Abstract
A method of producing a diffractive optical element (1) comprises the steps of providing at least one substrate (3) having a surface (4) and generating a relief structure (2) in the surface (4) of the substrate (3) using a processing device (5). The relief structure (2) is generated such that a distance (D) between a surface (8) of the relief structure (2) and the surface (4) of the substrate (3) along the third direction (z) varies essentially continuously. A diffractive optical element (1) comprises a relief structure (2), wherein at least in a portion of the relief structure (2) a distance (D) between the surface (8) of the relief structure (2) and the surface (4) of the substrate (3) varies essentially continuously. A virtual image display device comprises at least a first and a second of such diffractive optical elements (1).
Claims
1. A method of producing a diffractive optical element comprising the steps of: providing at least one substrate having a surface extending in a first direction and a second direction running perpendicularly to the first direction; and generating a relief structure in the surface of the substrate using a processing device; wherein the processing device comprises a probe having a tip, wherein the tip has a radius being smaller than about 1 micrometer; or smaller than about 20 nanometer, and wherein the probe is movable in the first direction, the second direction and a third direction running perpendicularly to the first direction and the second direction with respect to the substrate, and wherein the relief structure is generated by an action of the tip on the surface of the substrate such that a distance between a surface of the relief structure and the surface of the substrate along the third direction varies essentially continuously along at least one of the first direction and the second direction.
2. The method according to claim 1, wherein at least one of: i) the relief structure is generated by at least one of a mechanical and thermal action of the tip on the surface of the substrate, ii) the tip is in direct contact with the surface of the substrate upon the generation of the relief structure, and iii) the processing device is a thermal scanning-probe lithography device.
3. The method according to claim 1, wherein at least one of: i) the probe is moved at least one of in the first direction and in the second direction in steps of about 0.1 nanometer to 50 micrometer or in steps of about 0.1 nanometer to 100 nanometer or in steps of 5 nanometer to 50 nanometer or in steps of less than about 20 nanometer, ii) the probe is moved in the third direction in steps of about 0.1 nanometer to 1 micrometer or in steps of 0.2 nanometer to 25 nanometer or in steps of less than about 2 nanometer, and ii) the probe is moved at least one of in the first direction and the second direction with a rate of between about 1 hertz to 1,000 kilohertz or between about 1 kilohertz to 500 kilohertz.
4. The method according to claim 1, wherein the processing device further comprises a controller configured to control the probe based on controller data that is fed into the controller, wherein the controller data defines the relief structure along a horizontal plane being spanned by the first direction and the second direction and is based on one or more functions f(x,y).
5. The method according to claim 4, wherein the one or more sinusoidal functions are represented by the expression: wherein the parameter A.sub.n is the amplitude, wherein the parameter k.sub.n is the spatial frequency, wherein the parameter α.sub.n is the angular direction along the horizontal plane, wherein the parameter φ.sub.n is the phase, and wherein the parameter Δ.sub.n is an offset with respect to the third direction.
6. The method according to claim 4, wherein the controller data is based on two or more sinusoidal functions f.sub.n(x,y), and wherein said two or more sinusoidal functions f.sub.n(x,y) are summed up in a Fourier Series:
7. The method according to claim 4, wherein the controller data is generated by the steps of: (i) defining the relief structure to be generated in the horizontal plane with one or more functions f.sub.n(x,y) in a computing device, whereby a model relief structure is obtained; and (ii) discretizing the model relief structure of step (i) into pixels in the computing device, whereby discretized controller data is obtained.
8. The method according to claim 1, wherein at least one of a dielectric film or a metal film or a transition metal film such as a silver film is applied on the relief structure, whereby the relief structure is generated in the dielectric film or the metal film or the transition metal film, wherein a curable resin such as a UV-curable epoxy resin is deposited on the dielectric film or the metal film or the transition metal film, wherein a carrier is applied to the curable resin, wherein the curable resin is cured, and wherein a template stripping is performed such that the carrier, the cured resin and the dielectric film or the metal film or the transition metal film comprising a negative of the relief structure are removed from the substrate.
9. The method according to claim 1, further comprising the step of providing a further substrate, wherein the further substrate has a surface extending in the first direction and the second direction, wherein the substrate is provided on the surface of the further substrate, and wherein the relief structure of the substrate is etched into the surface of the further substrate.
10. The method according to claim 1, wherein one or more relief structures are generated in the surface of the substrate and, if applicable, in the surface of the further substrate.
