Patent Publication Number: US-2023152708-A1

Title: Optical devices and methods for manufacturing the optical devices

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application claims the benefit of and priority to U.S. Prov. App. No. 63/264,141 filed Nov. 16, 2021, the entirety of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     The resolution of designs on optical devices, i.e., the minimum size that the elements of a design can have, are limited by the fabrication technology used to produce the optical device. For example, when photolithography is used to apply designs to an optical device, there are limits on what minimum size can realistically be achieved for individual elements of the design, which impacts the design of the respective optical device. 
     The subject matter of the present disclosure is directed to overcoming, or at least reducing the effects of, one or more of the problems set forth above. 
     SUMMARY 
     The present disclosure is directed to methods for manufacturing optical devices. In one aspect of the disclosure, the methods include disposing a dielectric layer on top of a substrate. In another aspect of the disclosure, the methods may include applying photoresist on top of the dielectric layer. In one aspect of the disclosure, the methods may include primarily exposing the photoresist through a first photomask. Moreover, in one aspect of the disclosure the methods may include secondarily exposing the photoresist to UV light through a second photomask, such that the photoresist is exposed in areas not exposed during the primary exposure of the photoresist, where the second photomask increases the resolution of the photoresist. In one aspect of the disclosure, the methods may include removing the areas of photoresist not exposed. In yet another aspect of the disclosure, the methods may include removing the areas of the dielectric layer not covered by the photoresist according to the pattern. In yet another aspect of the disclosure, the methods may include removing the remaining photoresist. 
     In one aspect of the disclosure, the first and/or second photomask includes circles. In one aspect of the disclosure, the circles are arranged in a triangular, square, rectangular, or hexagonal lattice. In another aspect of the disclosure, the circles of the second photomask are smaller than the circles of the first photomask. Disclosed methods may include, for example: tertiary exposing the photoresist through a third photomask, such that the photoresist is exposed in areas not exposed during the primarily and secondary exposure of the photoresist, where the third photomask increases the resolution of the photoresist. 
     The present disclosure is also directed to optical devices manufactured in accordance with disclosed methods. In once aspect of the disclosure, the optical devices may include a substrate. In another aspect of the disclosure, disclosed optical devices may include a dielectric layer on top of a substrate. In yet another aspect of the disclosure, the dielectric layer may include features that are dimensioned such that light interacting with the dielectric layer experiences a phase delay according to a phase delay function. 
     In one aspect of the disclosure, each feature is a post, hole or trench. In another aspect of the disclosure, each feature is filled with air, vacuum, or a material with a refractive index differing from the refractive index of the substrate. In another aspect of the disclosure, the substrate is an optically transparent substrate, for example, glass or fused silica. In one aspect of the disclosure, the optical device is transmissive or reflective. In one aspect of the disclosure, each feature is smaller than the wavelength of light incident to, emerging from, and/or transmitted by that particular feature. In another aspect of the disclosure, each feature is a discrete, circumscribed non-recessed area surrounded by a recessed area of the dielectric layer. Yet in another aspect of the disclosure, each feature is a circumscribed post, column, pillar, or wall of the dielectric layer. 
     In another aspect of the disclosure, each feature includes a characteristic dimension, for example, a diameter and a height. The height and the diameter of each feature is dimensioned such that, when an optical wave, with a particular wavelength, travels through the optical device, the optical wave experiences a differential phase delay according to the phase delay function. Disclosed devices may further include: an optical medium that covers the dielectric layer. The optical medium has a different refractive index than the dielectric layer. 
     Disclosed herein are methods of fabricating an optical device. The methods of fabricating also include applying a resist layer to a device layer for the optical device; producing a set of first features in the resist layer using a first mask, the first features arranged in a period in a patterned grid and having one or more first characteristic dimensions; producing at least one set of additional features in the patterned grid in the resist layer using at least one additional mask offset at a fraction of the period in at least one planar dimension from the first features, the additional features having one or more additional characteristic dimensions; and producing the patterned grid of the first features and the additional features in the device layer. 
