US20130155516A1

US20130155516A1 - Nano fractal diffuser

Info

Publication number: US20130155516A1
Application number: US13/495,296
Authority: US
Inventors: Michael Lines; Eric W. Gardner; Mark Davis
Original assignee: Individual
Current assignee: Individual
Priority date: 2009-06-25
Filing date: 2012-06-13
Publication date: 2013-06-20
Also published as: US20100328768A1; WO2010151381A2; US8248696B2; WO2010151381A3

Abstract

A diffusive device has an array of discrete facets which may be of a size and pattern similar to a fractal. The facet dimensions can be greater than half the wavelength of incident light such that the facets substantially diffract light. A polarizing wire-grid layer comprised of an array of elongated parallel conductive wires with a period less than half the wavelength of incident light may be disposed between, beneath, or above the facets. The wire-grid polarizes the light by substantially reflecting light having an s-polarization orientation and substantially transmitting a portion of light having a p-polarization orientation.

Description

CLAIM OF PRIORITY

This is a continuation of U.S. patent application Ser. No. 12/491,513, filed on Jun. 25, 2009, which is hereby incorporated herein by reference in its entirety.

RELATED APPLICATION(S)/PATENT(S)

This is related to U.S. Pat. Nos. 6,081,376; 6,348,995 and 7,630,133, which are hereby incorporated herein by reference in their entirety.

BACKGROUND

1. Field of the Invention
The present invention relates generally to optical diffusers including diffusive wire-grid polarizers.
2. Related Art
Wire-grid polarizers have been developed that are capable of polarizing light, i.e. separating one polarization orientation from another, by transmitting one polarization orientation and reflecting the other. Wire grid polarizers are a periodic structure of conductive elements with a length greater than the wavelength and a period (p) less than half the wavelength of the incident light, or p≦λ/2. Wire grid polarizers have been proven to be effective for visible light (˜300-700 nm, or ˜0.3-0.7 microns or μm) and their use demonstrated as polarizers and beam splitters in optical imaging systems. Typically, however, the reflection from, and the light passing through, such wire-grid polarizers, is specular, or mirror-like.
Wire-Grid polarizers are different from diffraction gratings, which are a periodic structure of dielectric material with a period (p) greater than half the wavelength (λ) of incident light, or p≧λ/2. The diffraction grating scatters the incident light at discrete angles or directions in accordance with mλ=psinθ, where m is the order and θ is the angle with respect to normal from the diffraction grating. Thus, different wavelengths are reflected or scattered at different angles.
Various different types of wire-grid polarizers have been proposed that include patterning the wires incurved lines, rather than strait lines; or forming the wires in a lattice structure with reinforcing members. See US Patent Application Publication US 2002/0167727 A2; and U.S. Pat. Nos. 6,972,906; 7,009,768; and PCT Application PCT/US2005/032656 (WO 2006/036546).
Other types of wire-grid polarizers have been proposed to diffusely reflect incident light that include contoured surfaces at different angles. See U.S. Pat. Nos. 6,081,376 and 6,348,995. Such polarizers, however, still specularly reflect, only from within several differently oriented textured surfaces.
Sometimes it is desirable to reflect all incident light or transmit most or all incident light in a diffuse manner. In this situation a diffuser is desired, but not a polarizing diffuser. One example of this situation would be a thermal window with a metallic film. Without a diffuser, a specular reflection would result from the building windows. Another need for diffuse light may be in an LCD display or a projector system.