11. A diffractive optical element produced by a method according to claim 1.
12. A diffractive optical element comprising a substrate with a surface, wherein the substrate extends in a first direction, in a second direction running perpendicularly to the first direction, and in a third direction running perpendicularly to the first direction and the second direction, wherein the surface comprises a relief structure having a surface, wherein at least in a portion of the relief structure a distance between the surface of the relief structure and the surface of the substrate along the third direction varies essentially continuously along at least one of the first direction and the second direction, and wherein at least the portion of the relief structure when seen along at least one of the first direction and the second direction comprises a plurality of elevations and recesses, wherein at least one of: i. a minimal horizontal distance between at least one of a) two successive elevations and b) two successive recesses along at least one of the first direction and the second direction is smaller than about 1 micrometer or smaller than about 20 nanometer or wherein the minimal horizontal distance is about 10 nanometer, and ii. a minimal depth that extends in the third direction and that is formed between at least one of a) two successive elevations and b) two successive recesses along at least one of the first direction and the second direction is smaller than about 100 nanometer or smaller than about 10 nanometer or wherein the minimal depth is about 0.2 nanometer.
13. The diffractive optical element according to claim 11, wherein at least the portion of the relief structure is configured such, that at least one beam of electromagnetic radiation having a given wavelength can be incident on the portion of the relief structure under at least one desired incoming angle and can be diffracted under at least one desired outgoing angle.
14. The diffractive optical element according to claim 11, wherein at least the portion of the relief structure is configured such, that at least a first beam of electromagnetic radiation having a first wavelength and being incident on the portion of the relief structure under a first incoming angle is diffracted under a first outgoing angle and a second beam of electromagnetic radiation having a second wavelength differing from the first wavelength and being incident on the portion of the relief structure under a second incoming angle is diffracted under a second outgoing angle, and wherein: i. the first incoming angle essentially equals the second incoming angle and the first outgoing angle essentially equals the second outgoing angle, or ii. the first incoming angle essentially equals the second incoming angle and the first outgoing angle differs from the second outgoing angle, or iii. the first incoming angle differs from the second incoming angle and the first outgoing angle essentially equals the second outgoing angle, or iv. the first incoming angle differs from the second incoming angle and the first outgoing angle differs from the second outgoing angle.
15. A virtual image display device comprising: a source of radiation, a substrate, and at least a first and a second diffractive optical element as claimed in claim 11, wherein the source of radiation is configured to emit at least one beam of electromagnetic radiation; wherein the first diffractive optical element is arranged on or in the substrate such, that the at least one beam of electromagnetic radiation being incident on the first diffractive optical element is coupled into the substrate and propagates along the substrate, and wherein the second diffractive optical element is arranged on or in the substrate such, that the propagating at least one beam of electromagnetic radiation is coupled out of the substrate.
16. A virtual image display device comprising: a source of radiation, a substrate, and at least one diffractive optical element as claimed in claim 11, wherein the source of radiation is configured to emit at least one beam of electromagnetic radiation; wherein the diffractive optical element is arranged on or in the substrate such, that the at least one beam of electromagnetic radiation being incident on the diffractive optical element is diffracted in a manner that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.
17. The method according to claim 4, wherein the controller data is based on at least one of i) one or more continuous functions and ii) one or more sinusoidal functions.
18. The method according to claim 7, wherein at least one of i) the relief structure to be generated in the horizontal plane is defined with one or more sinusoidal functions f.sub.n(x,y) and ii) the discretized controller data is stored in a digital file.
19. The method according to claim 8, wherein the carrier comprises a dielectric material such as glass, a metal, a transition metal, a semiconductor material such as silicon, a polymerizable polymer, or a polymer.
20. The method according to claim 10, wherein said one or more relief structures are arranged immediately adjacent to one another or spaced apart from one another with respect to at least one of the first direction and the second direction.
21. The diffractive optical element according to claim 13, wherein the relief structure is configured such, that the at least one beam of electromagnetic radiation is diffracted in a manner that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.
22. The diffractive optical element according to claim 12, wherein at least the portion of the relief structure is configured such, that at least one beam of electromagnetic radiation having a given wavelength can be incident on the portion of the relief structure under at least one desired incoming angle and can be diffracted under at least one desired outgoing angle,
23. The diffractive optical element according to claim 12, wherein the relief structure is configured such, that the at least one beam of electromagnetic radiation is diffracted in a manner that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.