     In one aspect of the disclosure, a patterned grid may include a rectangular grid; where the at least one planar dimension may include first and second orthogonal dimensions; where the fraction of the period may include half of the period; and where producing the at least one set of the additional features in the patterned grid in the resist layer using the at least one additional mask offset at the fraction of the period in the at least one planar dimension from the first features may include: producing three sets of the additional features for the rectangular grid in the resist layer using three of the at least one additional mask, one of the three additional masks offset at half of the period in the first orthogonal dimension from the first features, another of the three additional masks offset at half of the period in the second orthogonal dimension from the first features, yet another of the three additional mask offset at half of the period in both the first and second orthogonal dimensions from the first features. The patterned grid may include a triangular grid; and where producing the at least one set of the additional features in the patterned grid in the resist layer using the at least one additional mask offset at the fraction of the period in the at least one planar dimension from the first features may include: producing three sets of the additional features for the triangular grid in the resist layer using three of the at least one additional mask, each of the three additional masks offset at the fraction of the period in one of three of the planar dimensions from the first features. The patterned grid may include a hexagonal grid; and where producing the at least one set of the additional features in the patterned grid in the resist layer using the at least one additional mask offset at the fraction of the period in the at least one planar dimension from the first features may include: producing five sets of the additional features for the rectangular grid in the resist layer using five of the at least one additional mask, each of the five additional masks being offset. 
     Disclosed herein are methods of fabricating an optical device. In one aspect of the disclosure, the methods may include applying a resist layer to a device layer for the optical device; producing a patterned grid of a set of first features in the resist layer using a first mask, the first features arranged in a period in the patterned grid and having one or more first characteristic dimensions; producing a set of second features for the patterned grid in the resist layer using a second mask offset at half of the period in a first planar dimension from the first features, the second features having one or more second characteristic dimensions; producing the patterned grid of the first and second features in the device layer. 
     Disclosed methods may include, in one aspect of the disclosure, producing a set of third features for the patterned grid in the resist layer using a third mask offset at half of the period in a second planar dimension from the first features, the third features having one or more third characteristic dimensions, where producing the patterned grid of the first and second features in the device layer further may include producing the pattered grid of the third features in the device layer. In one aspect of the disclosure, producing the patterned grid of the first, second, and third features in the device layer further may include producing the pattered grid of the fourth features in the device layer. In one aspect of the disclosure, the device layer is a substrate or is a dielectric layer disposed on the substrate. In one aspect of the disclosure, the resist layer is a photoresist layer. In one aspect of the disclosure, producing the patterned grid of the features in the device layer may include defining the patterned grid in the device layer using reactive ion etching. In one aspect of the disclosure, each of the one or more characteristic dimensions in a given set are the same as one another. In one aspect of the disclosure, each of the one or more characteristic dimensions in each set are different from one another. In one aspect of the disclosure, the patterned grid of the first features is a rectangular grid having the period of 500 nm center-to-center between adjacent ones of the first features in the first and second planar dimensions, where the first characteristic dimension ranges from 200 nm to 300 nm. In one aspect of the disclosure, the patterned grid of the features in the device layer is a rectangular grid having a period of 250 nm center-to-center between the adjacent ones of the respective features in the first and second planar dimensions, where the first, second, third, and fourth characteristic dimensions range from 200 nm to 300 nm. In one aspect of the disclosure, the method may include designing the optical device to impart a differential phase delay in a range 0 to 2π or multiple of 2π radians by selecting a thickness of the device layer and selecting a range of the first, second, third, and fourth characteristic dimensions for an electromagnetic wave propagating through the optical device. 
     In one aspect of the disclosure, a device for transforming an optical signal in an operational wavelength range incident thereto is disclosed. In one aspect of the disclosure, the device includes a transmissive layer that may include first and second optical media transparent over the operational wavelength range; the first and second optical media being arranged within the transmissive layer as a contiguous multitude of pixel features, where each pixel may include either the first optical medium or the second optical medium, but not both; the transmissive layer being configured to transform at least a portion of the optical signal incident thereto according to a specified effective phase transformation function that varies as a function of two-dimensional position coordinates x and y along a surface of the transmissive layer; the pixel features including: a set of first pixel features produced from resist exposed in a first exposure from a first mask, arranged in a period in a patterned grid, and having one or more first characteristic dimensions; and at least one set of additional features produced from the same resist exposed in at least one addition exposure from at least one additional mask, arranged in the patterned grid offset at a fraction of the period in at least one planar dimension from the first features, the additional features having one or more additional characteristic dimensions. One general aspect includes where the device is configured to transmit or reflect the transformed portion of the optical signal. 
