluminescent layer 110 was assumed to have an extinction coefficient of 0.003. As shown in FIG. 17D, the photoluminescent layer 110 has high absorptivity not only for the light emitted from the photoluminescent layer 110, but also for the excitation light, i.e., light of a wavelength of about 450 nm. This indicates that the incident light is effectively converted into a quasi-guided mode to increase the proportion of the light absorbed into the photoluminescent layer 110. The photoluminescent layer 110 also has high absorptivity for the emission wavelength, i.e., about 600 nm. This indicates that light of a wavelength of about 600 nm incident on this structure is similarly effectively converted into a quasi-guided mode. The periodic structure 120 shown in FIG. 17B is a two-dimensional periodic structure including structures having different periods (i.e., different periodic components) in the x direction and the y direction. Such a two-dimensional periodic structure including periodic components allows for high excitation efficiency and high output intensity. Although the excitation light is incident on the transparent substrate 140 in FIGS. 17A and 17B, the same effect can be achieved if the excitation light is incident on the periodic structure 120.

(192) Also available are two-dimensional periodic structures including periodic components as shown in FIGS. 18A and 18B. The structure shown in FIG. 18A includes periodically arranged projections having a hexagonal planar shape. The structure shown in FIG. 18B includes periodically arranged projections having a triangular planar shape. These structures have major axes (axes 1 to 3 in the examples in FIGS. 18A and 18B) that can be assumed to be periods. Thus, different periods can be assigned to different axial directions. These periods may be set so as to increase the directionality of light of different wavelengths or to efficiently absorb the excitation light. In any case, each period is set so as to satisfy the conditions corresponding to inequality (10).

(193) 5-3. Periodic Structure on Transparent Substrate

(194) As shown in FIGS. 19A and 19B, a periodic structure 120a may be formed on the transparent substrate 140, and the photoluminescent layer 110 may be located thereon. In the example in FIG. 19A, the photoluminescent layer 110 is formed along the texture of the periodic structure 120a on the transparent substrate 140. As a result, a periodic structure 120b with the same period is formed in the surface of the photoluminescent layer 110. In the example in FIG. 19B, the surface of the photoluminescent layer 110 is planarized. In these examples, directional light emission can be achieved by setting the period p of the periodic structure 120a so as to satisfy inequality (15).

(195) To verify the effect of these structures, the enhancement of light output from the structure in FIG. 19A in the front direction was calculated with varying emission wavelengths and varying periods of the periodic structure. In these calculations, the photoluminescent layer 110 was assumed to have a thickness of 1,000 nm and a refractive index n.sub.wav of 1.8, the periodic structure 120a was assumed to be a one-dimensional periodic structure uniform in the y direction having a height of 50 nm, a refractive index n.sub.p of 1.5, and a period of 400 nm, and the polarization of the light was assumed to be the TM mode, which has an electric field component parallel to the y direction. FIG. 19C shows the results of these calculations. In these calculations, light intensity peaks were observed at the periods that satisfy the conditions represented by inequality (15).

(196) 5-4. Powder

(197) According to the above embodiment, light of any wavelength can be enhanced by adjusting the period of the periodic structure and the thickness of the photoluminescent layer. For example, if the structure shown in FIGS. 1A and 1B is formed using a photoluminescent material that emits light over a wide wavelength range, only light of a certain wavelength can be enhanced. Accordingly, the structure of the light-emitting device 100 as shown in FIGS. 1A and 1B may be provided in powder form for use as a fluorescent material. Alternatively, the light-emitting device 100 as shown in FIGS. 1A and 1B may be embedded in resin or glass.

(198) The single structure as shown in FIGS. 1A and 1B can output only light of a certain wavelength in a particular direction and is therefore not suitable for outputting, for example, white light, which has a wide wavelength spectrum. Accordingly, as shown in FIG. 20, light-emitting devices 100 that differ in the conditions such as the period of the periodic structure and the thickness of the photoluminescent layer may be mixed in powder form to provide a light-emitting apparatus with a wide wavelength spectrum. In this case, the individual light-emitting devices 100 have sizes of, for example, several micrometers to several millimeters in one direction and can include, for example, one- or two-dimensional periodic structures with several periods to several hundreds of periods.

(199) 5-5. Array of Structures with Different Periods

(200) FIG. 21 is a plan view of an example two-dimensional array of periodic structures having different periods on the photoluminescent layer. In this example, three types of periodic structures 120a, 120b, and 120c are arranged without any space therebetween. The periods of the periodic structures 120a, 120b, and 120c are set so as to output, for example, light in the red, green, and blue wavelength ranges, respectively, in the front direction. Thus, structures having different periods can be arranged on the photoluminescent layer to output directional light with a wide wavelength spectrum. The periodic structures are not necessarily configured as described above, but may be configured in any manner.