24. The diffractive optical element according to claim 12, wherein at least the portion of the relief structure is configured such, that at least a first beam of electromagnetic radiation having a first wavelength and being incident on the portion of the relief structure under a first incoming angle is diffracted under a first outgoing angle and a second beam of electromagnetic radiation having a second wavelength differing from the first wavelength and being incident on the portion of the relief structure under a second incoming angle is diffracted under a second outgoing angle, wherein: i. the first incoming angle essentially equals the second incoming angle and the first outgoing angle essentially equals the second outgoing angle, or ii. the first incoming angle essentially equals the second incoming angle and the first outgoing angle differs from the second outgoing angle, or iii. the first incoming angle differs from the second incoming angle and the first outgoing angle essentially equals the second outgoing angle, or iv. the first incoming angle differs from the second incoming angle and the first outgoing angle differs from the second outgoing angle.
25. The virtual image display device as claimed in claim 15, wherein the source of radiation is at least one of an image display element and is configured to emit at least one image frame.
26. A virtual image display device comprising: a source of radiation, a substrate, and at least a first and a second diffractive optical element as claimed in claim 12, wherein the source of radiation is configured to emit at least one beam of electromagnetic radiation; wherein the first diffractive optical element is arranged on or in the substrate such, that the at least one beam of electromagnetic radiation being incident on the first diffractive optical element is coupled into the substrate and propagates along the substrate, and wherein the second diffractive optical element is arranged on or in the substrate such, that the propagating at least one beam of electromagnetic radiation is coupled out of the substrate.
27. The virtual image display device as claimed in claim 26, wherein the source of radiation is at least one of an image display element and is configured to emit at least one image frame.
28. A virtual image display device comprising: a source of radiation, a substrate, and at least one diffractive optical element as claimed in claim 12, wherein the source of radiation is configured to emit at least one beam of electromagnetic radiation; wherein the diffractive optical element is arranged on or in the substrate such, that the at least one beam of electromagnetic radiation being incident on the diffractive optical element is diffracted in a manner that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0067] Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings,
[0068] FIG. 1a shows a schematic illustration of a method of producing a diffractive optical element according to the invention in a first state, wherein a processing device comprising a probe is about to act on a surface of a substrate in order to generate a relief structure;
[0069] FIG. 1b shows a schematic illustration of the method of producing a diffractive optical element according to FIG. 1b in a second state, wherein the processing device comprising the probe acts on the surface of the substrate;
[0070] FIG. 2a shows different fabrication pathways for producing diffractive optical elements according to the method of the invention;
[0071] FIG. 2b shows schematic illustrations of different diffractive optical elements that are obtained by the fabrication pathways according to FIG. 2a;
[0072] FIG. 3 shows a schematic illustration of the physical relationship applying in the determination of the spatial frequency of the relief structure according to the method of the invention;
[0073] FIG. 4 shows a schematic illustration of possible diffraction scenarios when electromagnetic radiation impinges on the relief structure of a diffractive optical element according to another embodiment of the invention;
[0074] FIG. 5 shows a schematic illustration of another possible diffraction scenario when electromagnetic radiation impinges on the relief structure of a diffractive optical element according to another embodiment of the invention;
[0075] FIG. 6 shows a schematic illustration of another possible diffraction scenario when electromagnetic radiation impinges on the relief structure of the diffractive optical element according to FIG. 5;
[0076] FIG. 7 shows a schematic illustration of another possible diffraction scenario when electromagnetic radiation impinges on the relief structure of a diffractive optical element according to another embodiment of the invention;
[0077] FIG. 8a shows a bitmap for a single sinusoidal model relief structure;
[0078] FIG. 8b shows a cross-section of the bitmap taken along the dashed line A-A of FIG. 8a;
[0079] FIG. 9a shows a topography of a diffractive optical element comprising a relief structure in the shape of a single sinusoidal profile according to the invention;
[0080] FIG. 9b shows a cross-section of the topography taken along the dashed line B-B of FIG. 9a;
[0081] FIG. 10a shows a scanning electron micrograph of a diffractive optical element comprising a relief structure in the shape of a single sinusoidal profile according to the invention;
[0082] FIG. 10b shows a spectrally-resolved reflection measurement at normal incidence of the diffractive optical element according to FIG. 10a;
[0083] FIG. 11a shows a bitmap for a three-component sinusoidal model relief structure;
[0084] FIG. 11b shows a cross-section of the bitmap taken along the dashed line C-C of FIG. 11a;
[0085] FIG. 12a shows a topography of a diffractive optical element comprising a relief structure in the shape of a three-component sinusoidal profile according to the invention;
[0086] FIG. 12b shows a cross-section of the topography taken along the dashed line D-D of FIG. 12a;
[0087] FIG. 13a shows a scanning electron micrograph of a diffractive optical element comprising a relief structure in the shape of a three-component sinusoidal profile according to the invention;
[0088] FIG. 13b shows a spectrally-resolved reflection measurement at normal incidence of the diffractive optical element according to FIGS. 11 and 12;
[0089] FIG. 14a shows a bitmap for a two-dimensional model relief structure;
[0090] FIG. 14b shows topography data for the two-dimensional model relief structure according to FIG. 14a;
[0091] FIG. 14c shows a scanning electron micrograph of a diffractive optical element comprising a relief structure obtained from the bitmap and topography data according to FIGS. 14a and 14b;
[0092] FIG. 14d shows a k-space reflection measurement of the diffractive optical element according to FIG. 14c;
[0093] FIG. 15 shows a schematic illustration of a virtual image display device comprising diffractive optical elements according to the invention;
[0094] FIG. 16 shows a schematic illustration of another virtual image display device comprising diffractive optical elements according to the invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
[0095] In FIGS. 1a to 2b different aspects regarding the method of producing a diffractive optical element 1 comprising a relief structure 2 according to the invention are disclosed. The underlying physical relationship associated with the generation of the relief structure 2 and the resulting diffraction scenarios are illustrated in FIGS. 3 to 7. With respect to FIGS. 8 to 14d different examples of diffractive optical elements 1 according to the invention are shown and aspects regarding their production and characterization are discussed.
