Red omnidirectional structural color made from metal and dielectric layers

Abstract

A multilayer stack displaying a red omnidirectional structural color. The multilayer stack includes a reflector layer, a dielectric layer extending across the reflector layer, and an absorbing layer extending across the dielectric layer. The dielectric layer reflects more than 70% of incident white light that has a wavelength greater than 580 nanometers (nm). In addition, the absorbing layer absorbs more than 70% of the incident white light with a wavelength less than 580 nm. In combination, the reflector layer, dielectric layer, and absorbing layer form an omnidirectional reflector that reflects a narrow band of electromagnetic radiation with a center wavelength between 580-680 nm, has a width of less than 200 nm wide and a color shift of less than 100 nm when the reflector is viewed from angles between 0 and 45 degrees.

Claims

1. A multilayer stack displaying a red omnidirectional structural color comprising: a reflector layer; a dielectric layer extending across said reflector layer, said reflector layer and said dielectric layer reflecting more than 70% of incident white light with wavelengths greater than 550 nm; and a selective absorber layer extending across said dielectric layer, said selective absorber layer absorbing more than 70% of said incident white light with wavelengths less than 550 nm when the multilayer stack is viewed from angles between 0 and 45 degrees; said reflector layer, dielectric layer and selective absorber layer forming an omnidirectional reflector, said omnidirectional reflector reflecting a single narrow band of visible electromagnetic radiation with a center wavelength between 550-700 nm, a width of less than 200 nm wide and a color shift of less than 60 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees, the omnidirectional reflector displaying a red omnidirectional structural color.

2. The multilayer stack of claim 1, wherein said reflector layer has a thickness between 50-200 nm.

3. The multilayer stack of claim 2, wherein said dielectric layer has a thickness between 30-300 nm.

4. The multilayer stack of claim 3, wherein said selective absorber layer has a thickness between 20-80 nm.

5. The multilayer stack of claim 4, wherein said omnidirectional reflector has a total thickness less than 2 microns.

6. The multilayer stack of claim 4, wherein said total thickness is less than 1 micron.

7. The multilayer stack of claim 2, wherein said reflector layer contains a metal selected from the group consisting of Al, Ag, Pt, Cr, Cu, Zn, Au, Sn and alloys thereof.

8. The multilayer stack of claim 1, wherein said center wavelength has a hue shift of less than 30 degrees.

9. The multilayer stack of claim 1, wherein said dielectric layer has an optical thickness greater than 0.1 QW and less than 3.0 QW.

10. The multilayer stack of claim 9, wherein said optical thickness is less than 2.0 QW.

11. The multilayer stack of claim 1, wherein said dielectric layer has a refractive index greater than 1.6 and contains a dielectric material selected from the group consisting of ZnS, TiO2, HfO2, Nb2O5, Ta2O5 and combinations thereof.

12. The multilayer stack of claim 1, wherein said dielectric layer contains a colorful dielectric material selected from the group consisting of Fe2O3, Cu2O and combinations thereof.

13. The multilayer stack of claim 1, wherein said selective absorber layer contains a colorful metal selected from the group consisting of Cu, Au, Zn, Sn and alloys thereof.

14. The multilayer stack of claim 1, wherein said colorful absorber layer contains a colorful dielectric material selected from the group consisting of Fe2O3, Cu2O and combinations thereof.

15. The multilayer stack of claim 1, further comprising a second dielectric layer in addition to said previous mentioned dielectric layer, said second dielectric layer extending across said selective absorber layer and oppositely disposed said dielectric layer about said selective absorber layer; said reflector layer, dielectric layer, selective absorber layer and second dielectric layer forming said omnidirectional reflector.

16. The multilayer stack of claim 15, wherein said second dielectric layer has a thickness between 30-300 nm.

17. The multilayer stack of claim 16, further comprising a second selective absorber layer in addition to said previously mentioned selective absorber layer, said second selective absorber layer extending across said second dielectric layer and oppositely disposed said selective absorber layer about said second dielectric layer; said reflector layer, dielectric layer, selective absorber layer, second dielectric layer and second selective absorber layer forming said omnidirectional reflector.

18. The multilayer stack of claim 17, wherein said second selective absorber layer has a thickness between 10-80 nm.

19. The multilayer stack of claim 18, further comprising a third dielectric layer extending across said second absorber layer and oppositely disposed said second dielectric layer about said second selective absorber layer; said reflector layer, dielectric layer, selective absorber layer, second dielectric layer, second selective absorber layer and third dielectric layer forming said omnidirectional reflector.

20. The multilayer stack of claim 19, wherein said third dielectric layer has a thickness between 10-300 nm.

21. The multilayer stack of claim 1, further comprising a second selective absorber layer in addition to said previously mentioned selective absorber layer, said second selective absorber layer extending between said reflector layer and said dielectric layer; said reflector layer, dielectric layer, selective absorber layer and second selective absorber layer forming said omnidirectional reflector.

22. The multilayer stack of claim 21, further comprising a second dielectric layer in addition to said previously mentioned dielectric layer, said second dielectric layer extending across said selective absorber layer and oppositely disposed said dielectric layer about said selective absorber layer; said reflector layer, dielectric layer, selective absorber layer, second selective absorber layer and second dielectric layer forming said omnidirectional reflector.

23. The multilayer stack of claim 22, wherein said omnidirectional reflector has a total thickness less than 2 microns.

24. The multilayer stack of claim 23, wherein said total thickness is less than 1 micron.

25. The multilayer stack of claim 1, wherein said narrow band of visible electromagnetic radiation is a reflection band with a UV-sided edge, said UV-sided edge shifting less than 75 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees.

26. The multilayer stack of claim 25, wherein said UV-sided edge of said reflection band shifts less than 50 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees.

27. The multilayer stack of claim 26, wherein said UV-sided edge of said reflection band shifts less than 25 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees.