SUMMARY OF THE INVENTION

It has been recognized that it would be advantageous to develop a wire-grid polarizer for polarizing incident light by diffusely transmitting one polarization orientation and diffusely reflection the other polarization orientation.
It has also been recognized that it would be advantageous to develop a non-polarizing diffuser to either transmit or reflect light diffusively.
The invention provides a light diffuser comprising: a substrate having a top surface and a bottom surface; a layer disposed over the top surface of the substrate; and at least sixteen facets: having at least two different sizes; having a bottom surface disposed towards the substrate and a top surface opposing the bottom surface; formed in the layer with facet dimensions >λ/2, where λ is the wavelength of light incident on the at least sixteen facets to create a substantially diffuse light beam; and forming distinct groups arranged in a fractal pattern.
In addition, the invention provides a light diffuser comprising: a substrate having a top surface and a bottom surface; at least one layer disposed over the top surface of the substrate; and at least sixteen facets, with a bottom surface disposed towards the substrate and a top surface opposing the bottom surface, formed in one of the at least one layer with facet dimensions >λ/2 where λ is the wavelength of light incident on the at least two facets to create a substantially diffuse light beam.
Furthermore, the invention provides a light diffuser comprising: a substrate having a top surface and a bottom surface; a layer, disposed over the top surface of the substrate, and formed of the same material as the substrate; and at least sixteen facets: having at least four different sizes with at least four different surface areas; having a bottom surface disposed towards the substrate and a top surface opposing the bottom surface; formed in the layer with facet dimensions >λ/2, where λ is the wavelength of light incident on the at least sixteen facets; forming distinct groups arranged in a fractal pattern; and substantially diffracting incident light.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional features and advantages of the invention will be apparent from the detailed description which follows, taken in conjunction with the accompanying drawings, which together illustrate, by way of example, features of the invention; and, wherein:

FIG. 1 is a schematic top view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 2 is a schematic cross-sectional side view of the diffusive wire-grid polarizer of FIG. 1 taken along line 2-2 in FIG. 1;

FIG. 3 is a schematic partial perspective view of the diffusive wire-grid polarizer of FIG. 1;

FIGS. 4 a-f are schematic top views of various shaped facets;

FIG. 5 is a schematic top view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 6 is a schematic top view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 7 is a schematic top view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 8 is a schematic top view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 9 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 10 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 11 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 12 is a schematic partial perspective view a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 13 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 14 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 15 is a schematic cross-sectional side view of a diffusive wire-grid polarizer in accordance with an embodiment of the present invention;

FIG. 16 is a schematic top view of a diffuser in accordance with an embodiment of the present invention;

FIG. 17 is a schematic cross-sectional side view of the diffuser of FIG. 16 taken along line 17-17 in FIG. 16;

FIG. 18 is a schematic top view of a diffuser in accordance with an embodiment of the present invention;

FIG. 19 is a schematic cross-sectional side view of the diffuser of FIG. 18 taken along line 19-19 in FIG. 18;

FIG. 20 is a schematic top view of a diffuser in accordance with an embodiment of the present invention;

FIG. 21 is a schematic cross-sectional side view of the diffuser of FIG. 20 taken along line 21-21 in FIG. 20;

FIG. 22 is a schematic cross-sectional side view of a diffuser in accordance with an embodiment of the present invention

Reference will now be made to the exemplary embodiments illustrated, and specific language will be used herein to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