[0096] Hence, as follows from FIGS. 1a and 1b the method of producing a diffractive optical element 1 according to the invention comprises the steps of providing at least one substrate 3 having a surface 4 and generating a relief structure 2 in the surface 4 of the substrate 3 using a processing device 5. The substrate 3 extends in a first direction x, a second direction y running perpendicularly to the first direction x, and a third direction z running perpendicularly to the first direction x and the second direction y. The surface 4 of the substrate 3 extends in the first direction x and the second direction y, said first direction x and second direction y spanning a horizontal plane x-y. The processing device 5 comprises a prove 6 having a tip 7. The tip 7 has a radius R that is about 10 nanometer. The probe 6, and thus the tip 7, is movable in the first direction x, the second direction y and the third direction z with respect to the substrate 3. The relief structure 2 is generated by an action of the tip 7 on the surface 4 of the substrate 3 such that a distance D between a surface 8 of the relief structure 2 and the surface 4 of the substrate 3 along the third direction z varies essentially continuously along at least one of the first direction x and the second direction y, see e.g. FIGS. 4-7, 9a, 10a, 12a, 13a and 14c. As follows from FIG. 1b, for example, the surface 4 of the substrate 3 is understood as the surface of the substrate 3 before the substrate 3 has been processed by the processing device 5. In other words, after a processing of the substrate 3 by the processing device 5 said surface 4 corresponds to the surface of the substrate outside a region comprising the relief structure 2. This in turn means that the surface 8 of the relief structure 2 corresponds to the surface of the substrate 3 that comprises the relief structure 2. The probe 6 is movable in the first direction x and in the second direction y in steps of about 0.1 nanometer to 50 micrometer, for example in steps of less than about 20 nanometer, and the probe 6 is movable in the third direction z in steps of about 0.1 nanometer to 1 micrometer, preferably in steps of less than about 2 nanometer. Due to these small movement steps a relief structure 2 comprising a plurality of recesses 9 and elevations 10 is generated, wherein a minimal horizontal distance hd between two successive elevations 10 and recesses 9 along the first direction x and the second direction y is about 10 nanometer and a minimal depth vd that extends in the third direction z is about 0.2 nanometer. The tip 9 is further configured to scan over the surface 8 of the relief structure 2 while it is acting upon the surface 4 of the substrate 3. This generates a closed-loop feedback system that results in an accurate and precise profile of the surface relief structure 2. This reading process is schematically indicated by the corrugated arrow in FIG. 1b.
[0097] The particular movements of the probe 6 are carried out according to particular controller data that is fed to a controller 11 of the processing device 5 being configured to control the probe 6. Said controller data defines the relief structure 2 along the horizontal plane x-y and in the present examples is based on one sinusoidal function f.sub.n=1(x,y) (see FIGS. 8a to 10b) or on three sinusoidal functions f.sub.n=3(x,y)(see FIGS. 11a to 13b), wherein f.sub.n(x,y)=A.sub.n sin(k.sub.n(x cos α.sub.n−y sin α.sub.n)+φ.sub.n)+Δ.sub.n. However, it should be noted that any number of sinusoidal functions are conceivable. In the case of two or more sinusoidal functions said sinusoidal functions are summed up in a Fourer Series F(x,y)=Σ.sub.nf.sub.n(x,y). The parameters in this expression correspond to the amplitude A.sub.n, the spatial frequency k.sub.n, the angular direction α.sub.n along the horizontal plane x-y, the phase φ.sub.n, and the offset Δ.sub.n with respect to the third direction z.