(201) 5-6. Layered Structure

(202) FIG. 22 shows an example light-emitting device having a layered structure including photoluminescent layers 110 having a texture formed thereon and transparent substrates 140 between the photoluminescent layers 110. The texture formed on the photoluminescent layer 110 in each layer corresponds to a periodic structure. The example in FIG. 22 includes three periodic structures having different periods. The periods of these periodic structures are set so as to output light in the red, green, and blue wavelength ranges in the front direction. The photoluminescent layer 110 in each layer is made of a material that emits light of the color corresponding to the period of the periodic structure in that layer. Thus, periodic structures having different periods can be stacked on top of each other to output directional light with a wide wavelength spectrum.

(203) The number of layers and the constructions of the photoluminescent layer 110 and the periodic structure in each layer are not limited to those described above, but may be selected as appropriate. For example, for a structure including two layers, first and second photoluminescent layers are formed opposite each other with a light-transmissive substrate therebetween, and first and second periodic structures are formed on the surfaces of the first and second photoluminescent layers, respectively. In this case, the first photoluminescent layer and the first periodic structure may together satisfy the conditions corresponding to inequality (15), whereas the second photoluminescent layer and the second periodic structure may together satisfy the conditions corresponding to inequality (15). For a structure including three or more layers, the photoluminescent layer and the periodic structure in each layer may satisfy the conditions corresponding to inequality (15). The positional relationship between the photoluminescent layers and the periodic structures in FIG. 22 may be reversed. Although the layers illustrated by the example in FIG. 22 have different periods, they may all have the same period. In this case, although the spectrum cannot be broadened, the emission intensity can be increased.

(204) 5-7. Structure Including Protective Layer

(205) FIG. 23 is a sectional view of an example structure including a protective layer 150 between the photoluminescent layer 110 and the periodic structure 120. The protective layer 150 may be provided to protect the photoluminescent layer 110. However, if the protective layer 150 has a lower refractive index than the photoluminescent layer 110, the electric field of the light leaks into the protective layer 150 only by about half the wavelength. Thus, if the protective layer 150 is thicker than the wavelength, no light reaches the periodic structure 120. As a result, there is no quasi-guided mode, and the function of outputting light in a particular direction cannot be achieved. If the protective layer 150 has a refractive index higher than or similar to that of the photoluminescent layer 110, the light reaches the interior of the protective layer 150; therefore, there is no limitation on the thickness of the protective layer 150. Nevertheless, a thinner protective layer 150 is desirable because more light is output if most of the portion in which light is guided (this portion is hereinafter referred to as waveguide layer) is made of a photoluminescent material. The protective layer 150 may be made of the same material as the periodic structure (light-transmissive layer) 120. In this case, the light-transmissive layer 120 having the periodic structure functions as a protective layer. The light-transmissive layer 120 desirably has a lower refractive index than the photoluminescent layer 110.

(206) 6. Material and Method of Manufacture

(207) Directional light emission can be achieved if the photoluminescent layer (or waveguide layer) and the periodic structure are made of materials that satisfy the above conditions. The periodic structure may be made of any material. However, a photoluminescent layer (or waveguide layer) or a periodic structure made of a medium with high light absorption is less effective in confining light and therefore results in a lower peak intensity and Q value. Thus, the photoluminescent layer (or waveguide layer) and the periodic structure may be made of media with relatively low light absorption.

(208) For example, the periodic structure may be made of a dielectric with low light absorption. Examples of candidate materials for the periodic structure include magnesium fluoride (MgF.sub.2), lithium fluoride (LiF), calcium fluoride (CaF.sub.2), quartz (SiO.sub.2), glasses, resins, magnesium oxide (MgO), indium tin oxide (ITO), titanium oxide (TiO.sub.2), silicon nitride (SiN), tantalum pentaoxide (Ta.sub.2O.sub.5), zirconia (ZrO.sub.2), zinc selenide (ZnSe), and zinc sulfide (ZnS). To form a periodic structure having a lower refractive index than the photoluminescent layer, as described above, MgF.sub.2, LiF, CaF.sub.2, SiO.sub.2, glasses, and resins are desirably used, which have refractive indices of about 1.3 to 1.5.

