Patent Description:
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. <CIT> discloses a method of fabricating an optical device by producing features using two masks being offset relative to one another.

Thus, there is a need for overcoming, or at least reducing the effects of, one or more of the problems set forth above.

This objective has been achieved by a method of fabricating an optical device in accordance with claim <NUM>, including applying a resist layer to a dielectric layer for the optical device having a thickness; 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 wherein the at least one set of additional features is discrete from the set of first features; and producing the patterned grid of the first features and the additional features in the delectric layer, wherein the set of first features and the at least one set of additional features combine, based on the thickness, the period, the fraction of the period, the one or more first characteristic dimensions and the one or more additional characteristic dimension to impart a differential phase delay in a range <NUM> to 2π or multiple of 2π radians to an optical signal incident onto the optical device.

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 <NUM> center-to-center between adjacent ones of the first features in the first and second planar dimensions, where the first characteristic dimension ranges from <NUM> to <NUM>. In one aspect of the disclosure, the patterned grid of the features in the device layer is a rectangular grid having a period of <NUM> 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 <NUM> to <NUM>. In one aspect of the disclosure, the method may include designing the optical device to impart a differential phase delay in a range <NUM> 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.

The foregoing summary is not intended to summarize each potential embodiment or every aspect of the present disclosure.

The invention will be described based on figures. It will be understood that the embodiments and aspects of the invention described in the figures are only examples and do not limit the protective scope of the invention which is defined by the appended claims. It will be understood that features of one aspect or embodiment of the invention can be combined with a feature of a different aspect or aspects of other embodiments of the invention, in which:.

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 <CIT>; <CIT>; <CIT>; and <CIT> and in <CIT>.

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> shows a schematic cross-section of an example optical device <NUM> according to the present disclosure. The example optical device <NUM> is shown as being transmissive, which means light generally passes through the optical device <NUM>. The optical device <NUM> may include a substrate <NUM> and transmissive layer <NUM> that includes features <NUM> formed of dielectric layer <NUM> and/or an optical medium <NUM>. The dielectric layer <NUM> in example optical device <NUM> has a refractive index n<NUM>, and the optical medium <NUM> has a refractive index n<NUM> different from the refractive index n<NUM> of the dielectric layer <NUM>. The optical medium <NUM> can be solid, liquid, or gaseous, such as air or vacuum. The substrate <NUM> can be a solid material differing from the optical medium <NUM>.

In one arrangement, the dielectric layer <NUM> has a substantially uniform thickness, has a multitude of suitably sized and positioned perforations or holes <NUM>, and is immersed in the ambient optical medium <NUM> that surrounds the dielectric layer <NUM> and fills the holes <NUM>. The holes (also referred to as recesses herein) <NUM> and the intervening areas of the dielectric layer <NUM> form a plurality of features <NUM> that together form the transmissive layer <NUM> having the same substantially uniform thickness as the dielectric layer <NUM>.

The optical device <NUM> is structurally arranged so as to receive an optical signal <NUM> incident on the first surface <NUM> of the transmissive layer <NUM> and to transmit at least a portion of the incident optical signal <NUM> from a second surface <NUM> of the transmissive layer <NUM> as a transmitted optical signal <NUM> transformed according to the effective phase transformation function defined by the characteristic size and position of the features <NUM>.

The features <NUM> for the optical device <NUM> can be arranged in any suitable lattice pattern, e.g., triangular, square, rectangular, or hexagonal, or irregular patter. In one example, the features <NUM> are arranged in a lattice pattern having subwavelength (relative to the incident light <NUM>) features <NUM>, such that there may be little or no unwanted coherent scattering or diffraction from the transmissive layer <NUM>. Alternatively, the features <NUM> and/or the lattice may be larger than the wavelength if a different outcome is desired.

<FIG> shows a flowchart of an example method <NUM> for manufacturing disclosed optical devices, for example, optical device <NUM>, and will be discussed with reference to <FIG>. 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 <NUM>, a dielectric layer is disposed on top of a substrate. <FIG> shows a cross-sectional view of an example intermediate optical device 200A of an example optical device <NUM> (<FIG>). The intermediate optical device 200A includes a dielectric layer <NUM> disposed on top of a substrate <NUM> in accordance, for example, with step <NUM>. In some examples, the substrate <NUM> is an optically transparent substrate <NUM>, which can be, for example, glass or fused silica.