As illustrated in FIGS. 1-3, a diffusive wire-grid polarizer (WGP), indicated generally at 10, in an example implementation in accordance with the invention is shown. The diffusive WGP of the present invention can be used in situations in which non-specular, or non-mirror like, reflection of substantially one polarization orientation (namely a diffuse reflected beam 29 of s-polarization orientation) is desired of an incident beam 27. The diffusive WGP of the present invention can also be used in situations in which non-specular, or non-mirror like, transmission of substantially one polarization orientation (namely a diffuse transmitted beam 28 of p-polarization orientation) is desired of an incident beam 27. In such a situation, diffuse reflection or diffuse transmission may be more important than polarization contrast because the diffuse reflected beam 29 may also include a substantial amount of p-polarization orientation in addition to the s-polarization orientation. The incident beam 27 can be unpolarized, and can be visible light (or have one or more wavelengths in the range of ˜300-700 nm, or ˜0.3-0.7 microns or μm). Alternatively, the incident beam can be infrared or ultraviolet. In this patent application, light means ultraviolet, visible, or infrared.
The diffusive WGP 10 can include a substrate 26, such as glass, or another material that is substantially transparent to the incident light beam 27. Substrate 26 can be a single layer or can be multiple layers, with each layer made of the same material as, or different materials than, the other layers. Disposed on or over the substrate is a layer 25 of conductive material, such as aluminum or silver. The layer 25 can be deposited directly on the substrate. Alternatively, other layers can be disposed between the substrate 26 and the layer 25 of conductive material. The layer 25 can have a uniform and constant thickness t, and disposed over essentially the entire substrate.
The layer 25 can be patterned (such as by etching select areas) to form an array of facets 14 a-d arrayed across the substrate. The facets can be made of multiple sizes in order to optimize light diffraction. The facets 14 a-d extend essentially across the entire substrate with spaces or gaps 11 therebetween. The facets can be arranged in a fractal pattern. “Fractal” means geometrical structures whose shape appears to be the same regardless of the level of magnification used to view them. The facets 14 a-d can have widths w_1-4or diameters and lengths L_1-4greater than a wavelength λ of incident light, or greater than half the wavelength of incident light (w>λ/2 and L>λ/2, where w is a width or diameter or dimension of the facets transverse to the wires, and L is a length of the facets transverse to the width). Thus, the facets substantially diffract both the s-polarized light and the p-polarized light incident on the facets, or the light having s-polarization orientation and p-polarization orientation. A majority or substantially all of the light having s-polarization orientation will be diffracted, or diffusely reflected; while a portion of the light having p-polarization orientation will be transmitted, or diffusely transmitted. The type of fractal pattern used and material of the layer 25 affect the amount of p-polarized light that is transmitted.
In addition, layer 25 can be patterned to form a wire-grid including an array of elongated parallel conductive wires 12 filling the spaces 11 between the facets 14 a-d. Thus, the array of wires 12 extends across essentially the entire substrate. The facets 14 a-d and the array of wires 12 can be formed together with each facet integral with the plurality of wires. The array of facets 14 a-d interrupt and are interspersed through the array of wires 12. The plurality of facets interrupts the array of wires, and share a common layer.
The array of wires 12 has a period P less than half the wavelength λ/2 of incident light (P_WGP<λ/2, where P_WGPis the period of the wires, and λ is the wavelength of light incident on the wires). Thus, the array of wires at least partially polarizes the incident light 27 by substantially reflecting light 29 having an s-polarization orientation and substantially transmitting light 28 having a p-polarization orientation.
The array of wires and array of facets can be formed by lithography.
The facets 14 a-d can have at least two different sizes with at least two different surface areas, such as four different facets with four different sizes and four different surface areas, as shown. The facets can have rectilinear shapes, such as square with the width and length of each facet being essentially equal, or on the same order of magnitude. As shown in FIG. 4 a-f, the facets can also be circular 46, triangular 42, diamond shaped 43, polygonal 45, elliptical 44, irregular shaped 41, or other shape. Different shapes may be selected for improved optical performance or ease of manufacturability. Facet dimensions d_1-9are greater than a wavelength λ of incident light, or greater than half the wavelength of incident light (d>λ/2). Although most figures show square shaped facets, any shaped facet may be used in all invention embodiments. Although most figures show two to four different sized facets, any number of different sized facets may be used in all invention embodiments.
FIG. 1 shows square shaped facets 14 a-d, with widths w_1-4transverse to the wires and lengths L_1-4transverse to the width, arranged in a fractal pattern. FIG. 5 shows a diffusive WGP, indicated generally at 50, in another example implementation in accordance with the invention. This diffusive WGP has square shaped facets 54 a-d, arranged in a fractal pattern. While the width of the square shape is not orthogonal to the wires, and the length of the square shape is not parallel to the wires, the square shape has a diameter or dimension transverse to the wires that is greater than a wavelength λ of incident light, or greater than half the wavelength of incident light.