28. A paint pigment in the form of a multilayer stack, said paint pigment comprising: a reflector layer; a dielectric layer extending across said reflector layer, said reflector layer and said dielectric layer reflecting more than 70% of incident white light with wavelengths greater than 550 nm; and a selective absorber layer extending across said dielectric layer, said selective absorber layer absorbing more than 70% of said incident white light with wavelengths less than 550 nm when the multilayer stack is viewed from angles between 0 and 45 degrees; said reflector layer, dielectric layer and selective absorber layer forming an omnidirectional reflector, said omnidirectional reflector reflecting a single narrow band of visible electromagnetic radiation with a center wavelength between 550-700 nm, a width of less than 100 nm wide and a color shift of less than 60 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees, the omnidirectional reflector displaying a red omnidirectional structural color.

29. A paint pigment in the form of a multilayer stack, said paint pigment comprising: a reflector layer; a dielectric layer extending across said reflector layer, said reflector layer and said dielectric layer reflecting more than 70% of incident white light with wavelengths greater than 550 nm; and a selective absorber layer extending across said dielectric layer, said selective absorber layer absorbing more than 70% of said incident white light with wavelengths less than 550 nm when the multilayer stack is viewed from angles between 0 and 45 degrees; said reflector layer, dielectric layer and selective absorber layer forming an omnidirectional reflector, said omnidirectional reflector reflecting a single narrow band of visible electromagnetic radiation with a UV-sided edge and an IR edge of the IR spectrum, said single narrow band of visible electromagnetic radiation having a width of less than 200 nm wide and a shift of said UV-sided edge of less than 75 nm when said omnidirectional reflector is viewed from angles between 0 and 45 degrees, the omnidirectional reflector displaying a red omnidirectional structural color.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a schematic illustration of a zero or near-zero electric field point within a ZnS dielectric layer exposed to electromagnetic radiation (EMR) having a wavelength of 500 nm;

(2) FIG. 1B is a graphical illustration of the absolute value of electric field squared (|E|.sup.2) versus thickness of the ZnS dielectric layer shown in FIG. 1A when exposed to EMR having wavelengths of 300, 400, 500, 600 and 700 nm;

(3) FIG. 2 is a schematic illustration of a dielectric layer extending over a substrate or reflector layer and exposed to electromagnetic radiation at an angle θ relative to a normal direction to the outer surface of the dielectric layer;

(4) FIG. 3 is a schematic illustration of a ZnS dielectric layer with a Cr absorber layer located at the zero or near-zero electric field point within the ZnS dielectric layer for incident EMR having a wavelength of 434 nm;

(5) FIG. 4 is a graphical representation of percent reflectance versus reflected EMR wavelength for a multilayer stack without a Cr absorber layer (e.g., FIG. 1A) and a multilayer stack with a Cr absorber layer (e.g., FIG. 3A) exposed to white light;

(6) FIG. 5A is a graphical illustration of first harmonics and second harmonics exhibited by a ZnS dielectric layer extending over an Al reflector layer (e.g., FIG. 1A);

(7) FIG. 5B is a graphical illustration of percent reflectance versus reflected EMR wavelength for a multilayer stack with a ZnS dielectric layer extending across an Al reflector layer, plus a Cr absorber layer located within the ZnS dielectric layer such that the second harmonics shown in FIG. 5A are absorbed;

(8) FIG. 5C is a graphical illustration of percent reflectance versus reflected EMR wavelength for a multilayer stack with a ZnS dielectric layer extending across an Al reflector layer, plus a Cr absorber layer located within the ZnS dielectric layer such that the first harmonics shown in FIG. 5A are absorbed;

(9) FIG. 6A is a graphical illustration of electric field squared versus dielectric layer thickness showing the electric field angular dependence of a Cr absorber layer for exposure to incident light at 0 and 45 degrees;

(10) FIG. 6B is a graphical illustration of percent absorbance by a Cr absorber layer versus reflected EMR wavelength when exposed to white light at 0 and 45° angles relative to normal of the outer surface (0° being normal to surface);

(11) FIG. 7A is a schematic illustration of a red omnidirectional structural color multilayer stack according to an embodiment of the present invention;

(12) FIG. 7B is a graphical illustration of percent absorbance of the Cu absorber layer shown in FIG. 7A versus reflected EMR wavelength for white light exposure to the multilayer stack shown in FIG. 7A at incident angles of 0 and 45°;

(13) FIG. 8 is a graphical comparison between calculation/simulation data and experimental data for percent reflectance versus reflected EMR wavelength for a proof of concept red omnidirectional structural color multilayer stack exposed to white light at an incident angle of 0°;

(14) FIG. 9 is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention;

(15) FIG. 10 is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention;

(16) FIG. 11 is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention; and

(17) FIG. 12 is a schematic illustration of an omnidirectional structural color multilayer stack according to an embodiment of the present invention.

(18) FIG. 13 is a scanning electron microscopy (SEM) image of flakes or pigments having a multilayer stack structure according to an embodiment of the present invention;

(19) FIG. 14 is an SEM image of a cross section of an individual flake shown in FIG. 13;

(20) FIG. 15A is a schematic illustration of a panel painted using pigments designed and manufactured according to an embodiment of the present invention and having an orange color with a hue of 36° on the color map shown in FIG. 15D;

(21) FIG. 15B is a schematic illustration of a panel painted using pigments designed and manufactured according to an embodiment of the present invention and having a dark red color with a hue of 26° on the color map shown in FIG. 15D;

(22) FIG. 15C is a schematic illustration of a panel painted using pigments designed and manufactured according to an embodiment of the present invention and having a bright pink color with a hue of 354° on the color map shown in FIG. 15D;

(23) FIG. 15 D is an a*b* color map using the CIELAB color space;

(24) FIG. 15E is a schematic illustration of an eleven-layer design used for the pigments in the paint represented in FIGS. 15A-15C;

(25) FIG. 16A is a schematic illustration of a seven-layer stack according to an embodiment of the present invention;