[0098] As follows from FIG. 2a, said one sinusoidal function or Fourier Series is generated in a computing device 12, whereby a so-called model relief structure of Fourier surface design is obtained. In a next step, said model relief structure is discretized into pixels, whereby discretized controller data is obtained that is stored in a digital file such as a bitmap file. In FIG. 2a this step is referred to as grayscale bitmap generation, since the continuity provided by the sinusoidal functions results here in a grayscale bitmap. Depending on the desired end application of the diffractive optical element 1, an adequate fabrication scheme is then selected for the further production of the diffractive optical element 1.
[0099] As further follows from FIGS. 1, 2a and 2b, said different fabrication schemes encompass direct writing, etching or template stripping as they are known in the art. That is, the substrate 3 can be a polymer such as PPA or PMMA/MA, wherein the relief structure 2 is generated into the surface 4 of said substrate 3 by the action of the probe 6 on the surface 4, and whereby the diffractive optical element 1 is obtained. This process is depicted in FIG. 1. However, and as follows from FIG. 2b, it is also conceivable to apply such a polymer substrate 3 on the surface 15 of a further substrate 14 by means of spin coating, see step (a) for example. In a next step (b) the relief structure 2 is generated in the surface 4 of the polymer being applied to the further substrate 14 by means of the tip 7 acting on the surface 4. Thereby, another diffractive optical element 1 is generated. However, a different diffractive optical element 1 is obtained if said two-layer structure consisting of the polymer substrate 3 and the further substrate 14 is subject to an etching process or a template stripping process, see step (c). In the former case a dielectric film or a metal film or a transition metal film such as a silver film 16 can be applied on the relief structure 2 generated in the polymer layer 3 whereby the relief structure 2 is generated in the film 16, see step (d). In a further step, a curable resin such as a UV-curable epoxy resin is deposited on said film 16. Again in a further step (e), a carrier 19 such as a glass plate is applied to the curable resin. Then, the curable resin is cured In a next step (f), the carrier 19, the cured resin and the film 16 comprising the relief structure 2 are removed from the substrate 3. The thus produced relief structure 2 generated by template stripping corresponds to a diffractive optical element 1. In the present examples the production of such grayscale diffractive optical elements 1 is conducted with a tip 7 being heated to a temperature of approximately 750° C., a typical pixel size of approximately 10 nm, a total depth of the relief structure 2 in the third direction z of approximately 50-100 nm, and a dimension of the relief structure 2 in the horizontal plane x-y of approximately 10-20 micrometer.
[0100] In the following, different diffractive optical elements 1 that are obtained by the method according to the invention are discussed in greater detail. All of these diffractive optical elements 1 have in common that the controller data that was used to control the probe 6 of the processing device 5 is based on one or more sinusoidal functions having predetermined values of their parameters.
[0101] One underlying physical principle that was utilized corresponds to the momentum-matching principle, which enables a choice of the spatial frequency of the relief structure 2 of the diffractive optical element 1 such that the in-plane wavevector of the incident electromagnetic radiation is matched to the in-plane wavevector of the outgoing electromagnetic radiation. Said principle is described in greater detail in the section “summary of the invention” of this application and is schematically illustrate in FIG. 3. In FIG. 3, ![custom-character]()
is the in-plane wavevector of the outgoing electromagnetic radiation, ![custom-character]()
is the in-plane wavevector of the incident electromagnetic radiation, {circumflex over (k)}.sub.0,in is the unit vector along the direction of propagation of the incident electromagnetic radiation, ![custom-character]()
is the wavevector of the diffractive optical element 1, and θ.sub.in is the angle of the incident electromagnetic radiation relative to a normal direction (dashed line).