FIG. 6 shows a diffusive WGP, indicated generally at 60, in another example implementation in accordance with the invention. This diffusive WGP has triangular shaped facets 64 a-d, arranged in a fractal pattern. As described above, the triangular shaped faces have a diameter or dimension (such as d₃or d₄of FIG. 4) transverse to the wires that is greater than a wavelength λ. of incident light, or greater than half the wavelength of incident light. Different fractal patterns may be selected for improved optical performance or ease of manufacturability.
As illustrated in FIGS. 7-8, indicated generally at 70 and 80 respectively, fractal patterns different from that shown in FIGS. 1 and 6 may be used. In the example of FIG. 7, the wire gridded area 74 of the diffusive WGP 70 comprises a fractal pattern and the area between the fractal pattern 71 comprises facets 72. The facets 72 form distinct groups or areas 74 in the array of wires which include or define the fractal pattern, and can include at least sixteen facets with four different sizes arranged in a fractal pattern. The facets 72 can have the same shape. Alternatively, as shown in FIG. 8, the facets 84 of the diffusive WGP 80 may comprise a fractal pattern and the area between the fractal pattern 81 may comprise a wire grid. Optical properties, such as transmissivity or extinction, may be optimized by selection of the wire grid or facets to form a fractal pattern. In all embodiments of this invention, the facets or the wire grid may comprise a fractal.
As illustrated in FIG. 9, another diffusive wire-grid polarizer, shown generally at 90, has facets 94 a-c disposed over a wire grid layer 92 with an array of elongated parallel conductive wires as described above. The facets 94 a-c can be any material with the desired optical properties. Use of a transparent material for facets 94 a-c can result in higher transmission of the p-polarized light. In this embodiment, the wire grid layer 92 can extend over all, or substantially all, of the surface of the substrate 26. To make such a device, a first layer 92 may be added to a substrate 26 by sputtering, chemical vapor deposition, evaporation, or other similar method. The first layer 92 may be patterned and etched to form the wire grid. Another layer 95 may be added on top of the wire grid layer by sputtering, chemical vapor deposition, evaporation, or other similar method. The top layer 95 may be patterned and etched to form the facets 94 a-c. The facets may comprise a fractal pattern, as described above. The exposed wire grid, in areas where there are no facets, may comprise a fractal pattern, as described above. Different facets may all be etched to the same depth such that the facet thicknesses t_1-3are the same, as shown in FIG. 9. Different facets may be etched to different depths such that the facet thicknesses t_1-3are not the same. This may be done by use of separate masking and etching steps for different depth facets. Facets of different sizes or shapes help to create diffuse transmitted or reflected light. Facets of different depths also create diffuse transmitted or reflected light because the light travels through different thicknesses t_1-3of material.
As illustrated in FIG. 10, another diffusive wire-grid polarizer, shown generally at 100, has facets 104 a-b disposed over the wire grid layer 92 in multiple layers. The facets 104 a-b may be any material with the desired optical properties. There may be more than two layers of facets. All layers may be the same material or the layers of facets may be made of different materials. Multiple layers can provide improved light control and improved wavelength specificity. To make such a device, additional layer deposition, patterning, and etching steps can be used following making the basic structure 90 of FIG. 9.
As illustrated in FIG. 11, another diffusive wire-grid polarizer, shown generally at 110, has facets 114 a-b disposed below the wire grid layer 92. To make such a device, a lower facet layer or multiple lower facet layers are added on top of the substrate 26 by deposition, patterning, and etching steps. Another layer 113 is then added on top of the facets. Layer 113 can be the same as the substrate 26 or can be a different material as shown by dividing line 111. A wire grid layer 92 and facet layers 114 c-d may be added on top of layer 113. In a similar fashion, other layers 113 b-c may be added on top to allow added wire grid layers 92 b, facet layers, and/or combined facet plus wire grid layers 115. The facets 114 a-d may be any material with the desired optical properties. This stacking of wire grid layers 92 b, facet layers, and/or combined facet plus wire grid layers may apply to other embodiments of the invention. Multiple layers can provide improved light control and improved wavelength specificity.
As illustrated in FIG. 12, another diffusive wire-grid polarizer, shown generally at 120, has facets 124 a created by etching away facet areas rather than by masking facet areas such as in FIGS. 1-2. In other embodiments of this invention, facets may also be created by etching the desired facet area and masking between facet areas. Thus, areas of the upper surface of the substrate without wires 12 can form the facets 124 a. This embodiment can have an advantage of improved transmissivity.