(209) The term photoluminescent material encompasses fluorescent materials and phosphorescent materials in a narrow sense, encompasses inorganic materials and organic materials (e.g., dyes), and encompasses quantum dots (i.e., tiny semiconductor particles). In general, a fluorescent material containing an inorganic host material tends to have a higher refractive index. Examples of fluorescent materials that emit blue light include M.sub.10(PO.sub.4).sub.6Cl.sub.2:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), BaMgAl.sub.10O.sub.17:Eu.sup.2+, M.sub.3MgSi.sub.2O.sub.8:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), and M.sub.5SiO.sub.4Cl.sub.6:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca). Examples of fluorescent materials that emit green light include M.sub.2MgSi.sub.2O.sub.7:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), SrSi.sub.5AlO.sub.2N.sub.7:Eu.sup.2+, SrSi.sub.2O.sub.2N.sub.2:Eu.sup.2+, BaAl.sub.2O.sub.4:Eu.sup.2+, BaZrSi.sub.3O.sub.9:Eu.sup.2+, M.sub.2SiO.sub.4:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), BaSi.sub.3O.sub.4N.sub.2:Eu.sup.2+, Ca.sub.8Mg(SiO.sub.4).sub.4Cl.sub.2:Eu.sup.2+, Ca.sub.3SiO.sub.4Cl.sub.2:Eu.sup.2+, CaSi.sub.12(m+n)Al.sub.(m+n)O.sub.nN.sub.16-n:Ce.sup.3+, and -SiAlON:Eu.sup.2+. Examples of fluorescent materials that emit red light include CaAlSiN.sub.3:Eu.sup.2+, SrAlSi.sub.4O.sub.7:Eu.sup.2+, M.sub.2Si.sub.5N.sub.8:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), MSiN.sub.2:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), MSi.sub.2O.sub.2N.sub.2:Yb.sup.2+ (where M is at least one element selected from Sr and Ca), Y.sub.2O.sub.2S:Eu.sup.3+, Sm.sup.3+, La.sub.2O.sub.2S:Eu.sup.3+, Sm.sup.3+, CaWO.sub.4:Li.sup.1+, Eu.sup.3+, Sm.sup.3+, M.sub.2SiS.sub.4:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), and M.sub.3SiO.sub.5:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca). Examples of fluorescent materials that emit yellow light include Y.sub.3Al.sub.5O.sub.12:Ce.sup.3+, CaSi.sub.2O.sub.2N.sub.2:Eu.sup.2+, Ca.sub.3Sc.sub.2Si.sub.3O.sub.12:Ce.sup.3+, CaSc.sub.2O.sub.4:Ce.sup.3+, -SiAlON:Eu.sup.2+, MSi.sub.2O.sub.2N.sub.2:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca), and M.sub.7(SiO.sub.3).sub.6Cl.sub.2:Eu.sup.2+ (where M is at least one element selected from Ba, Sr, and Ca).

(210) Examples of quantum dots include materials such as CdS, CdSe, core-shell CdSe/ZnS, and alloy CdSSe/ZnS. Light of various wavelengths can be emitted depending on the material. Examples of matrices for quantum dots include glasses and resins.

(211) The transparent substrate 140, as shown in, for example, FIGS. 1C and 1D, is made of a light-transmissive material having a lower refractive index than the photoluminescent layer 110. Examples of such materials include MgF.sub.2, LiF, CaF.sub.2, SiO.sub.2, glasses, and resins.

(212) Example methods of manufacture will now be described.

(213) An example method for manufacturing the structure shown in FIGS. 1C and 1D includes depositing a thin film of fluorescent material on the transparent substrate 140 by a process such as evaporation, sputtering, or coating to form the photoluminescent layer 110 and then depositing a dielectric and patterning it by a process such as photolithography to form the periodic structure 120. Alternatively, the periodic structure 120 may be formed by nanoimprinting. As shown in FIG. 24, the periodic structure 120 may also be formed by partially processing the photoluminescent layer 110. In this case, the periodic structure 120 is made of the same material as the photoluminescent layer 110.

(214) The light-emitting device 100 shown in FIGS. 1A and 1B can be manufactured, for example, by fabricating the light-emitting device 100a shown in FIGS. 1C and 1D and then stripping the photoluminescent layer 110 and the periodic structure 120 from the substrate 140.

(215) The structure shown in FIG. 19A can be manufactured, for example, by forming the periodic structure 120a on the transparent substrate 140 by a process such as a semiconductor process or nanoimprinting and then depositing thereon the material for the photoluminescent layer 110 by a process such as evaporation or sputtering. The structure shown in FIG. 19B can be manufactured by filling the recesses in the periodic structure 120a with the photoluminescent layer 110 by a process such as coating.

(216) The above methods of manufacture are for illustrative purposes only, and the light-emitting devices according to the embodiments of the present disclosure may be manufactured by other methods.

EXAMPLES

(217) Light-emitting devices according to embodiments of the present disclosure are illustrated by the following examples.

(218) A sample light-emitting device having the same structure as in FIG. 19A was fabricated and evaluated for its properties. The light-emitting device was fabricated as follows.