The dielectric layer <NUM> is, for example, etchable, has a certain refractive index n<NUM>, and a height D, which may be the same or about the same height as the resulting transmissive layer <NUM>. In this example, the dielectric layer <NUM> 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 <NUM> is made of the same material as the substrate <NUM> or is part of the substrate <NUM>.

At step <NUM> of method <NUM> (<FIG>), photoresist is applied on top of the dielectric layer. <FIG> shows the intermediate optical device 200B, which is the same or similar to the intermediate optical device 200A of <FIG> with photoresist <NUM> applied on top of the dielectric layer <NUM>, in accordance with step <NUM> of method <NUM>.

As will be discussed further below, at steps <NUM> and <NUM>, the photoresist <NUM> 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 <NUM>) allowing such features <NUM> 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 <NUM>, 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> shows a schematic top view of the photoresist <NUM> (<FIG>) with an example first pattern 201A. The first pattern 201A, as shown, includes first circles <NUM> representing example areas of exposure. The surrounding negative spaces (between first circles <NUM>) represent areas not yet exposed during the first or primary exposure. The first circles <NUM> have a distance P to the neighboring first circles <NUM>. In other words, the first circles <NUM> are arranged in a rectangular lattice with a center-to-center distance P. The first circles <NUM> 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 201A 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 <NUM> have characteristic dimensions, e.g., diameters, ranging from <NUM> to <NUM>. The first circles <NUM> may be disposed on a rectangular or square lattice with a side length between lattice points ranging from <NUM> to <NUM>. 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 <NUM>, the photoresist is secondarily exposed (through one or more additional exposures through repetition of step <NUM>) 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. <FIG> show some example patterns of photoresist after the photoresist is exposed to UV light through additional successive photomasks.

<FIG> shows a schematic top view of the photoresist with a second pattern 201B resulting from a second light exposure. The pattern 201B is produced by a second photomask (not shown in <FIG>) layered over previously exposed pattern 201A. The second light exposure created second circles <NUM> that are, for example, smaller in diameter than the first circles <NUM>. The second circles <NUM> are offset and disposed in between the first circles <NUM> at, for example, half the period distance P in the x-direction only. Therefore, if the lattice period P were <NUM>, then the second circles <NUM> would be offset <NUM> in a single linear dimension x, as shown.

<FIG> shows a schematic top view of the photoresist with a third pattern 201C resulting from a third light exposure (through repetition of step <NUM>). The pattern 201C is created with a third photomask (not shown in <FIG>) layered over previously exposed patterns 201A, 201B. The pattern 201C, may include, for example third circles <NUM> in addition to the first and second circles <NUM>, <NUM>. The third circles <NUM> are disposed between the first circles <NUM> in the y-direction at half the distance P. The third circles <NUM> are shown having the same diameter as the second circles <NUM>, but they need not be.

<FIG> shows a schematic top view of the photoresist with a fourth pattern 201D resulting from a fourth light exposure (through repetition of step <NUM>). The fourth pattern 201D is created with a fourth photomask (not shown in <FIG>) layered over previously exposed patterns 201A, 201B, 201C. The fourth pattern 201D may include, for example, fourth circles <NUM> in addition to the first, second, and third circles <NUM>, <NUM>, <NUM>. The fourth circles <NUM> may have, for example, the same diameter as the first circles <NUM> or they may be different. The fourth circles <NUM> are disposed between the second and third circles <NUM>, <NUM> at half the distance P in x- and y-direction. Thus, the resultant optical device of FIG. 2D would have features <NUM> of different characteristic dimensions on a resulting <NUM> grid assuming a P of <NUM> (250x250 nm features). The Line A-A in <FIG> shows an example cross-sectional plane representing the views of FIGS. 1A-1B, although the example optical device <NUM> may have differing patterns. As shown, through multiple successive exposures through different photomasks, a higher resolution pattern (e.g., 201D) can be obtained compared to, for example, pattern 201A.