     The foregoing summary is not intended to summarize each potential embodiment or every aspect of the present disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows a schematic cross-section of an optical device, according to the present disclosure. 
         FIG.  2 A  shows a cross-sectional view of an intermediate stage of an optical device, according to one or more embodiments. 
         FIG.  2 B  shows another intermediate stage of the optical device, according to one or more embodiments. 
         FIG.  3 A  shows a schematic top view of a patterned photoresist, according to one or more embodiments. 
         FIG.  3 B  shows a schematic top view of a photoresist with a second pattern, according to one or more embodiments. 
         FIG.  3 C  shows a schematic top view of a photoresist with a third pattern, according to one or more embodiments. 
         FIG.  3 D  shows a schematic top view of a photoresist with a fourth pattern, according to one or more embodiments. 
         FIG.  3 E  shows a schematic top view of the photoresist with a fifth pattern. 
         FIG.  3 F  shows a schematic top view of the photoresist with a sixth pattern. 
         FIG.  4 A  shows a cross-sectional view of an intermediate stage of the optical device, according to one or more embodiments. 
         FIG.  4 B  shows a cross-sectional view of an optical device, according to one or more embodiments. 
         FIG.  5    shows a flowchart of method steps for manufacturing an optical device, according to one or more embodiments. 
         FIG.  6 A  shows schematic top views of unit cells of optical devices. 
         FIG.  6 B  shows schematic top views of other unit cells of optical devices. 
         FIG.  7 A  shows a top view of an optical device with features distributed in an optical device according to one or more embodiments. 
         FIG.  7 B  shows a magnification of a part of  FIG.  7 A . 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSURE 
     As disclosed herein, an optical device has features patterned therein, for example, located on a patterned grid (e.g., rectangular, triangular, or hexagonal grid) or other distributions, which may or may not be regular. The disclosed optical devices can be, for example, a meta lens, a phase plate, a phase delay diffractive optical element, an optical phase delay plate, or a phase-transforming optical element. For example, the optical device can be generally similar in their function to devices disclosed in U.S. Pat. Nos. 9,618,664; 10,386,553; 10,539,723; and 10,823,889 and in US Pat. Pub. 2020/0271837, which are each incorporated herein by reference in their entireties. But as described below, will contain additional features and methods of formation. 
     Example optical devices disclosed can be transmissive or reflective. The optical devices include a transmissive layer having two different optical media having differing refractive indices arranged in discrete features, volumes, areal regions, or pixels disposed along the transmissive layer. These features are arranged in the transmissive layer such that an optical signal incident on the optical device will be transformed by its interaction with the features in the transmissive layer to obtain a desired phase function or other result. 
     For example, disclosed optical devices can include a substrate having a first optical media disposed therein or thereon. While the remainder of this disclosure will refer to this first optical media as a device layer or a dielectric layer, it should be noted that first optical media need not be a dielectric so long as it has the desired optical properties. The dielectric layer (e.g. the first optical media or device layer) disposed on or as part of the substrate has a certain refractive index. The features are etched into or etched from the dielectric layer, and those features that were etched are filled with air, vacuum, or a material of different refractive index as the dielectric layer which will function as a second optical media. Each feature (which may also be referred to herein as a “pixel feature” or “feature” may thus be formed from the first optical media or the second optical media depending on whether the pixel is formed of what remains of the dielectric layer after etching (e.g., a “post” or “pillar”) or is formed of the second optical media (e.g. a “hole”). And together, the region/layer where both posts and hole reside is the transmissive layer. To avoid confusion, the first optical medium, e.g., the dielectric layer, will be referred to as a dielectric layer, and the second optical medium (e.g. that which fills in between etched or removed dielectric layer) will be referred to as the optical medium. Each feature has a certain dimension (e.g., a diameter of a post or a hole). Alteration of the dimension of a feature changes the phase delay/phase function experienced by an electromagnetic or light wave propagating through the respective feature. 