(219) A one-dimensional periodic structure (stripe-shaped projections) having a period of 400 nm and a height of 40 nm was formed on a glass substrate, and a photoluminescent material, i.e., YAG:Ce, was deposited thereon to a thickness of 210 nm. FIG. 25 shows a cross-sectional transmission electron microscopy (TEM) image of the resulting light-emitting device. FIG. 26 shows the results of measurements of the spectrum of light output from the light-emitting device in the front direction when YAG:Ce was excited with an LED having an emission wavelength of 450 nm. FIG. 26 shows the results (ref) for a light-emitting device including no periodic structure, the results for the TM mode, and the results for the TE mode. The TM mode has a polarization component parallel to the one-dimensional periodic structure. The TE mode has a polarization component perpendicular to the one-dimensional periodic structure. The results show that the intensity of light of a particular wavelength in the case with the periodic structure is significantly higher than without a periodic structure. The results also show that the light enhancement effect is greater for the TM mode, which has a polarization component parallel to the one-dimensional periodic structure.

(220) FIGS. 27A, 27B, 28A, and 28B show the results of measurements and calculations of the angular dependence of the intensity of light output from the same sample. FIGS. 27A and 27B show the results of measurements (top) and calculations (bottom) for rotation about an axis parallel to the line direction of the one-dimensional periodic structure (i.e., the periodic structure 120). FIGS. 28A and 28B show the results of measurements (top) and calculations (bottom) for rotation about an axis perpendicular to the line direction of the one-dimensional periodic structure (i.e., the periodic structure 120). FIGS. 27A, 27B, 28A, and 28B show the results for linearly polarized light in the TM mode and the TE mode. FIG. 27A shows the results for linearly polarized light in the TM mode. FIG. 27B shows the results for linearly polarized light in the TE mode. FIG. 28A shows the results for linearly polarized light in the TE mode. FIG. 28B shows the results for linearly polarized light in the TM mode. As can be seen from FIGS. 27A, 27B, 28A, and 28B, the enhancement effect is greater for the TM mode, and the enhanced wavelength shifts with angle. For example, light of a wavelength of 610 nm is observed only in the TM mode and in the front direction, indicating that the light is directional and polarized. In addition, the top and bottom parts of each figure match each other. Thus, the validity of the above calculations was experimentally demonstrated.

(221) Among the above results of measurements, for example, FIG. 29 shows the angular dependence of the intensity of light of a wavelength of 610 nm for rotation about an axis perpendicular to the line direction. As shown in FIG. 29, the light was significantly enhanced in the front direction and was little enhanced at other angles. The angle of directionality of the light output in the front direction is less than 15. The angle of directionality is the angle at which the intensity is 50% of the maximum intensity and is expressed as the angle of one side with respect to the direction with the maximum intensity. This demonstrates that directional light emission was achieved. In addition, all the light was the TM mode, which demonstrates that polarized light emission was simultaneously achieved.

(222) Although YAG:Ce, which emits light in a wide wavelength range, was used in the above experiment, directional and polarized light emission can also be achieved using a similar structure including a photoluminescent material that emits light in a narrow wavelength range. Such a photoluminescent material does not emit light of other wavelengths and can therefore be used to provide a light source that does not emit light in other directions or in other polarized states.

(223) 7. Example Structures for Improving Luminous Efficiency

(224) Example structures for further improving the luminous efficiency will now be described.

(225) FIG. 31 is a schematic sectional view of an example where a photoluminescent layer (waveguide) 110 having a periodic structure 120 (i.e. a light-transmissive layer 120 on which a submicron structure is defined) thereon is formed on a low-refractive-index layer 190. The low-refractive-index layer 190 is made of a material with a lower refractive index (e.g., about 1.1 to 1.6) than the photoluminescent layer 110. Examples of such materials include SiO.sub.2, glasses, resins, and porous materials. The conditions for further improving the luminous efficiency with this structure were studied.

(226) FIG. 32 is a graph showing the results of calculations of emission enhancement for each wavelength with varying thicknesses t.sub.W of the photoluminescent layer 110. In these calculations, the periodic structure 120 was assumed to have a period p of 350 nm, a height h.sub.p of 50 nm, a refractive index n.sub.p of 1.75, and a filling factor f of 0.5. The term filling factor refers to the ratio of the volume of the recesses to the sum of the volumes of the projections and the recesses that form the periodic structure 120. The photoluminescent layer 110 was assumed to have a refractive index n.sub.W of 1.75. The low-refractive-index layer 190 was assumed to have a refractive index n.sub.L of 1.5.

(227) In FIG. 32, a darker color indicates a higher output light intensity, i.e., a higher emission enhancement. As shown, the intensity of the output light at each wavelength changes with the thickness t.sub.W of the photoluminescent layer 110. The arrows in FIG. 32 indicate particularly high emission enhancements. These calculations show that no emission enhancement occurs at wavelengths of about 525 nm or less, at which inequality (11) is not satisfied.