(26) FIG. 16B is a schematic illustration of a seven-layer stack according to an embodiment of the present invention;

(27) FIG. 16C is a schematic illustration of a seven-layer stack according to an embodiment of the present invention;

(28) FIG. 16D is a schematic illustration of a seven-layer stack according to an embodiment of the present invention;

(29) FIG. 17 is a graphical representation of a portion of an a*b* color map using the CIELAB color space in which the chroma and hue shift are compared between a conventional paint and the paint used to paint the panel illustrated in FIG. 15B;

(30) FIG. 18 is a graphical illustration of reflectance versus wave length for a seven-layer design according to an embodiment of the present invention; and

(31) FIG. 19 is a graphical illustration of reflectance versus wave length for a seven-layer design according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

(32) A multilayer stack affording an omnidirectional structural color, e.g. a red omnidirectional color, is provided. As such, the multilayer stack has use as a paint pigment, a thin film that provides a desired color, and the like.

(33) The multilayer stack affording the omnidirectional structural color includes a reflector layer and a dielectric layer extending across the reflector layer. The reflector layer and the dielectric layer reflect more than 70% of incident white light that has a wavelength greater than 550 nm. It is appreciated that the thickness of the dielectric layer can be predefined such that the wavelength at which greater than 70% of incident white light that is reflected is greater than 550 nm, 560 nm, 580 nm, 600 nm, 620 nm, 640 nm, 660 nm, 680 nm or wavelengths therebetween. Stated differently, the thickness of the dielectric layer can be chosen and produced such that a particular color having a desired hue, chroma and/or lightness on a Lab color system map is reflected and observed by the human eye.

(34) In some instances, the multilayer stack has a hue between 315° and 45° in lab color space. Also, the multilayer stack has a chroma greater than 50 and a hue shift of less than 30°. In other instances the chroma is greater than 55, preferably greater than 60, and more preferably greater than 65, and/or the hue shift is less than 25°, preferably less than 20°, more preferably less than 15° and still more preferably less than 10°.

(35) Extending across the dielectric layer is an absorbing layer that absorbs more than 70% of the incident white light for all wavelengths generally less than the wavelengths corresponding to the desired reflected wavelength of the dielectric layer. For example, if the dielectric layer has a thickness such that greater than 70% of incident white light having a wavelength of greater than 600 nm is reflected, the absorbing layer extending across the dielectric layer absorbs more than 70% of incident white light having a wavelength of generally less than 600 nm. In this manner, a sharp reflected peak having a wavelength in the red color space is provided. In some instances, the reflector layer and the dielectric layer reflect more than 80% of incident white light that has a wavelength greater than 550 nm, and in other instances more than 90%. Also, in some instances the absorber layer absorbs more than 80% of wavelengths generally less than the wavelengths corresponding to the desired reflected wavelength of the dielectric layer, and in other instances more than 90%.

(36) It is appreciated that the term “generally” in this context, refers to plus and/or minus 20 nm in some instances, plus and/or minus 30 nm in other instances, plus and/or minus 40 nm in still other instances and plus and/or minus 50 nm in still yet other instances.

(37) The reflector layer, the dielectric layer, and the absorbing layer form an omnidirectional reflector that reflects a narrow band of electromagnetic radiation (hereafter referred to as reflection peak or reflection band) with a center wavelength between 550 nm and the visible-IR edge of the EMR spectrum, a reflection band that has a width of less than 200 nm, and a color shift of less than 100 nm when the omnidirectional reflector is exposed to white light and viewed from angles between 0 and 45 degrees. The color shift can be in the form of a shift of a center wavelength of the reflection band, or in the alternative, a shift of a UV-sided edge of the reflection band. For purposes of the present invention, the width of the reflected band of electromagnetic radiation is defined as the width of the reflection band at half the reflected height of the maximum reflected wavelength within the visible spectrum. In addition, the narrow band of reflected electromagnetic radiation, i.e. the “color” of the omnidirectional reflector, has a hue shift of less than 25 degrees. In some instances, the reflector layer has a thickness between 50-200 nm and is made or contains a metal such as aluminum, silver, platinum, tin, alloys thereof, and the like.

(38) Regarding the dielectric layer that extends across the reflector layer, the dielectric layer has an optical thickness between 0.1 and 2.0 QW. In some instances, the dielectric layer has an optical thickness between 0.1 and 1.9 QW, while in other instances, the dielectric layer has a thickness between 0.1 and 1.8 QW. In still yet other instances, the dielectric layer has an optical thickness less than 1.9 QW, for example less than 1.8 QW, less than 1.7 QW, less than 1.6 QW, less than 1.5 QW, less than 1.4 QW, less than 1.3 QW, less than 1.2 QW or less than 1.1 QW. In the alternative, the dielectric layer has an optical thickness can of greater than 2.0 QW.

(39) The dielectric layer has a refractive index greater than 1.60, 1.62, 1.65 or 1.70, and can be made from a dielectric material such as ZnS, TiO.sub.2, HfO.sub.2, Nb.sub.2O.sub.5, Ta.sub.2O.sub.5, combinations thereof, and the like. In some instances, the dielectric layer is a colorful or selective dielectric layer made from a colorful dielectric material such as Fe.sub.2O.sub.3, Cu.sub.2O, and the like. For the purposes of the present invention, the term “colorful dielectric material” or “colorful dielectric layer” refers to a dielectric material or dielectric layer that transmits only a portion of incident white light while reflecting another portion of white light. For example, the colorful dielectric layer can transmit electromagnetic radiation having wavelengths between 400 and 600 nm and reflect wavelengths greater than 600 nm. As such, the colorful dielectric material or colorful dielectric layer has a visual appearance of orange, red and/or reddish-orange.