       FIG.  1    shows a schematic cross-section of an example optical device  100  according to the present disclosure. The example optical device  100  is shown as being transmissive, which means light generally passes through the optical device  100 . The optical device  100  may include a substrate  103  and transmissive layer  220  that includes features  102  formed of dielectric layer  202  and/or an optical medium  106 . The dielectric layer  202  in example optical device  100  has a refractive index n 2 , and the optical medium  106  has a refractive index n 1  different from the refractive index n 2  of the dielectric layer  202 . The optical medium  106  can be solid, liquid, or gaseous, such as air or vacuum. The substrate  103  can be a solid material differing from the optical medium  106 . 
     In one arrangement, the dielectric layer  202  has a substantially uniform thickness, has a multitude of suitably sized and positioned perforations or holes  105 , and is immersed in the ambient optical medium  106  that surrounds the dielectric layer  202  and fills the holes  105 . The holes (also referred to as recesses herein)  105  and the intervening areas of the dielectric layer  202  form a plurality of features  102  that together form the transmissive layer  220  having the same substantially uniform thickness as the dielectric layer  202 . 
     The optical device  100  is structurally arranged so as to receive an optical signal  110  incident on the first surface  116  of the transmissive layer  220  and to transmit at least a portion of the incident optical signal  110  from a second surface  112  of the transmissive layer  220  as a transmitted optical signal  114  transformed according to the effective phase transformation function defined by the characteristic size and position of the features  102 . 
     The features  102  for the optical device  100  can be arranged in any suitable lattice pattern, e.g., triangular, square, rectangular, or hexagonal, or irregular patter. In one example, the features  102  are arranged in a lattice pattern having subwavelength (relative to the incident light  110 ) features  102 , such that there may be little or no unwanted coherent scattering or diffraction from the transmissive layer  220 . Alternatively, the features  102  and/or the lattice may be larger than the wavelength if a different outcome is desired. 
       FIG.  5    shows a flowchart of an example method  500  for manufacturing disclosed optical devices, for example, optical device  100 , and will be discussed with reference to  FIGS.  2 A through  4 B . Disclosed methods improve upon the limits of traditional photolithographic resolution. Example disclosed methods increase the resolution by exposing the same photoresist using multiple photomasks and exposures prior to development, as described below. 
     At step  502 , a dielectric layer is disposed on top of a substrate.  FIG.  2 A  shows a cross-sectional view of an example intermediate optical device  200 A of an example optical device  100  ( FIG.  1   ). The intermediate optical device  200 A includes a dielectric layer  202  disposed on top of a substrate  103  in accordance, for example, with step  502 . In some examples, the substrate  103  is an optically transparent substrate  103 , which can be, for example, glass or fused silica. 
     The dielectric layer  202  is, for example, etchable, has a certain refractive index n 2 , and a height D, which may be the same or about the same height as the resulting transmissive layer  220 . In this example, the dielectric layer  202  is formed of an optical media, through which light may also propagate. The optical media has discrete features, volumes, and areas. In some embodiments, the dielectric layer  202  is made of the same material as the substrate  103  or is part of the substrate  103 . 
     At step  504  of method  500  ( FIG.  5   ), photoresist is applied on top of the dielectric layer.  FIG.  2 B  shows the intermediate optical device  200 B, which is the same or similar to the intermediate optical device  200 A of  FIG.  2 A  with photoresist  201  applied on top of the dielectric layer  202 , in accordance with step  504  of method  500 . 
     As will be discussed further below, at steps  506  and  508 , the photoresist  201  will be exposed two or more times through successive different photomasks to overlap multiple patterns without interceding development. As will be shown, such successive exposures will increase the potential resolution of exposed regions (and ultimately features  102 ) allowing such features  102  to be formed with photolithography where other fabrication techniques, such as an electron beam resist exposure process, may be too slow or costly to be practical for use in producing a desired optical device. 
     At step  506 , the photoresist is primarily exposed through a first photomask. The methods of exposing (e.g., hardening) a photoresist will vary depending on the type of photoresist chosen for a particular application. However, in one example, the photoresist may be exposed through application of ultraviolet (UV) light. The photoresist is exposed to UV light through a first photomask. The photomask shields the UV light from certain areas of the photoresist causing those masked areas not to react to the UV light. By exposure to the UV light (in areas not masked), the photoresist is made non-dissolvable if using a negative resist. While the remaining disclosure will make reference to the use of a negative photo resist, which is shown forming pillars (or non-recessed regions), other embodiments may use a positive photoresist (in which exposure to UV light makes such photoresist dissolvable) to form holes (or recessed regions). 