(228) Significant emission enhancement occurs at a particular thickness t.sub.W due to the interference of light. To study this effect in more detail, the transmittance for light incident perpendicularly on the surface of the photoluminescent layer 110 adjacent to the periodic structure 120 was calculated.

(229) FIG. 33 is a graph showing the results of these calculations. FIG. 33 shows the dependence of light transmittance on the wavelength and the thickness t.sub.W. The term transmittance as used herein refers to the ratio of the intensity of light transmitted through the photoluminescent layer 110 into the low-refractive-index layer 190 to the intensity of all incident light. In FIG. 33, a darker color indicates a higher transmittance. The transmittance at each wavelength changes with the thickness t.sub.W of the photoluminescent layer 110. The periodic change in transmittance with the thickness t.sub.W indicates that this is due to interference. FIG. 33 also shows periodic peaks (black stripes) due to the coupling of light into a quasi-guided mode by the periodic structure 120.

(230) A comparison between the results of FIGS. 32 and 33 shows that significant emission enhancement occurs in a high-transmittance region. The interference of light in the photoluminescent layer 110 and the low-refractive-index layer 190 creates a situation where light is more readily introduced into the structure. This allows more light to be coupled into a quasi-guided mode and to be output and thus results in significant emission enhancement. Thus, the thickness t.sub.W of the photoluminescent layer 110 may be set so as to maximize the transmittance.

(231) FIG. 34 is a schematic view illustrating the interference of light in the structure shown in FIG. 31. A situation is assumed in FIG. 34 where light is incident at point A on the surface of the photoluminescent layer 110 adjacent to the periodic structure 120 at an angle of incidence . The conditions where the transmittance is maximized (i.e., the reflectance is minimized) are represented by equation (18):
(.sub.2.sub.B)(.sub.1+.sub.A)+.sub.P=(2m1) (where m is a natural number)(18)
where .sub.A is the phase shift of light when the light is reflected at point A, .sub.1 is the phase shift of light when the light travels from point A to point D, .sub.B is the phase shift of light when the light is reflected at point B, .sub.2 is the phase shift of light when the light travels from point A to point B and then to point C, and .sub.p is the phase difference due to the optical path length difference caused by the periodic structure 120.

(232) The conditions where the reflectance is maximized (i.e., the transmittance is minimized) are represented by equation (19):
(.sub.2+.sub.B)(.sub.1+.sub.A)+.sub.P=2m (where m is a natural number)(19)

(233) Here, .sub.2.sub.1=4n.sub.Wt.sub.W cos /.sub.a, where .sub.a, is the wavelength of the incident light in air. Taking into account the filling factor f, the optical path length difference .sub.P caused by the periodic structure 120 is expressed as .sub.P=4n.sub.ph.sub.pf cos /.sub.a. Hence, equation (18) can be transformed as follows:
n.sub.Wt.sub.W cos /.sub.a+n.sub.ph.sub.pf cos /.sub.a+(.sub.B.sub.A)/4=(2m1)/4 (where m is a natural number)(20)

(234) In particular, if light is incident perpendicularly on the photoluminescent layer 110, cos =1, .sub.A=, and .sub.B=0. Hence, the conditions where the transmittance is maximized are represented by equation (21):
h.sub.pn.sub.pf+n.sub.Wt.sub.W=m.sub.a/2(where m is a natural number)(21)

(235) The conditions where the reflectance is maximized are represented by equation (22):
h.sub.pn.sub.pf+n.sub.Wt.sub.W=(2m1).sub.a/4(where m is a natural number)(22)

(236) Hence, the conditions where the transmittance is equal to the average are represented by equation (23):
h.sub.pn.sub.pf+n.sub.Wt.sub.W=(4m1).sub.a/8 (where m is a natural number)(23)

(237) Hence, the conditions where the transmittance is higher than the average are represented by inequality (24):
(4m1).sub.a/8<h.sub.pn.sub.pf+n.sub.Wt.sub.W<(4m+1).sub.a/8 (where m is a natural number)(24)

(238) Thus, a higher transmittance than normal is achieved if the height h.sub.p, refractive index n.sub.p, and filling factor f of the periodic structure 120 and the refractive index n.sub.W and thickness t.sub.W of the photoluminescent layer 110 are set so as to satisfy inequality (24). This results in a higher luminous efficiency.

(239) Another example structure will now be described.

(240) FIG. 35 is a partial sectional view of an example light-emitting device including, in sequence, a high-refractive-index layer 210, a low-refractive-index layer 190, a photoluminescent layer 110, and a periodic structure 120. The low-refractive-index layer 190 is made of a material with a lower refractive index (e.g., about 1.1 to 1.6) than the photoluminescent layer 110. Examples of such materials include SiO.sub.2, glasses, resins, and porous materials. The high-refractive-index layer 210 is made of a material with a higher refractive index than the low-refractive-index layer 190. For example, the high-refractive-index layer 210 may be made of a material with relatively high heat resistance, such as GaN or sapphire. For example, the high-refractive-index layer 210 may be a substrate for a light source, such as a blue LED, that emits excitation light.