[0102] In FIGS. 4 to 7 different conceivable diffraction scenarios are depicted. Namely, in FIG. 4 electromagnetic radiation EM.sub.in with a given wavelength is incident on the relief structure 2 of a diffractive optical element 1 according to the invention at an angle θ.sub.in. In the present example said electromagnetic radiation EM.sub.in is incident from above the relief structure 2, for example from a top layer (not shown) that is applied on top of the surface 4 of the substrate 3 comprising the relief structure 2. It should be noted that a top layer is not a requirement. Instead, it is likewise conceivable that no top layer is present and that the electromagnetic radiation is incident from a vacuum environment or air environment. Moreover, it should be noted that it can be incident on the relief structure 2 from any direction, such as from within the substrate 3 comprising the relief structure 2 or from below. The incident electromagnetic radiation EM.sub.in diffracts as outgoing electromagnetic radiation EM.sub.out from the relief structure 2 and depending on the design of the relief structure 2 it can diffract such that it travels in the direction back to the top layer (θ.sub.diff,1), into the substrate 3 (θ.sub.diff,2), or diffract through the substrate 3 to another side (θ.sub.diff,3). FIG. 5 depicts an embodiment of a grayscale diffractive optical element 1 according to the invention where the relief structure 2 is generated directly in a substrate 3 being a waveguide layer such that incident electromagnetic radiation EM.sub.in from a top layer (not shown) diffracts to a waveguide mode EM.sub.out that travels along the substrate 3. FIG. 6 depicts an embodiment of a grayscale diffractive optical element 1 where the relief structure 2 is generated directly in a substrate 3 being a waveguide layer such that incident electromagnetic radiation EM.sub.in from the waveguide layer diffracts to a freespace mode that propagates as EM.sub.out in a top layer (not shown). The same can be achieved for a mode that diffracts into a bottom layer of a diffractive optical element 1. In particular, FIG. 7 depicts an embodiment of a diffractive optical element 1 according to the invention which acts as a RGB coupler in a waveguide layer stack that is commonly used in augmented-reality devices. Here, the substrate 3 in the form of a top layer corresponds to a layer being made of a polymer having a high refractive index, such as CSAR. However, other materials having a high refractive index are likewise conceivable. Said top layer has a higher refractive index than the further substrate 14 in the form of a middle layer such that the top layer supports a waveguide mode. Conceivable materials for said middle layer 14 are thermally grown silicon dioxide (SiO.sub.2) and the like. Red, green, and blue light EM.sub.in (further distinguished by the letters “R”, “G” and “B”) reaches the diffractive optical element 1 from normal incidence and diffracts to an angle such that it couples to the waveguide mode and travels along the waveguide as EM.sub.out. Moreover, a further substrate 17 forming a bottom layer is arranged after the middle layer 14 when seen from the top layer 3 towards the middle layer 14 along the third direction z. Said bottom layer 17 can be made of Silicon, although other materials are likewise conceivable.
[0103] As mentioned initially, depending on the end application of the diffractive optical element 1 the controller data can be based on predetermined values of the amplitude A.sub.n, the spatial frequency k.sub.n, the angular direction α.sub.n, the phase φ.sub.n, and the offset Δ.sub.n that are used to define the model relief structure 18 based on sinusoidal functions. FIG. 8a depicts a grayscale bitmap 13 for a single sinusoidal surface relief. The sinusoidal modulation is along the first direction x, and the model relief structure 18 is constant along the second direction y. The bitmap 13 is constructed using square pixels with a side length of 10 nm. The model relief structure 18 is divided into 256 depth levels (8-bit precision) along the third direction z, see FIG. 8b.
[0104] FIG. 9a depicts a topography of a single sinusoidal relief structure 2 that has been generated in polymer resist 3. The topography is measured in situ by the thermal scanning probe 6 during the patterning process. The grayscale colour map indicates the height of the measured points, where the zero value is normalized to the flat surface 4 outside the patterned region 2. The cross-section of the topography taken along the dashed line in FIG. 9a has been averaged over 1 micrometer (100 pixels). The black line is a fit of the desired relief structure 2, in this case a single sinusoid, which was used to generate the bitmap 13 and the relief structure 2. The fitted sinusoidal function is represented by the formula f(x)=A sin(kx−φ)+Δ. The fit parameters return values of 24.8 nm, 10.1 micrometer.sup.−1, −3.14 radians, −32.9 nm for the parameters defining the amplitude, spatial frequency, phase, and offset, respectively, of the sinusoidal function.
[0105] FIG. 10a depicts a scanning electron micrograph of a single sinusoidal relief structure 2 generated on a silver surface 16. The relief structure 2 was transferred to the silver surface 16 using template stripping, where the polymer surface 4 in FIG. 9a was used as the template. FIG. 10b corresponds to a spectrally-resolved reflection measurement at normal incidence of the single sinusoidal relief structure 2 on the silver surface 16 depicted in FIG. 10a. The dip in reflectivity at a photon energy of ˜1.9 eV shows that electromagnetic radiation being incident on the relief structure 2 is diffracted to modes that propagate along the silver surface 16.
[0106] FIG. 11a depicts a grayscale bitmap 13 for a three-component sinusoidal model relief structure 18. The sinusoidal modulation is along the first direction x, and the model relief structure 18 is constant along the second direction y. The bitmap 13 is constructed using square pixels with a side length of 10 nm. The model relief structure 18 is divided into 256 depth levels (8-bit precision) along the third direction z, see FIG. 11b.