As illustrated in FIG. 13, another diffusive wire-grid polarizer, shown generally at 130, has facets 134 a-c formed by etching into the substrate 26 or into a layer 133 on top of the substrate. Layer 133 may be the same as the substrate 26 or may be a separate material separated at dashed line 131. Different facets may all be etched to the same depth (not shown but such that the etch depths or substrate thicknesses t_2-4at the facets are the same). Different facets may be etched to different depths, as shown, such that etch depths or substrate thicknesses t_2-4at the facets are not the same. This may be done by use of separate masking and etching steps for different depth facets. Facets of different sizes or shapes help to create diffuse transmitted or reflected light. Facets of different depths also create diffuse transmitted or reflected light because the light travels through different thicknesses t_1-4of material.
As illustrated in FIG. 14, another diffusive wire-grid polarizer, shown generally at 140, has thicknesses t_2-4of the substrate 26 beneath the facets 144 a-c that are thicker than the thickness t₁of the substrate beneath the wire grid. This polarizer may be created by separate pattern and etch steps. For example, one pattern and etch step may be used to create facets of the thickness of facet 144 b. A different pattern and etch step may be used to etch to the top of the desired wire grid 141. Another pattern and etch step may then be used to etch down to level 142 to create the wire grid 12. Facets of different thicknesses, as shown in FIGS. 13 & 14 may be used with other embodiments of the invention. Facets of different depths also create diffuse transmitted or reflected light because the light travels through different thicknesses t_1-4of material.
As illustrated in FIG. 15, another diffusive wire-grid polarizer, shown generally at 150, has a wire grid 153 a-c disposed over facets in addition to the areas between the facets. This polarizer may be created by separate pattern and etch steps. For example, one pattern and etch step may be used to etch to the top of the desired wire grid 151. Another pattern and etch step may then be used to etch down to level 152 to create the wire grid 153 b. Wire grids may be disposed over the facets of other invention embodiments. Use of wire grid over the facets can improve polarization contrast.
All of the previously described embodiments may be non-polarizing diffusers instead of diffusive wire grid polarizers through use of a non polarizing material, such as a non-conductive material, to make the wire grid layer. Alternatively, the following described embodiments are alternative non-polarizing diffusers.
As illustrated in FIGS. 16-17, a diffuser, shown generally at 160, has facets used to create a non-polarizing diffuser. This embodiment may be useful if diffuse, non-polarized light is desired. A diffuser has a substrate 176 which may be made of materials that are, or are not, transparent to the incoming light 27. If the substrate is not transparent (or is opaque), then substantially all of the incoming light 27 can be reflected diffusely 179. If the substrate is transparent, then some of the incoming light can be reflected diffusely 179 and some or substantially all can be transmitted diffusely 178. The reflected and transmitted light will not be polarized. To make this device 160, facet layer 175 is etched completely between the facets 11 rather than patterned to form wire grids. Because polarization is not desired, facet layer 175 can be substantially any material that will provide the desired optical properties. Facet layer 175 and the substrate 176 can be the same material or may be different materials. Facet layer 175 can be deposited directly on the substrate 176. Alternatively, other layers can be disposed between the substrate 176 and layer 175.
As illustrated in FIGS. 18-19, the facets 184 a-d of another diffuser 180 are the locations that are cut into a layer or substrate rather than raised areas which were masked during etching. Facet layer 175 and substrate (or underlying layer) 176 may be the same, or facet layer 175 may be a different material from the substrate or underlying layer 176. Similar to the diffusive WGP 130 of FIG. 13, the thicknesses t_2-5may be the same or may be different. This diffuser 180 may be manufactured similarly to polarizer 130, except that no wire grids are formed. Facets of different sizes or shapes help to create diffuse transmitted or reflected light. Facets of different depths also create diffuse transmitted or reflected light because the light travels through different thicknesses t_1-4of material.
As illustrated in FIGS. 20-21, the facets of 204 a-d another diffuser 200 are the locations that were masked during etching and thus are raised above surrounding etched locations. This diffuser 200 may be manufactured similarly to polarizer 140, except that no wire grids are formed. Facets of different sizes or shapes help to create diffuse transmitted or reflected light. Facets of different depths also create diffuse transmitted or reflected light because the light travels through different thicknesses t_1-4of material.
As illustrated in FIG. 22, the facets of another diffuser 220 may be disposed on top of other facets. Facets 224 a-b may be any material with the desired optical properties. There may be more than two layers of facets. All layers may be the same material or the layers of facets may be made of different materials. This diffuser 220 may be manufactured similarly to polarizer 100, except that no wire grids are formed. Multiple layers can provide improved light control and improved wavelength specificity.
While the forgoing examples are illustrative of the principles of the present invention in one or more particular applications, it will be apparent to those of ordinary skill in the art that numerous modifications in form, usage and details of implementation can be made without the exercise of inventive faculty, and without departing from the principles and concepts of the invention. Accordingly, it is not intended that the invention be limited, except as by the claims set forth below.