(40) In addition to a dielectric layer, the omnidirectional reflector can include a selective absorber layer that has a thickness between 5-200 nm. In some instances, the colorful absorber layer takes the place or substitutes for the absorber layer described above. Similar to the description above, a selective absorber layer can absorb light with wavelengths associated with violet, blue, yellow, green, etc., and yet reflect wavelengths corresponding to orange, red, reddish-orange, etc. In some instances, the colorful absorber layer contains or is made from a colorful metal such as copper, gold, alloys thereof such as bronze, brass, etc., and the like. In still other instances, the colorful absorber layer can contain or be made from a colorful dielectric material such as Fe.sub.2O.sub.3, Cu.sub.2O, etc.

(41) The location of the absorber layer is such that a zero or near-zero energy interface is present between the absorber layer and the dielectric layer. Stated differently, the dielectric layer has a thickness such that a zero or near-zero energy field is located at the dielectric layer-absorber layer interface. It is appreciated that the thickness of the dielectric layer at which the zero or near-zero energy field is present is a function of the incident EMR wavelength. In addition, it is also appreciated that the wavelength corresponding to the zero or near-zero electric field will be transmitted through the dielectric layer-absorber layer interface whereas wavelengths not corresponding to the zero or near-zero electric field at the interface will not pass therethrough. As such, the thickness of the dielectric layer is designed and manufactured such that a desired wavelength of incident white light is transmitted through the dielectric layer-absorber layer interface, reflected off of the reflector layer, and then transmitted back through the dielectric layer-absorbing layer interface. Likewise, the thickness of the dielectric layer is manufactured such that undesired wavelengths of incident white light are not transmitted through the dielectric layer-absorber layer interface.

(42) Given the above, wavelengths not corresponding to the desired zero or near-zero electric field interface are absorbed by the absorber layer and thus not reflected. In this manner, a desired “sharp” color, also known as a structural color, is provided. In addition, the thickness of the dielectric layer is such that reflection of desired first harmonics and/or second harmonics is produced in order to provide a surface with a red color that also has an omnidirectional appearance.

(43) The multilayer stack can include a second dielectric layer in addition to the previously mentioned dielectric layer (also known as the first dielectric layer), the second dielectric layer extending across the absorber layer. In addition, the second dielectric layer is oppositely disposed from the first mentioned dielectric layer about the absorber layer.

(44) Regarding the thickness of the dielectric layer and the zero or near-zero electric field point mentioned above, FIG. 1A is a schematic illustration of a ZnS dielectric layer extending across an Al reflector layer. The ZnS dielectric layer has a total thickness of 143 nm, and for incident electromagnetic radiation with a wavelength of 500 nm, a zero or near zero energy point is present at 77 nm. Stated differently, the ZnS dielectric layer exhibits a zero or near-zero electric field at a distance of 77 nm from the Al reflector layer for incident EMR having a wavelength of 500 nm. In addition, FIG. 1B provides a graphical illustration of the energy field across the ZnS dielectric layer for a number of different incident EMR wavelengths. As shown in the graph, the dielectric layer has a zero electric field for the 500 nm wavelength at 77 nm thickness, but a non-zero electric field at the 77 nm thickness for EMR wavelengths of 300, 400, 600 and 700 nm.

(45) Not being bound by theory, calculation of the zero or near zero energy point thickness for a dielectric layer such as the one illustrated in FIG. 1A is discussed below.

(46) Referring to FIG. 2, a dielectric layer 4 having a total thickness ‘D’, an incremental thickness ‘d’ and an index of refraction ‘n’ on a substrate or core layer 2 having a index of refraction n.sub.s is shown. Incident light strikes the outer surface 5 of the dielectric layer 4 at angle θ relative to line 6, which is perpendicular to the outer surface 5, and reflects from the outer surface 5 at the same angle. Incident light is transmitted through the outer surface 5 and into the dielectric layer 4 at an angle θ.sub.F relative to the line 6 and strikes the surface 3 of substrate layer 2 at an angle θ.sub.s.

(47) For a single dielectric layer, θ.sub.s=θ.sub.F and the energy/electric field (E) can be expressed as E(z) when z=d. From Maxwell's equations, the electric field can be expressed for s polarization as:
{right arrow over (E)}(d)={u(z),0,0}exp(ikαy)|.sub.z=d  (1)
and for p polarization as:

(48) $\begin{array}{cc}\stackrel{.Math.}{E}\left(d\right)=\left\{0,u\left(z\right),-\frac{\alpha }{\widetilde{\mathrm{.Math.}}\left(z\right)}v\left(z\right)\right\}\exp \left(ik\alpha y\right){.Math.}_{z=d}& \left(2\right)\end{array}$
where

(49) $k=\frac{2\pi }{\lambda }$
and γ is a desired wavelength to be reflected. Also, α=n.sub.s sin θ.sub.s where ‘s’ corresponds to the substrate in FIG. 1 and {tilde over (∈)} (z) is the permittivity of the layer as a function of z. As such,
|E(d)|.sup.2=|u(z)|.sup.2exp(2ikαy)|.sub.z=d  (3)
for s polarization and

(50) $\begin{array}{cc}{.Math.E\left(d\right).Math.}^2=\left[{.Math.u\left(z\right).Math.}^2+{.Math.\frac{\alpha }{\sqrt{n}}v\left(z\right).Math.}^2\right]\exp \left(2ik\alpha y\right){.Math.}_{z=d}& \left(4\right)\end{array}$
for p polarization.