       FIG.  3 A  shows a schematic top view of the photoresist  201  ( FIG.  2 B ) with an example first pattern  201 A. The first pattern  201 A, as shown, includes first circles  302  representing example areas of exposure. The surrounding negative spaces (between first circles  302 ) represent areas not yet exposed during the first or primary exposure. The first circles  302  have a distance P to the neighboring first circles  302 . In other words, the first circles  302  are arranged in a rectangular lattice with a center-to-center distance P. The first circles  302  define the lattice points. The lattice is defined by a x-direction and a y-direction, wherein the x- and y-direction are orthogonal to each other. However, it will be appreciated that other lattices can be used, such as a hexagonal lattice. 
     While first pattern  201 A shows only circles for individual elements, other geometries may also be used, for example, ovals, rectangles, diamonds, or other combinations of curved and linear sided shapes. 
     In some embodiments, the first circles  302  have characteristic dimensions, e.g., diameters, ranging from 200 to 300 nm. The first circles  302  may be disposed on a rectangular or square lattice with a side length between lattice points ranging from 400 to 500 nm. As will be discussed below, this example optical device can form a unit cell and be combined with other unit cells. The smaller the distance between the lattice points, the higher effective resolution of the light passing through the optical device. 
     At step  508 , the photoresist is secondarily exposed (through one or more additional exposures through repetition of step  508 ) to UV light through a second (or follow-on) photomask(s), such that the photoresist is exposed in areas not exposed during the primary exposure of the photoresist, wherein the second photomask increases the resolution of the photoresist.  FIGS.  3 B- 3 F  show some example patterns of photoresist after the photoresist is exposed to UV light through additional successive photomasks. 
       FIG.  3 B  shows a schematic top view of the photoresist with a second pattern  201 B resulting from a second light exposure. The pattern  201 B is produced by a second photomask (not shown in  FIG.  3 B ) layered over previously exposed pattern  201 A. The second light exposure created second circles  304  that are, for example, smaller in diameter than the first circles  302 . The second circles  304  are offset and disposed in between the first circles  302  at, for example, half the period distance P in the x-direction only. Therefore, if the lattice period P were 500 nm, then the second circles  304  would be offset 250 nm in a single linear dimension x, as shown. 
       FIG.  3 C  shows a schematic top view of the photoresist with a third pattern  201 C resulting from a third light exposure (through repetition of step  508 ). The pattern  201 C is created with a third photomask (not shown in  FIG.  3 C ) layered over previously exposed patterns  201 A,  201 B. The pattern  201 C, may include, for example third circles  306  in addition to the first and second circles  302 ,  304 . The third circles  306  are disposed between the first circles  302  in the y-direction at half the distance P. The third circles  306  are shown having the same diameter as the second circles  304 , but they need not be. 
       FIG.  3 D  shows a schematic top view of the photoresist with a fourth pattern  201 D resulting from a fourth light exposure (through repetition of step  508 ). The fourth pattern  201 D is created with a fourth photomask (not shown in  FIG.  3 D ) layered over previously exposed patterns  201 A,  201 B,  201 C. The fourth pattern  201 D may include, for example, fourth circles  308  in addition to the first, second, and third circles  302 ,  304 ,  306 . The fourth circles  308  may have, for example, the same diameter as the first circles  302  or they may be different. The fourth circles  308  are disposed between the second and third circles  304 ,  306  at half the distance P in x- and y-direction. Thus, the resultant optical device of  FIG.  2 D  would have features  102  of different characteristic dimensions on a resulting 250 nm grid assuming a P of 500 nm (250×250 nm features). The Line A-A in  FIG.  3 D  shows an example cross-sectional plane representing the views of  FIGS.  1 A- 1 B , although the example optical device  100  may have differing patterns. As shown, through multiple successive exposures through different photomasks, a higher resolution pattern (e.g.,  201 D) can be obtained compared to, for example, pattern  201 A. 
     Each of the first, second, third, and fourth circles  302 ,  304 ,  306 ,  308  may have different diameters and offset distances from one another to create a desirable phase delay or optical transformation. Other patterns of the photoresist are possible, for example alternative patterns are shown in  FIGS.  3 E and  3 F  and described below. 