Claims

1. A light diffuser comprising:

a. a substrate having a top surface and a bottom surface;

b. a layer disposed over the top surface of the substrate; and

c. at least sixteen facets:

i. having at least two different sizes;

ii. having a bottom surface disposed towards the substrate and a top surface opposing the bottom surface;

iii. formed in the layer with facet dimensions >λ/2, where λ is the wavelength of light incident on the at least sixteen facets to create a substantially diffuse light beam; and

iv. forming distinct groups arranged in a fractal pattern.

2. The light diffuser of claim 1, wherein the substrate and the layer are formed of the same material.

3. The light diffuser of claim 1, wherein the substrate and the layer comprise a different material.

4. The light diffuser of claim 1, wherein the facets are locations that are cut into the layer.

5. The light diffuser of claim 1, wherein the at least sixteen facets have at least two different thicknesses.

6. The light diffuser of claim 1, wherein the at least sixteen facets have at least four different thicknesses.

7. The light diffuser of claim 1, wherein the at least sixteen facets have square shapes.

8. The light diffuser of claim 1, wherein the facets are locations that were masked during etching and are raised above surrounding etched locations.

9. The light diffuser of claim 1, wherein the at least one layer comprises at least two layers and the at least sixteen facets are disposed over at least sixteen other facets.

10. The light diffuser of claim 9, wherein the at least two layers are formed of the same material.

11. The light diffuser of claim 9, wherein the at least two layers comprise a different material.

12. The light diffuser of claim 1, wherein the substrate comprises a material that is opaque to the light such that substantially all of the incoming light is diffusely reflected.

13. The light diffuser of claim 1, wherein the at least sixteen facets have at least four different sizes.

14. The light diffuser of claim 1, wherein the facets are a solid material surrounded by areas of the layer which have been removed.

15. The light diffuser of claim 1, wherein the at least sixteen facets comprise areas of the layer which have been removed, and are surrounded by areas of the layer which have not been removed.

16. The light diffuser of claim 1, wherein a distance from the bottom surface of the substrate to a top surface of at least one of the at least sixteen facets is different than a distance from the bottom surface of the substrate to a top surface of another of the at least sixteen facets.

17. The light diffuser of claim 1, wherein areas of the top surface of the substrate which is not covered with any of the at least sixteen facets are covered by a wire grid and the wire grid comprises a non polarizing material.

18. The light diffuser of claim 1, wherein the top surface of the at least sixteen facets is covered with wire grid and the wire grid comprises a non polarizing material.

19. A light diffuser comprising:

a. a substrate having a top surface and a bottom surface;

b. at least one layer disposed over the top surface of the substrate; and

c. at least sixteen facets, with a bottom surface disposed towards the substrate and a top surface opposing the bottom surface, formed in one of the at least one layer with facet dimensions >λ/2 where λ is the wavelength of light incident on the at least two facets to create a substantially diffuse light beam.

20. A light diffuser comprising:

a. a substrate having a top surface and a bottom surface;

b. a layer, disposed over the top surface of the substrate, and formed of the same material as the substrate; and

c. at least sixteen facets:

i. having at least four different sizes with at least four different surface areas;

iii. formed in the layer with facet dimensions >λ/2, where λ is the wavelength of light incident on the at least sixteen facets;

iv. forming distinct groups arranged in a fractal pattern; and

v. substantially diffracting incident light.