(241) As described above, the photoluminescent layer 110 contains a photoluminescent material such as a fluorescent material, a phosphorescent material, or quantum dots. For example, if a YAG:Ce-based fluorescent material is used for the photoluminescent layer 110, a thin film of YAG is formed on a substrate and is then heated at elevated temperature, e.g. about 1,000 C. to 1,500 C. This heat treatment is intended to crystallize the thin film of YAG for efficient fluorescence. Accordingly, for example, the high-refractive-index layer 210 may be made of a material resistant to temperatures of about 1,000 C. to 1,500 C.

(242) A substrate with high heat resistance generally has a high refractive index. In particular, GaN and sapphire, which are commonly used as substrate materials for blue LEDs, have higher refractive indices than common luminescent materials. A structure in which the photoluminescent layer 110 is directly formed on a substrate with a high refractive index cannot form a guided mode in the photoluminescent layer 110.

(243) In this example structure, the low-refractive-index layer 190 is between the high-refractive-index layer 210 and the photoluminescent layer 110. This structure can form a guided mode in the photoluminescent layer 110 even if a substrate with a higher refractive index than the photoluminescent layer 110 is used.

(244) For this structure, the thickness t.sub.W of the photoluminescent layer 110 and the thickness t.sub.L of the low-refractive-index layer 190 can be appropriately set to increase the emission enhancement by the interference of light.

(245) FIG. 36 is a graph showing the results of calculations of emission enhancement for each wavelength with varying thicknesses t.sub.W of the photoluminescent layer 110. In these calculations, the periodic structure 120 was assumed to have a period p of 370 nm, a height h.sub.p of 50 nm, a refractive index n.sub.p of 1.75, and a filling factor f of 0.5. The photoluminescent layer 110 was assumed to have a refractive index n.sub.W of 1.75. The low-refractive-index layer 190 was assumed to have a refractive index n.sub.L of 1.5 and a thickness of 400 nm. The high-refractive-index layer 210 was assumed to have a refractive index n.sub.H of 2.0.

(246) As shown in FIG. 36, the peak intensity of the output light at each wavelength changes with the thickness t.sub.W of the photoluminescent layer 110. This phenomenon is due to the interference of light. To study this effect in more detail, the transmittance for light incident perpendicularly on the surface of the photoluminescent layer 110 adjacent to the periodic structure 120 was calculated.

(247) FIG. 37 is a graph showing the results of these calculations. FIG. 37 shows the dependence of light transmittance on the wavelength and the thickness t.sub.W. The transmittance changes with the thickness t.sub.W of the photoluminescent layer 110. The periodic change in transmittance with the thickness t.sub.W indicates that this is due to interference. FIG. 37 also shows periodic peaks due to the coupling of light into a quasi-guided mode by the periodic structure 120.

(248) The results in FIGS. 36 and 37 show that significant emission enhancement occurs in a high-transmittance region in this example. The interference of light in the photoluminescent layer 110 and the low-refractive-index layer 190 creates a situation where light is more readily introduced into the structure. This allows more light to be coupled into a quasi-guided mode and to be output and thus results in significant emission enhancement. Thus, the thickness t.sub.W of the photoluminescent layer 110 may be set so as to maximize the transmittance.

(249) FIG. 38 is a graph showing the results of calculations of the intensity of output light for each wavelength with varying thicknesses t.sub.L of the low-refractive-index layer 190. In these calculations, the photoluminescent layer 110 was assumed to have a thickness t.sub.W of 420 nm, and the thickness t.sub.L of the low-refractive-index layer 190 was varied with the other parameters being the same as in the above calculations.

(250) FIG. 39 is a graph showing the results of calculations of the transmittance for light incident perpendicularly on the surface of the photoluminescent layer 110 adjacent to the periodic structure 120. FIG. 39 shows the dependence of light transmittance on the wavelength and the thickness t.sub.L. The results show that significant emission enhancement occurs in a high-transmittance region, as in the above calculations. The results also show that the emission enhancement is significantly low if the low-refractive-index layer 190 has a thickness t.sub.L of 100 nm or less. Such a thin low-refractive-index layer 190 cannot form a guided mode effective in confining light because the leaking portion of the electric field of the guided mode (i.e., evanescent light) reaches the high-refractive-index layer 210.