[0107] FIG. 12a depicts a topography of a three-component sinusoidal relief structure 2 in polymer resist 3. The topography is measured in situ by the thermal scanning probe 6 during the patterning process. The grayscale colour map indicates the height of the measured points, where the zero value is normalized to the flat surface 4 outside the patterned region 2. The cross-section depicted in FIG. 12b has been averaged over 1 micrometer (100 pixels). The black line is a fit of the desired relief structure, in this case a three-component sinusoid, which was used to generate the bitmap 13 and model relief structure 18. The fitted sinusoidal function is represented by the formula f(x)=A.sub.1 sin(k.sub.1x−φ.sub.1)+A.sub.2 sin(k.sub.2x−φ.sub.2)+A.sub.3 sin(k.sub.3x−φ.sub.3)+Δ. The fit parameters return values of 10.5 nm, 10.1 micrometer.sup.−1, and −3.0 radians for the parameters defining the amplitude, spatial frequency, and phase, respectively, of the first sinusoidal function. The fit parameters return values of 8.8 nm, 12.1 micrometer.sup.−1, and −1.3 radians for the parameters defining the amplitude, spatial frequency, and phase, respectively, of the second sinusoidal function. The fit parameters return values of 7.6 nm, 14.1 micrometer.sup.−1, and 0.95 radians for the parameters defining the amplitude, spatial frequency, and phase, respectively, of the third sinusoidal function. The fit parameters return a value of −34.9 nm for the offset parameter.
[0108] FIG. 13a depicts a scanning electron micrograph of a three-component sinusoidal relief structure 2 on a silver surface 16. The relief structure 2 was transferred to the silver surface 16 using template stripping, where a polymer surface 4 similar to the one depicted in FIG. 12a was used as the template. FIG. 13b corresponds to a spectrally-resolved reflection measurement at normal incidence of the three-component sinusoidal relief structure 2 on a silver surface 16 with a profile from FIGS. 11 and 12. The dip in reflectivity at photon energies of ˜1.9 eV, ˜2.2 eV, and ˜2.6 eV shows that light with those particular wavelengths that is normally incident on the relief structure 2 is diffracted to modes that propagate along the silver surface 16.
[0109] FIG. 14a depicts a bitmap 13 for two-dimensional grayscale model relief structure 18 (quasicrystal with 8-fold rotational symmetry). FIG. 14b depicts topography data for said two-dimensional grayscale pattern. FIG. 14c depicts a scanning electron micrograph of said two-dimensional grayscale relief structure 2. FIG. 14d corresponds to a k-space reflection measurement of the two-dimensional grayscale relief structure 2 showing 8-fold rotational symmetry.
[0110] FIGS. 15 and 16 depict different embodiments of a virtual image display device 20 comprising diffractive optical elements 1 according to the invention. In particular, FIG. 15 depicts a virtual image display device 20 comprising a source of radiation in the form of an image display element 21, an optical system in the form of a lens 22, for example a collimating lens, a substrate 3 in the form of an optical waveguide, and three diffractive optical elements 1 according to the invention. The image display device 21 is configured to generate an image frame EM.sub.in which is collimated by means of the lens 22 onto the first diffractive optical element 1a being provided in a surface 4 of the optical waveguide 3. The first diffractive optical element 1a is configured such, that the incident image frames EM.sub.in are coupled into the optical waveguide 3 and can propagate along the optical waveguide 3. Due to the surface profile of the relief structure 2 of the first diffractive optical element 1a, the incident image frames EM.sub.in are diffracted such that they propagate along opposite directions within the optical waveguide 3. One of the propagating image frames is then coupled out of the optical waveguide 3 at the second diffractive optical element 1b and the other of the propagating image frames is coupled out of the optical waveguide 3 at the third diffractive optical element 1c. As follows from FIG. 15, the second and third diffractive optical elements 1b, 1c are configured such, that the out-coupled beams EM.sub.out propagate parallel to one another.
[0111] The virtual image display device 20 according to FIG. 16 comprises a first diffractive optical element 1a that is configured such, that incident electromagnetic radiation is coupled into the substrate 3 in the form of an optical waveguide. In the present example the relief structure 2 of said first diffractive optical element 1a is configured such, that three beams of electromagnetic radiation having different wavelengths are coupled into the optical waveguide. Here, said three beams corresponds to red, green and blue light EM.sub.in,R, EM.sub.in,G and EM.sub.in_B. The first diffractive optical element 1a is further configured such, that the three beams propagate parallel to one another and parallel to the surface 4 of the optical waveguide 3. When the propagating beams are incident on the second diffractive optical element 1b, said beams are coupled out of the second diffractive optical element. In the present example the second diffractive optical element 1b is configured such, that the out-coupled beams EM.sub.out interfere with one another, whereby an interference pattern is generated to form a specific light field. Said interference pattern can constitute a hologram, for example.