(51) It is appreciated that variation of the electric field along the Z direction of the dielectric layer 4 can be estimated by calculation of the unknown parameters u(z) and v(z) where it can be shown that:

(52) $\begin{array}{cc}{\left(\begin{array}{c}u\\ v\end{array}\right)}_{z=d}=\left(\begin{array}{cc}\cos \phi & \left(i/q\right)\sin \phi \\ iq\sin \phi & \cos \phi \end{array}\right){\left(\begin{array}{c}u\\ v\end{array}\right)}_{z=0,\mathrm{substrate}}& \left(5\right)\end{array}$
Naturally, ‘i’ is the square root of −1. Using the boundary conditions u|.sub.z=0=1, v|.sub.z=0=q.sub.s, and the following relations:
q.sub.s=n.sub.s cos θ.sub.s for s-polarization  (6)
q.sub.s=n.sub.s/cos θ.sub.s for p-polarization  (7)
q=n cos θ.sub.F for s-polarization  (8)
q=n/cos θ.sub.F for p-polarization  (9)
φ=k.Math.n.Math.d cos(θ.sub.F)  (10)
u(z) and v(z) can be expressed as:

(53) $\begin{array}{cc}\begin{array}{c}u\left(z\right){.Math.}_{z=d}=u{.Math.}_{z=0}\cos \phi +v{.Math.}_{z=o}\left(\frac{i}{q}\sin \phi \right)\\ =\cos \phi +\frac{i.Math.q_s}{q}\sin \phi \mathrm{and}\end{array}& \left(11\right)\\ \begin{array}{c}v\left(z\right){.Math.}_{z=d}=iqu{.Math.}_{z=0}\sin \phi +v{.Math.}_{z=0}\cos \phi \\ =iq\sin \phi +q_s\cos \phi \end{array}& \left(12\right)\end{array}$
Therefore:

(54) $\begin{array}{cc}\begin{array}{c}{.Math.E\left(d\right).Math.}^2=\left[{\cos }^2\phi +\frac{q_s^2}{q^2}{\sin }^2\phi \right]e^{2ik\alpha \gamma }\\ =\left[{\cos }^2\phi +\frac{n_s^2}{n^2}{\sin }^2\phi \right]e^{2ik\alpha \gamma }\end{array}& \left(13\right)\end{array}$
for s polarization with φ=k.Math.n.Math.d cos(θ.sub.F), and:

(55) $\begin{array}{cc}\begin{array}{c}{.Math.E\left(d\right).Math.}^2=\left[{\cos }^2\phi +\frac{n_s^2}{n^2}{\sin }^2\phi +\frac{{\alpha }^2}{n}\left(q_s^2{\cos }^2\phi +q^2{\sin }^2\phi \right)\right]\\ =\left[\left(1+\frac{{\alpha }^2{q}_s^2}{n}\right){\cos }^2\phi +\left(\frac{n_s^2}{n^2}+\frac{{\alpha }^2{q}^2}{n}\right){\sin }^2\phi \right]\end{array}& \left(14\right)\end{array}$
for p polarization where:

(56) $\begin{array}{cc}\alpha =n_s\sin {\theta }_s=n\sin {\theta }_F& \left(15\right)\\ q_s=\frac{n_s}{\cos {\theta }_s}\mathrm{and}& \left(16\right)\\ q_s=\frac{n}{\cos {\theta }_F}& \left(17\right)\end{array}$
Thus for a simple situation where θ.sub.F=0 or normal incidence, φ=k.Math.n.Math.d, and α=0:

(57) $\begin{array}{cc}\begin{array}{c}{.Math.E\left(d\right).Math.}^2\mathrm{for}s\text{-}\mathrm{polarization}={.Math.E\left(d\right).Math.}^2\mathrm{for}p\text{-}\mathrm{polarization}\\ =\left[{\cos }^2\phi +\frac{n_s^2}{n^2}{\sin }^2\phi \right]\\ =\left[{\cos }^2\left(k.Math.n.Math.d\right)+\frac{n_s^2}{n^2}{\sin }^2\left(k.Math.n.Math.d\right)\right]\left(19\right)\end{array}& \left(18\right)\end{array}$
which allows for the thickness ‘d’ to be solved for, i.e. the position or location within the dielectric layer where the electric field is zero.

(58) Referring now to FIG. 3, Equation 19 was used to calculate that the zero or near-zero electric field point in the ZnS dielectric layer shown in FIG. 1A when exposed to EMR having a wavelength of 434 nm is at 70 nm (instead of 77 nm for a 500 nm wavelength). In addition, a 15 nm thick Cr absorber layer was inserted at a thickness of 70 nm from the Al reflector layer to afford for a zero or near-zero electric field ZnS—Cr interface. Such an inventive structure allows light having a wavelength of 434 nm to pass through the Cr—ZnS interfaces, but absorbs light not having a wavelength of 434 nm. Stated differently, the Cr—ZnS interfaces have a zero or near-zero electric field with respect to light having a wavelength of 434 nm and thus 434 nm light passes through the interfaces. However, the Cr—ZnS interfaces do not have a zero or near-zero electric field for light not having a wavelength of 434 nm and thus such light is absorbed by the Cr absorber layer and/or Cr—ZnS interfaces and not reflected by the Al reflector layer.

(59) It is appreciated that some percentage of light within +/−10 nm of the desired 434 nm will pass through the Cr—ZnS interface. However, it is also appreciated that such a narrow band of reflected light, e.g. 434+/−10 nm, still provides a sharp structural color to a human eye.

(60) The result of the Cr absorber layer in the multilayer stack in FIG. 3 is illustrated in FIG. 4 where percent reflectance versus reflected EMR wavelength is shown. As shown by the dotted line, which corresponds to the ZnS dielectric layer shown in FIG. 3 without a Cr absorber layer, a narrow reflected peak is present at about 400 nm, but a much broader peak is present at about 550+ nm. In addition, there is still a significant amount of light reflected in the 500 nm wavelength region. As such, a double peak that prevents the multilayer stack from having or exhibiting a structural color is present.

(61) In contrast, the solid line in FIG. 4 corresponds to the structure shown in FIG. 3 with the Cr absorber layer present. As shown in the figure, a sharp peak at approximately 434 nm is present and a sharp drop off in reflectance for wavelengths greater than 434 nm is afforded by the Cr absorber layer. It is appreciated that the sharp peak represented by the solid line visually appears as sharp/structural color. Also, FIG. 4 illustrates where the width of a reflected peak or band is measured, i.e. the width of the band is determined at 50% reflectance of the maximum reflected wavelength, also known as full width at half maximum (FWHM).