(251) The leakage distance of the evanescent light is proportional to the wavelength of the light. Light of a wavelength .sub.a of about 600 nm in air is not enhanced if the low-refractive-index layer 190 has a thickness t.sub.L of 100 nm or less. Thus, the low-refractive-index layer 190 desirably has a thickness t.sub.L of .sub.a/6 or more.

(252) The conditions where a higher transmittance is achieved by interference will now be discussed.

(253) FIG. 40 is a schematic view illustrating the interference of light in the structure shown in FIG. 35. A situation is assumed in FIG. 40 where light is incident at point A on the surface of the photoluminescent layer 110 adjacent to the periodic structure 120 at an angle of incidence . The influence of interference in the individual layers is determined by the reflectance of the interfaces therebetween. The reflectance increases with increasing refractive index difference. In the structure in FIG. 35, the interface having the highest reflectance is the interface between air and the photoluminescent layer 110. The interface having the second highest refractive index depends on whether the refractive index n.sub.W of the photoluminescent layer 110, which serves as a waveguide, or the refractive index n.sub.H of the high-refractive-index layer 210 is higher.

(254) If n.sub.W>n.sub.H, the reflectance of the interface between the photoluminescent layer 110 and the low-refractive-index layer 190 is higher than the reflectance of the interface between the low-refractive-index layer 190 and the high-refractive-index layer 210. Thus, the interference depending on the thickness t.sub.W of the photoluminescent layer 110 is greater than the interference depending on the thickness t.sub.L of the low-refractive-index layer 190. In this case, the desirable conditions are similar to those represented by inequality (24).

(255) If n.sub.W<n.sub.H, the reflectance of the interface between the low-refractive-index layer 190 and the high-refractive-index layer 210 is higher than the reflectance of the interface between the photoluminescent layer 110 and the low-refractive-index layer 190. Thus, both of the thickness t.sub.W of the photoluminescent layer 110 and the thickness t.sub.L of the low-refractive-index layer 190 have a significant influence on interference.

(256) In this case, the conditions where the transmittance is maximized are represented by equation (25):
(n.sub.Lt.sub.L+n.sub.Wt.sub.W)cos /.sub.a+n.sub.ph.sub.pf cos /.sub.a+(.sub.B.sub.A)/4=(2m1)/4 (where m is a natural number)(25)

(257) In particular, if light is incident perpendicularly on the photoluminescent layer 110, cos =1, .sub.A=, and .sub.B=. Hence, the conditions where the transmittance is maximized are represented by equation (26):
n.sub.Lt.sub.L+n.sub.Wt.sub.W=(2m1).sub.a/4 (where m is a natural number)(26)

(258) The conditions where the transmittance is minimized are represented by equation (27):
n.sub.Lt.sub.L+n.sub.Wt.sub.W=2m.sub.a/4 (where m is a natural number)(27)

(259) Hence, the conditions where a higher transmittance than normal is achieved by interference is represented by inequality (28):
(4m3).sub.a/8<n.sub.Lt.sub.L+n.sub.Wt.sub.W<(4m1).sub.a/8 (where m is a natural number)(28)

(260) In this embodiment, the periodic structure 120 is provided; taking into account the optical path length thereof, the conditions where a higher transmittance is achieved are represented by inequality (29):
(4m3).sub.a/8<h.sub.pn.sub.pf+n.sub.Lt.sub.L+n.sub.Wt.sub.W<(4m1).sub.a/8 (where m is a natural number) (29)

(261) To confirm the validity of inequality (28), the transmittance was calculated with varying thicknesses t.sub.L of the low-refractive-index layer 190 and varying thicknesses t.sub.W of the photoluminescent layer 110. In these calculations, the periodic structure 120 was omitted to examine the effect of interference alone. The light was assumed to have a wavelength of 600 nm.

(262) FIG. 41 is a graph showing the results of these calculations. As can be seen from FIG. 41, the transmittance changes depending on the thickness t.sub.L of the low-refractive-index layer 190 and the thickness t.sub.W of the photoluminescent layer 110. The results demonstrate that a higher transmittance is achieved if inequality (28) is satisfied.

(263) For the example structure shown in FIG. 35, in which the periodic structure 120 is provided, the height h.sub.p, refractive index n.sub.p, and filling factor f of the periodic structure 120, the refractive index n.sub.L and thickness t.sub.L of the low-refractive-index layer 190, and the refractive index n.sub.W and thickness t.sub.W of the photoluminescent layer 110 may be set so as to satisfy inequality (29). This results in a higher transmittance than normal and therefore a higher luminous efficiency.

(264) Light-emitting devices including the low-refractive-index layer 190 and the high-refractive-index layer 210 according to modifications will now be described.