       FIG.  3 E  shows a schematic top view of the exposed photoresist with an alternative (fifth) pattern  201 E. The pattern  201 E resulted from multiple photomasks arranged in planar dimensions having offsets along axis d1, d2, d3 at half the periods of the lattice points within circles  302 E. The lattice of the pattern  201 E has a triangular unit cell with circles  302 E at each lattice point, and circles  304 E,  306 E, and  308 E therebetween. Each lattice point has a distance P to the neighboring lattice points, i.e., the period between circles  302 E. 
     The pattern may be formed using successive photomasks in a similar process as that described with reference to  FIGS.  3 A- 3 D . For example, a first photomask (and exposure) may be used to create the first circles  302 E at each of the lattice points of the pattern  201 E representing the exposed regions of the photoresist. A second photomask and exposure may then be used to create the second circles  304 E offset a fraction of distance P. The second circles  304 E of  FIG.  3 E  are disposed between the first circles  302 E along the axis d1 at half the distance P. 
     A third photomask and exposure may then be used to create the third circles  306 E of the photoresist  201 E. The third circles  306 E are disposed between the first circles  302 E along the axis d2 at half the distance P. A fourth photomask and exposure may then be used to create fourth circles  308 E of the photoresist  201 E. The fourth circles  308 E are disposed between the first circles  302 E along the axis d3 at half the distance P. 
     Each of the first, second, third, and fourth circles  302 E,  304 E,  306 E,  308 E are shown having varying diameters. However, the diameters of the first, second, third, and fourth circles  302 E,  304 E,  306 E,  308 E may also be the same depending on the desired configuration of the resultant optical device. In some embodiments, photomasks of different sizes are used to create bigger or smaller circles than the circles shown in  FIG.  3 E  or alternatively with different spacing between pattern circles. Further, the pattern need not be comprised solely of circular shapes. 
       FIG.  3 F  shows a schematic top view of the photoresist with a sixth example pattern  301 F. 
     The sixth pattern  301 F is created using a photomask (and exposure) with a hexagonal pattern to create circles  302 F with a distance P from each circle  302 F to the neighboring circle  302 F. Additional photomasks can be used to create second circles at, for example, half the distance P. The circles  302 F are shown, for example, having equal diameters. The circles  302 F can be arranged in a lattice with any suitable pattern, e.g., triangular, square, rectangular, or hexagonal. 
     Upon completion of the exposures at step  506  of method  500  ( FIG.  5   ) and subsequent secondary exposure(s) at step  508  to form the desired pattern of exposed photoresist, the photoresist on the intermediate optical device that has not been exposed, e.g. not exposed to UV light (represented by the negative space between the circles of  FIGS.  3 A through  3 F ) are removed at step  510  through the use of an appropriate developer and process, e.g., spray development, dipping baths, etc.) selected for the chosen photoresist which will remove the unexposed photoresist, but not the exposed photoresist. 
     After the photoresist has a final pattern following development at step  510 , at step  512  of method  500 , the dielectric layer  202  is removed in areas where the photoresist is not present according to the final pattern of the photoresist (e.g., the negative of patterns discussed with reference to  FIGS.  3 A through  3 F ). In other words, the dielectric layer  202  is removed in areas not covered by photoresist. The patterned photoresist is used as an etch-mask to etch the dielectric layer for producing features  102  ( FIG.  1   ). In some embodiments, the dielectric layer  202  is removed by reactive ion etching (RIE), however other etching processes compatible with the chosen photoresist may also be utilized. RIE is a type of dry etching. RIE uses chemically reactive plasma to remove the dielectric layer  202 . The plasma is generated under low pressure or vacuum by an electromagnetic field. High-energy ions from the plasma attack the dielectric layer  202  and react with the dielectric layer  202  not covered with activated or exposed photoresist. 
       FIG.  4 A  shows a cross-sectional view of intermediate optical device  400 A, which is the same or similar to the intermediate optical device  200 B of  FIG.  2 B , after steps  506 ,  508 ,  510 , and  512  have been completed, in which areas of the dielectric layer  202  not covered by the patterned photoresist  201  have been removed, for example via etching, according to step  512 . The pattern of the dielectric layer  202  is resultant from the pattern of the photoresist  201 . 