[0112] Here, the virtual image display devices 20 according to both figures comprise a substrate 3 in the form of an optical waveguide being made of a material having a high refractive index. Said optical waveguide is arranged on a further substrate 14 in the form of a middle layer which is in turn arranged on a bottom layer 17 as they have been described with reference to FIG. 7 above.
[0113] The diffractive optical elements 1 depicted in the figures were produced by using poly(methyl methacrylate-co-methacrylic acid) (PMMA/MA, 33% methacrylic acid, AR-P 617.03, Allresist) as the thermally sensitive polymer into which grayscale relief structures 2 were generated, i.e. patterned, using thermal scanning-probe lithography. As further substrates 2-inch silicon wafers were taken directly from factory packaging without any cleaning or additional preparation steps. An approximately 150 nm-thick film of PMMA/MA was spin-coated onto the silicon substrate using a two-step spin-coating process (Step 1: 5 seconds spin time, 500 rpm spin speed, 500 rpm/s acceleration. Step 2: 40 seconds spin time, 2000 rpm spin speed, 2000 rpm/s acceleration). After spin-coating, the substrate with a PMMA/MA layer was baked on a hot plate at 180° C. for 5 minutes.
[0114] The model relief structure, here grayscale model relief structures, were designed in MATLAB. Analytical sinusoidal functions were used to define the model relief structure. The model relief structure was then discretized into square pixels with 10 nm side length in the first and second directions x, y. The depth of the relief structure 2 along the third direction z was discretized to 256 depth levels, generating an 8-bit grayscale bitmap.
[0115] The grayscale relief structures 2 were fabricated in the PMMA/MA layer using a commercial thermal scanning-probe lithography tool 5 (NanoFrazor Explore, SwissLitho AG). The bitmap relief structure, i.e. the discretized controller data, was uploaded to the tool, where the 8-bit depth information was assigned to a physical patterning depth in the PMMA/MA layer. A silicon-based thermal scanning-probe cantilever 6 (provided by SwissLitho AG) was loaded into the tool 5. The tool 5 was calibrated in the first, second and third directions x, y, and z by writing simple patterns in the PMMA/MA layer, measuring the topography of these patterns in-situ, and adjusting the tip 7 temperature and writing force to minimize the error between the pattern design and the measured pattern depth. After calibration, the tool carried out the desired patterning functions.
[0116] After patterning, the PMMA/MA layer acted as a template for transferring the grayscale surface pattern or relief structure 2 to silver surfaces. The patterned polymer template was loaded into a thermal evaporator (Kurt J. Lesker Nano36) where it was pumped down to a vacuum level of approximately 1×10−7 Torr. Evaporation was performed with silver pellets (99.99%, Kurt J. Lesker) in a tungsten boat at a deposition rate of 25 Å/s to cover the template with high-quality optically thick silver films (>500 nm). After evaporation, UV-curable epoxy was deposited on the silver film, and a glass microscope slide was placed on top. The epoxy was cured for 2 hours under a UV lamp, after which the silver film was removed from the template such that the grayscale surface pattern 2 was formed on the smooth side of the silver film that was in contact with the template.
[0117] Optical measurements were performed using an inverted optical microscope (Nikon, Ti-U) with an air objective. The sample was illuminated with a broadband halogen lamp, and the reflected light was collected and imaged onto a complimentary-metal-oxide-semiconductor (CMOS) camera attached to a grating spectrometer. The illumination and reflected light were separated using a beamsplitter. A linear polarizer was placed in the collection path to filter out TE-polarized light.
TABLE-US-00001 LIST OF REFERENCE SIGNS 1,1a, 1b,1c diffractive optical element 2 relief structure 3 substrate 4 surface of substrate 5 processing device 6 probe 7 tip 8 surface of relief structure 9 recess 10 elevation 11 controller 12 computing device 13 bitmap 14 further substrate 15 surface of further substrate 16 film 17 further substrate 18 model relief structure 19 carrier 20 virtual image display device 21 image display element 22 optical system x first direction y second direction z third direction x-yhorizontal plane D distance R radius hd horizontal distance vd depth EM.sub.in incident electromagnetic radiation EM.sub.out outgoing electromagnetic radiation