(62) Regarding omnidirectional behavior of the multilayer structure shown in FIG. 3, the thickness of the ZnS dielectric layer can be designed or set such that only the first harmonics of reflected light is provided. It is appreciated that this is sufficient for a “blue” color, however the production of a “red” color requires additional considerations. For example, the control of angular independence for red color is difficult since thicker dielectric layers are required, which in turn results in a high harmonic design, i.e. the presence of the second and possible third harmonics is inevitable. Also, the dark red color hue space is very narrow. As such, a red color multilayer stack has a higher angular variance.

(63) In order to overcome the higher angular variance for red color, the instant application discloses a unique and novel design/structure that affords for a red color that is angular independent. For example, FIG. 5A illustrates a dielectric layer exhibiting first and second harmonics for incident white light when an outer surface of the dielectric layer is viewed from 0 and 45 degrees. As shown by the graphical representation, low angular dependence (small Δλ.sub.c) is provided by the thickness of the dielectric layer, however, such a multilayer stack has a combination of blue color (1.sup.st harmonic) and red color (2.sup.nd harmonic) and thus is not suitable for a desired “red only” color. Therefore, the concept/structure of using an absorber layer to absorb an unwanted harmonic series has been developed. FIG. 5A also illustrates an example of the location of the reflected band center wavelength (λ.sub.c) for a given reflection peak and the dispersion or shift of the center wavelength (Δλ.sub.c) when the sample is viewed from 0 and 45 degrees.

(64) Turning now to FIG. 5B, the second harmonic shown in FIG. 5A is absorbed with a Cr absorber layer at the appropriate dielectric layer thickness (e.g. 72 nm) and a sharp blue color is provided. More importantly for the instant invention, FIG. 5C illustrates that by absorbing the first harmonics with the Cr absorber at a different dielectric layer thickness (e.g. 125 nm) a red color is provided. However, FIG. 5C also illustrates that the use of the Cr absorber layer still results in more than desired angular dependence by the multilayer stack, i.e. a larger than desired Δλ.sub.c.

(65) It is appreciated that the relatively large shift in λ.sub.c for the red color compared to the blue color is due to the dark red color hue space being very narrow and the fact that the Cr absorber layer absorbs wavelengths associated with a non-zero electric field, i.e. does not absorb light when the electric field is zero or near-zero. As such, FIG. 6A illustrates that the zero or non-zero point is different for light wavelengths at different incident angles. Such factors result in the angular dependent absorbance shown in FIG. 6B, i.e. the difference in the 0° and 45° absorbance curves. Thus in order to further refine the multilayer stack design and angular independence performance, an absorber layer that absorbs, e.g. blue light, irrespective of whether or not the electric field is zero or not, is used.

(66) In particular, FIG. 7A shows a multilayer stack with a Cu absorber layer instead of a Cr absorber layer extending across a dielectric ZnS layer. The results of using such a “colorful” or “selective” absorber layer is shown in FIG. 7B which demonstrates a much “tighter” grouping of the 0° and 45° absorbance lines for the multilayer stack shown in FIG. 7A. As such, a comparison between FIG. 6B and FIG. 7B illustrates the significant improvement in absorbance angular independence when using a selective absorber layer rather than non-selective absorber layer.

(67) Based on the above, a proof of concept multilayer stack structure was designed and manufactured. In addition, calculation/simulation results and actual experimental data for the proof of concept sample were compared. In particular, and as shown by the graphical plot in FIG. 8, a sharp red color was produced (wavelengths greater than 700 nm are not typically seen by the human eye) and very good agreement was obtained between the calculation/simulation and experimental light data obtained from the actual sample. Stated differently, calculations/simulations can and/or are used to simulate the results of multilayer stack designs according to one or more embodiments of the present invention and/or prior art multilayer stacks.

(68) A list of simulated and/or actually produced multilayer stack samples is provided in the Table 1 below. As shown in the table, the inventive designs disclosed herein include at least 5 different layered structures. In addition, the samples were simulated and/or made from a wide range of materials. Samples that exhibited high chroma, low hue shift and excellent reflectance were provided. Also, the three and five layer samples had an overall thickness between 120-200 nm; the seven layer samples had an overall thickness between 350-600 nm; the nine layer samples had an overall thickness between 440-500 nm; and the eleven layer samples had an overall thickness between 600-660 nm.

(69) TABLE-US-00001 TABLE 1 Ave. Chroma Max. (0-45) Δh (0-65) Reflectance Sample Name  3 layer 90 2 96 3-1  5 layer 91 3 96 5-1  7 layer 88 1 92 7-1 91 3 92 7-2 91 3 96 7-3 90 1 94 7-4 82 4 75 7-5 76 20 84 7-6 9 layer 71 21 88 9-1 95 0 94 9-2 79 14 86 9-3 90 4 87 9-4 94 1 94 9-5 94 1 94 9-6 73 7 87 9-7 11 layer 88 1 84 11-1  92 1 93 11-2  90 3 92 11-3  89 9 90 11-4 

(70) Regarding the actual sequence of layers, FIG. 9 illustrates half of a five-layer design at reference numeral 10. The omnidirectional reflector 10 has a reflector layer 100, a dielectric layer 110 extending across the reflector layer 100 and an absorber layer 120 extending across the dielectric layer 110. It is appreciated that another dielectric layer and another absorber layer can be oppositely disposed the reflector layer 100 to provide the five-layer design.

(71) Reference numeral 20 in FIG. 10 illustrates half of a seven-layer design in which another dielectric layer 130 extends across the absorber layer 120 such that the dielectric layer 130 is oppositely disposed from the dielectric layer 110 about the absorber layer 120.

(72) FIG. 11 illustrates half of a nine-layer design in which a second absorber layer 105 is located between the reflector layer 100 and the dielectric layer 110. Finally, FIG. 12 illustrates half of an eleven-layer design in which another absorber layer 140 extends over the dielectric layer 130 and yet another dielectric layer 150 extends over the absorber layer 140.