     After the dielectric layer  202  is removed, e.g. etched, the dielectric layer  202  includes recessed areas  404 , that correspond to holes  105  ( FIG.  1   ), and non-recessed areas  408 , that will correspond to the dielectric layer  202  of  FIG.  1   . 
     At step  514  of method  500 , the remaining photoresist  201  may be removed from dielectric layer  202 . The photoresist  201  can be removed, for example, by a suitable means for the chosen photoresist. For example, chemical removal, mechanical removal, a liquid resist stripper, by oxygen containing plasma by oxidizing the photoresist (ashing), or any other suitable removal method. A resist stripper chemically alters previously exposed photoresist such that the photoresist no longer adheres to the dielectric layer  202 . Another method for removing the photoresist is using 1-Methyl-2-pyrrolidone (NMP) solvent. Following removal of the remaining photoresist  201 , the resulting optical device  400  ( FIG.  4 B ) may be used as is with the ambient atmosphere filling in the recessed areas  404  or an alternative optical media  106  may be added to optical device  400 . Optical device  400 , shown as a cross-sectional view is an example of another optical device  100  ( FIG.  1 F ). 
     As stated previously with respect to optical device  100 , the optical device  400  can be transmissive or reflective. An example reflective optical device may include a reflector (not shown) to reflect an incident optical signal transmitted through the transmissive layer. The optical device  400  can be, for example, one or more of a lens, a meta lens, a phase delay diffractive optical element, or phase-transforming optical element. In should be noted that descriptions of optical device  400  are equally applicable to optical device  100 . 
     With reference to  FIG.  4 B , the recessed areas  404  and the non-recessed areas  408  are each considered features  402 , similar or equivalent to features  102  of  FIG.  1   . Each feature  402  has a circular shaped cross section if formed with any of the patterns discussed with respect to  FIGS.  3 A- 3 F . Furthermore, each feature  402  has a diameter, or characteristic dimension, suited for a particular wavelength of an optical signal to be propagated through the particular feature  402 . The features  402  may be subwavelength in size, which means the features are smaller than the wavelength of light incident to, emerging from, and/or transmitted by the feature  402 . The features  402  may also be larger than the wavelength of the light incident to, emerging from, and/or transmitted by the features. The features  402 , either alone or in conjunction with neighboring features  402  generate a specific phase delay or transformation to the light that is propagated through that particular feature  402 . 
     Any particular feature  402  includes either the dielectric material  202  having refractive index n 2 , or the optical medium  106  ( FIG.  1   ) having a refractive index n 1 . However, in the examples shown, a feature  402  does not include both (excluding portions of optical medium  106  above the transmissive layer  220  ( FIG.  1   ). 
     In some embodiments, a feature  402  is a discrete, circumscribed non-recessed area  408  surrounded by a recessed area  404 . In other embodiments, a feature  402  is a circumscribed post, column, pillar, or wall surrounded by a recessed area  404 . Yet in other embodiments, a feature  402  is a discrete, circumscribed recessed areas  404  surrounded by a non-recessed area  408 . A non-recessed area  408  may be a circumscribed hole, elongated region, or other shape surrounded by a recessed area  404 . In should be noted that a single embodiment of an optical device  400  may contain features  402  that are non-recessed areas  408  and other features  402  that are recessed areas  404 . 
     In some embodiments, the recessed areas  404  are filled with air, vacuum, or a material with a refractive index differing from the refractive index of the non-recessed areas  408 , e.g., of dielectric  202  layer. Alteration of the dimension of the features  402  changes the phase delay/phase function experienced by an electromagnetic or light wave propagating through the respective features  402 . 
     In one example, the height D of the dielectric layer  202  and the diameters of the features  402  are dimensioned such that, when an optical wave, with a particular wavelength, travels through the optical device  400 , the optical wave experiences a differential phase delay in a range 0 to 2π. In other words, the features, regions of features, and/or unit cells including features are sized and distributed to achieve a desired phase delay function as a set of features. Each etched pixel feature has a certain characteristic dimension (e.g., a diameter of a post or a hole). Alteration of the characteristic dimension changes the phase delay experienced by an electromagnetic wave propagating through the respective pixel feature. The thickness of the dielectric layer and the range of sizes for the pixel features may be selected to impart differential phase delay in the range 0 to 2π or in multiples of 2π radians. Thus, the arrangement of the disclosed pixel features can be considered as representing a phase delay function as a set of pixels, each having a substantially constant phase delay. 