(265) FIG. 42 is a partial sectional view of a light-emitting device according to a first modification. This light-emitting device is fabricated by forming a low-refractive-index layer 190 on a high-refractive-index layer 210, forming a texture (i.e., a periodic structure 120e) thereon, and forming a photoluminescent layer 110 thereon. As a result, a texture of the same period (i.e., a periodic structure 120d) is formed in the interface (hereinafter referred to as top surface) between the photoluminescent layer 110 and an external layer (e.g., an air layer as a light-transmissive layer). Thus, periodic structures may be provided on both sides of the photoluminescent layer 110. This structure is advantageous in that it can be more easily fabricated than a structure in which a periodic structure is provided only on the top surface of the photoluminescent layer 110. In this case, the thickness t.sub.W of the photoluminescent layer 110 is defined as the distance between the interface between the periodic structure 120d and the photoluminescent layer 110 and the average height of the texture that forms the periodic structure 120e (indicated by the second dashed line from top in FIG. 42). The thickness of the low-refractive-index layer 190 is defined as the distance between the interface between the high-refractive-index layer 210 and the low-refractive-index layer 190 and the average height of the texture that forms the periodic structure 120e. The periodic structure 120d has a thickness h.sub.p. In this example, if n.sub.W>n.sub.H, emission enhancement occurs if inequality (24) is satisfied, whereas if n.sub.W<n.sub.H, emission enhancement occurs if inequality (29) is satisfied. The high-refractive-index layer 210 may be omitted from the structure in FIG. 42. In this case, the structure may be designed so as to satisfy inequality (24).

(266) FIG. 43 is a schematic partial sectional view of a light-emitting device according to a second modification. This light-emitting device is fabricated by forming a texture (i.e., a periodic structure 120f) on a high-refractive-index layer 210 and forming thereon a low-refractive-index layer 190 and a photoluminescent layer 110. As a result, a periodic structure 120e is formed in the interface between the low-refractive-index layer 190 and the photoluminescent layer 110, and a periodic structure 120d is formed on the top surface of the photoluminescent layer 110. This structure is advantageous in that it can be more easily fabricated than a structure in which a periodic structure is provided only on the top surface of the photoluminescent layer 110. This structure provides similar effects to the first modification. In this example, the thickness t.sub.W of the photoluminescent layer 110 is defined as the distance between the interface between the periodic structure 120d and the photoluminescent layer 110 and the center of the periodic structure 120e across the thickness thereof (indicated by the second dashed line from top in FIG. 43). The thickness t.sub.L of the low-refractive-index layer 190 is defined as the distance between the centers of the periodic structures 120e and 120f across the thickness thereof. In this example, if n.sub.W>n.sub.H, emission enhancement occurs if inequality (24) is satisfied, whereas if n.sub.W<n.sub.H, emission enhancement occurs if inequality (29) is satisfied.

(267) FIG. 44 is a schematic partial sectional view of a light-emitting device according to a third modification. This light-emitting device is fabricated by forming a low-refractive-index layer 190 having a texture (i.e., a periodic structure 120e) on a high-refractive-index layer 210 and forming a photoluminescent layer 110 thereon so as to fill the texture. Thus, the periodic structure 120e may be formed only in the interface between the photoluminescent layer 110 and the low-refractive-index layer 190. In this example, the thickness t.sub.W of the photoluminescent layer 110 is defined as the distance between the top surface of the photoluminescent layer 110 and the center of the periodic structure 120e across the thickness thereof. The thickness t.sub.L of the low-refractive-index layer 190 is defined as the distance between the interface between the high-refractive-index layer 210 and the low-refractive-index layer 190 and the center of the periodic structure 120e across the thickness thereof. This structure corresponds to a structure shown in FIG. 42 in which the periodic structure 120d has a thickness h.sub.p of 0. In this example, therefore, emission enhancement occurs if inequality (28), which is given by substituting h.sub.p=0 into inequality (29), is satisfied.

(268) Although the periodic structures 120e, 120d, and 120f in these modifications have the same period, they may have different periods. Each periodic structure may include portions with different periods that are coupled together, for example, as in the structure shown in FIG. 21. The periodic structures 120e, 120d, and 120f are not necessarily one-dimensional periodic structures, but may be two-dimensional periodic structures. Instead of the periodic structures 120e, 120d, and 120f, a submicron structure may be used in which projections and recesses are randomly arranged in one or two dimensions. In this case, the term period of the submicron structure refers to the average period of the submicron structure.

(269) In one embodiment, the submicron structure may include at least one periodic structure defined by at least the projections or recesses, and the at least one periodic structure may include a first periodic structure satisfying the following relationship:
.sub.a/n.sub.wav-a<p.sub.a<.sub.a
where p.sub.a is the period of the first periodic structure.

(270) The light-emitting devices according to the embodiments of the present disclosure, which can be used to provide directional light-emitting apparatuses, are applicable to, for example, optical devices such as lighting fixtures, displays, and projectors.