(73) A scanning electron microscopy (SEM) image of a plurality of pigments having a multilayer structure according to an embodiment of the present invention is shown in FIG. 13. FIG. 14 is an SEM image of one of the pigments at a higher magnification showing the multilayer structure. Such pigments were used to produce three different red paints that were then applied to three panels for testing. FIGS. 15A-15C are schematic illustrations of the actual painted panels since actual photographs of the panels appear gray/black when printed and copied and in back and white. FIG. 15A represents an orange color with a hue of 36°, FIG. 15B represents a dark red color with a hue of 26° and FIG. 15C represents a bright pink color with a hue of 354° on the color map shown in FIG. 15D. Also, the dark red color panel represented in FIG. 15B, had a lightness L* of 44 and a chroma C* of 67.

(74) FIG. 15E is a schematic illustration of an eleven-layer design that represents the pigments used to paint the panels illustrated in FIGS. 15A-15C. Regarding exemplary thicknesses of the various layers, Table 2 provides the actual thicknesses for each of the corresponding multilayer stack/pigments. As shown by the thickness values in Table 2, the overall thickness of the eleven-layer design is less than 2 microns and can be less than 1 micron.

(75) TABLE-US-00002 TABLE 2 Color Orange Dark Red Bright Pink Layer Layer Layer Layer Thickness (nm) Thickness (nm) Thickness (nm) ZnS 28 31 23 Cu 25 28 28 ZnS 141 159 40 Cu 32 36 72 ZnS 55 63 41 Al 80 80 80 ZnS 55 63 41 Cu 32 36 72 ZnS 141 159 40 Cu 25 28 28 ZnS 28 31 23

(76) It is appreciated that seven-layer designs and seven-layer multilayer stacks can be used to produce such pigments. Examples of a four seven-layer multilayer stacks are shown in FIGS. 16A-16D. FIG. 16A illustrates a seven-layer stack which has: (1) reflector layer 100; (2) a pair of dielectric layers 110 extending across and oppositely disposed about reflector layer 100; (3) a pair of selective absorber layers 120a extending across an outer surface of the pair of dielectric layers 110; and (4) a pair of dielectric layers 130 extending across an outer surface of the pair of selective absorber layers 120a.

(77) Naturally, the thickness of the dielectric layer 110 and selective absorber layer 120a is such that the interface between selective absorber layer 120a and dielectric layer 110 and the interface between the selective absorber selective absorber 120a and dielectric layer 130 exhibit a zero or near-zero electric field with respect to a desired light wavelength in the pink-red-orange region (315°<hue<45° and/or 550 nm<λ.sub.c<700 nm) of the color map shown in FIG. 15D. In this manner, a desired red colored light passes through layers 130-120a-110, reflects off of layer 100, and passes back through layers 110-120a-130. In contrast, non-red colored light is absorbed by the selective absorber layer 120a. Furthermore, the selective absorber layer 120a has an angle independent absorbance for non-red colored light as discussed above and shown in FIGS. 7A-7B.

(78) It is appreciated that the thickness of the dielectric layer 100 and/or 130 is such that the reflectance of red colored light by the multilayer stack is omnidirectional. The omnidirectional reflection is measured or determined by a small Δλ.sub.c of the reflected light. For example, in some instances, Δλ.sub.c is less than 120 nm. In other instances, Δλ.sub.c is less than 100 nm. In still other instances, Δλ.sub.c is less than 80 nm, preferably less than 60 nm, still more preferably less than 50 nm, and even still yet more preferably less than 40 nm.

(79) The omnidirectional reflection can also be measured by a low hue shift. For example, the hue shift of pigments manufactured from multilayer stacks according an embodiment of the present invention is 30° or less, as shown in FIG. 17 (see Δθ.sub.1), and in some instances the hue shift is 25° or less, preferably less than 20°, more preferably less than 15° and still more preferably less than 10°. In contrast, traditional pigments exhibit hue shift of 45° or more (see Δθ.sub.2).

(80) FIG. 16B illustrates a seven-layer stack which has: (1) a selective reflector layer 100a; (2) a pair of dielectric layers 110 extending across and oppositely disposed about reflector layer 100a; (3) a pair of selective absorber layers 120a extending across an outer surface of the pair of dielectric layers 110; and (4) a pair of dielectric layers 130 extending across an outer surface of the pair of selective absorber layers 120a.

(81) FIG. 16C illustrates a seven-layer stack which has: (1) a selective reflector layer 100a; (2) a pair of dielectric layers 110 extending across and oppositely disposed about reflector layer 100a; (3) a pair of non-selective absorber layers 120 extending across an outer surface of the pair of dielectric layers 110; and (4) a pair of dielectric layers 130 extending across an outer surface of the pair of absorber layers 120.

(82) FIG. 16D illustrates a seven-layer stack which has: (1) a reflector layer 100; (2) a pair of dielectric layers 110 extending across and oppositely disposed about reflector layer 100; (3) a pair of absorber layers 120 extending across an outer surface of the pair of dielectric layers 110; and (4) a pair of dielectric layers 130 extending across an outer surface of the pair of selective absorber layers 120.

(83) Turning now to FIG. 18, a plot of percent reflectance versus reflected EMR wavelength is shown for a seven-layer design omnidirectional reflector when exposed to white light at angles of 0 and 45° relative to the surface of the reflector. As shown by the plot, a single narrow band of visible electromagnetic radiation is reflected and both the 0° and 45° curves illustrate very low reflectance, e.g. less than 10%, provided by the omnidirectional reflector for wavelengths less than 550 nm. However, the reflector, as shown by the curves, provides a sharp increase in reflectance at wavelengths between 560-570 nm and reaches a maximum of approximately 90% at 700 nm. It is appreciated that the portion or region of the graph on the right hand side (IR side) of the curve represents the IR-portion of the reflection band provided by the reflector.