     Due to the periodicity, any phase delay function can be replaced with an equivalent modulo 2π function. Therefore, each value of the phase delay function can be replaced by the corresponding value from 0 to 2π that differs from the original value by an integer multiple of 2π A phase delay function and its modulo 2π equivalent produce the same delay on an optical signal. In addition, phase delay functions that differ from one another at any given point by an integer multiple of 2π (and not necessarily the same multiple of 2π at each point) can be regarded as being equal to one another. 
     In some embodiments, the features  402  are sized and positioned irregularly, randomly, or pseudo-randomly. In other embodiments, the features  402  are arranged in a regular two-dimensional transverse lattice pattern across the optical device  400 . In some embodiments, the features  402  can be arranged in a two-dimensional spatial pattern. 
     The pattern of the features can be analogous to “digitizing” the phase delay function so there can only be certain discrete values determined by the spacing of the features. However, spatial averaging arising from the wave nature of an input optical signal tends to “smooth out” the “digitized” approximation and imparts a substantially continuous phase delay function or an operationally acceptable approximation thereof. An example optical device  400  can delay a light wave such that the phase of the light wave changes. 
     The pixel features  102  can likewise be arranged in several types of unit cells  600  of an optical device  100 ,  400 . For example,  FIG.  6 A  schematically illustrates several examples of unit cells  600  having none, one, or multiple circumscribed pixel features  102  (i.e., areal regions of posts or holes) for use in a transmissive layer of the disclosed optical device. 
     In other examples, each one of the pixel features  102  is arranged so that, within each unit cell  600 , a single simply connected volume of the first optical medium is surrounded by the second optical medium, or vice versa. For example,  FIG.  6 B  schematically illustrates several examples of unit cells  600  having only a single circumscribed pixel feature  102  (i.e., areal region of post or hole) of varying sizes. 
     Accordingly, each unit cell  600  of a non-empty subset of the grid pattern can have pixel features  102  arranged as one or more discrete, circumscribed non-recessed areal regions  408  surrounded by a recessed areal region  404  (i.e., circumscribed posts, columns, pillars, or walls surrounded by recessed areas) shown within unit cell  600 A of unit cells  600 . Alternatively, each unit cell  600  of a non-empty subset of the grid pattern can have pixel features  102  arranged as one or more discrete, circumscribed recessed areal regions  404  surrounded by a non-recessed areal region  408  (i.e., circumscribed holes or trenches surrounded by non-recessed areas) shown, for example within unit cell  600 B of unit cells  600 . Any given grid-based example can contain at least a subset of unit cells  600  of the post type (e.g. non-recessed areas  408 ) or at least a subset of unit cells  600  of the hole type (e.g. recessed areas  404 ); in some examples both types can be present. In addition to post-type or hole-type unit cells  600  (or both), some grid-based examples can also include a subset of unit cells  600  that are entirely recessed, a subset of unit cells  600  that are entirely non-recessed, or both. An example of such a cell  600  is shown as cell  600 C (although this view does not show whether the cell  600 C is entirely recessed or non-recessed). The pixel features  102  and or unit cells  600  can be arranged in two-dimensional spatial patterns to approximate a desired phase function.  FIGS.  7 A- 7 B  schematically illustrate a density distribution of pixel features  102  of a transmission layer  220  arranged to function as a lens. The higher-index layer (light shading in the figures) is produced in a pattern according to procedures disclosed herein. The resulting etched regions (dark shading in the figures) have a lower index. The arrangement produces an approximated modulo 2π quadratic phase function, which causes the resulting optical device  400  to act as a positive lens. 
     The foregoing description of preferred and other embodiments is not intended to limit or restrict the scope or applicability of the inventive concepts conceived of by the Applicants. It will be appreciated with the benefit of the present disclosure that features described above in accordance with any embodiment or aspect of the disclosed subject matter can be utilized, either alone or in combination, with any other described feature, in any other embodiment or aspect of the disclosed subject matter.