(84) The sharp increase in reflectance provided by the omnidirectional reflector is characterized by a UV-sided edge of each curve that extends from a low reflectance portion at wavelengths below 550 nm up to a high reflectance portion, e.g. >70%. A linear portion 200 of the UV-sided edge is inclined at an angle (β) greater than 60° relative to the x-axis, has a length L of approximately 40 on the Reflectance-axis and a slope of 1.4. In some instances, the linear portion is inclined at an angle greater than 70° relative to the x-axis, while in other instances β is greater than 75°. Also, the reflection band has a visible FWHM of less than 200 nm, and in some instances a visible FWHM of less than 150 nm, and in other instances a visible FWHM of less than 100 nm. In addition, the center wavelength λ.sub.c for the visible reflection band as illustrated in FIG. 18 is defined as the wavelength that is equal-distance between the UV-sided edge of the reflection band and the IR edge of the IR spectrum at the visible FWHM.

(85) It is appreciated that the term “visible FWHM” refers to the width of the reflection band between the UV-sided edge of the curve and the edge of the IR spectrum range, beyond which reflectance provided by the omnidirectional reflector is not visible to the human eye. In this manner, the inventive designs and multilayer stacks disclosed herein use the non-visible IR portion of the electromagnetic radiation spectrum to provide a sharp or structural color. Stated differently, the omnidirectional reflectors disclosed herein take advantage of the non-visible IR portion of the electromagnetic radiation spectrum in order to provide a narrow band of reflected visible light, despite the fact that the reflectors may reflect a much broader band of electromagnetic radiation that extends into the IR region.

(86) Referring now to FIG. 19, a plot of percent reflectance versus wavelength is shown for another seven-layer design omnidirectional reflector when exposed to white light at angles of 0 and 45° relative to the surface of the reflector. In addition, a definition or characterization of omnidirectional properties provided by omnidirectional reflectors disclosed herein is shown. In particular, and when the reflection band provided by an inventive reflector has a maximum, i.e. a peak, as shown in the figure, each curve has a center wavelength (λ.sub.c) defined as the wavelength that exhibits or experiences maximum reflectance. The term maximum reflected wavelength can also be used for λ.sub.c.

(87) As shown in FIG. 19, a single narrow band of visible electromagnetic radiation is reflected and there is shift or displacement of λ.sub.c when an outer surface of the omnidirectional reflector is observed from an angle 45° (λ.sub.c(45°)), e.g. the outer surface is tiled 45° relative to a human eye looking at the surface, compared to when the surface is observed from an angle of 0° ((λ.sub.c(0°)), i.e. normal to the surface. This shift of λ.sub.c (Δλ.sub.c) provides a measure of the omnidirectional property of the omnidirectional reflector. Naturally a zero shift, i.e. no shift at all, would be a perfectly omnidirectional reflector. However, omnidirectional reflectors disclosed herein can provide a Δλ.sub.c of less than 100 nm, which to the human eye can appear as though the surface of the reflector has not changed color and thus from a practical perspective the reflector is omnidirectional. In some instances, omnidirectional reflectors disclosed herein can provide a Δλ.sub.c of less than 75 nm, in other instances a Δλ.sub.c of less than 50 nm, and in still other instances a Δλ.sub.c of less than 25 nm, while in still yet other instances a Δλ.sub.c of less than 15 nm. Such a shift in Δλ.sub.c can be determined by an actual reflectance versus wavelength plot for a reflector, and/or in the alternative, by modeling of the reflector if the materials and layer thicknesses are known.

(88) Another definition or characterization of a reflector's omnidirectional properties can be determined by the shift of a side edge for a given set of angle refection bands. For example, a shift or displacement of a UV-sided edge (ΔS.sub.L) for reflectance from an omnidirectional reflector observed from 0° (S.sub.L(0°)) compared to the UV-sided edge for reflectance by the same reflector observed from 45° (S.sub.L(45°)) provides a measure of the omnidirectional property of the omnidirectional reflector. In addition, using ΔS.sub.L as a measure of omnidirectionality can be preferred to the use of Δλ.sub.c, e.g. for reflectors that provide a reflectance band similar to the one shown in FIG. 18, i.e. a reflection band with a peak corresponding to a maximum reflected wavelength that is not in the visible range (see FIG. 18). It is appreciated that the shift of the UV-sided edge (ΔS.sub.L) is and/or can be measured at the visible FWHM.

(89) Naturally a zero shift, i.e. no shift at all (ΔS.sub.L=0 nm), would characterize a perfectly omnidirectional reflector. However, omnidirectional reflectors disclosed herein can provide a ΔS.sub.L of less than 100 nm, which to the human eye can appear as though the surface of the reflector has not changed color and thus from a practical perspective the reflector is omnidirectional. In some instances, omnidirectional reflectors disclosed herein can provide a ΔS.sub.L of less than 75 nm, in other instances a ΔS.sub.L of less than 50 nm, and in still other instances a ΔS.sub.L of less than 25 nm, while in still yet other instances a ΔS.sub.L of less than 15 nm. Such a shift in ΔS.sub.L can be determined by an actual reflectance versus wavelength plot for a reflector, and/or in the alternative, by modeling of the reflector if the materials and layer thicknesses are known.

(90) Methods for producing the multilayer stacks disclosed herein can be any method or process known to those skilled in the art or one or methods not yet known to those skilled in the art. Typical known methods include wet methods such as sol gel processing, layer-by-layer processing, spin coating and the like. Other known dry methods include chemical vapor deposition processing and physical vapor deposition processing such as sputtering, electron beam deposition and the like.

(91) The multilayer stacks disclosed herein can be used for most any color application such as pigments for paints, thin films applied to surfaces and the like.

(92) The above examples and embodiments are for illustrative purposes only and changes, modifications, and the like will be apparent to those skilled in the art and yet still fall within the scope of the invention. As such, the scope of the invention is defined by the claims and all equivalents thereof.