Each of the first, second, third, and fourth circles <NUM>, <NUM>, <NUM>, <NUM> 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 <FIG> and described below.

<FIG> shows a schematic top view of the exposed photoresist with an alternative (fifth) pattern 201E. The pattern 201E 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 302E. The lattice of the pattern 201E has a triangular unit cell with circles 302E at each lattice point, and circles 304E, 306E, and 308E therebetween. Each lattice point has a distance P to the neighboring lattice points, i.e., the period between circles 302E.

The pattern may be formed using successive photomasks in a similar process as that described with reference to <FIG>. For example, a first photomask (and exposure) may be used to create the first circles 302E at each of the lattice points of the pattern 201E representing the exposed regions of the photoresist. A second photomask and exposure may then be used to create the second circles 304E offset a fraction of distance P. The second circles 304E of <FIG> are disposed between the first circles 302E along the axis d1 at half the distance P.

A third photomask and exposure may then be used to create the third circles 306E of the photoresist 201E. The third circles 306E are disposed between the first circles 302E along the axis d2 at half the distance P. A fourth photomask and exposure may then be used to create fourth circles 308E of the photoresist 201E. The fourth circles 308E are disposed between the first circles 302E along the axis d3 at half the distance P.

Each of the first, second, third, and fourth circles 302E, 304E, 306E, 308E are shown having varying diameters. However, the diameters of the first, second, third, and fourth circles 302E, 304E, 306E, 308E 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> or alternatively with different spacing between pattern circles. Further, the pattern need not be comprised solely of circular shapes.

<FIG> shows a schematic top view of the photoresist with a sixth example pattern 301F.

The sixth pattern 301F is created using a photomask (and exposure) with a hexagonal pattern to create circles 302F with a distance P from each circle 302F to the neighboring circle 302F. Additional photomasks can be used to create second circles at, for example, half the distance P. The circles 302F are shown, for example, having equal diameters. The circles 302F can be arranged in a lattice with any suitable pattern, e.g., triangular, square, rectangular, or hexagonal.

Upon completion of the exposures at step <NUM> of method <NUM> (<FIG>) and subsequent secondary exposure(s) at step <NUM> 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 <FIG>) are removed at step <NUM> 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 <NUM>, at step <NUM> of method <NUM>, the dielectric layer <NUM> 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 <FIG>). In other words, the dielectric layer <NUM> 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 <NUM> (<FIG>). In some embodiments, the dielectric layer <NUM> 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 <NUM>. The plasma is generated under low pressure or vacuum by an electromagnetic field. High-energy ions from the plasma attack the dielectric layer <NUM> and react with the dielectric layer <NUM> not covered with activated or exposed photoresist.

<FIG> shows a cross-sectional view of intermediate optical device 400A, which is the same or similar to the intermediate optical device 200B of <FIG>, after steps <NUM>, <NUM>, <NUM>, and <NUM> have been completed, in which areas of the dielectric layer <NUM> not covered by the patterned photoresist <NUM> have been removed, for example via etching, according to step <NUM>. The pattern of the dielectric layer <NUM> is resultant from the pattern of the photoresist <NUM>.

After the dielectric layer <NUM> is removed, e.g. etched, the dielectric layer <NUM> includes recessed areas <NUM>, that correspond to holes <NUM> (<FIG>), and non-recessed areas <NUM>, that will correspond to the dielectric layer <NUM> of <FIG>.

At step <NUM> of method <NUM>, the remaining photoresist <NUM> may be removed from dielectric layer <NUM>. The photoresist <NUM> 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 <NUM>. Another method for removing the photoresist is using <NUM>-Methyl-<NUM>-pyrrolidone (NMP) solvent. Following removal of the remaining photoresist <NUM>, the resulting optical device <NUM> (<FIG>) may be used as is with the ambient atmosphere filling in the recessed areas <NUM> or an alternative optical media <NUM> may be added to optical device <NUM>. Optical device <NUM>, shown as a cross-sectional view is an example of another optical device <NUM> (FIG.

As stated previously with respect to optical device <NUM>, the optical device <NUM> 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 <NUM> 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 <NUM> are equally applicable to optical device <NUM>.

With reference to <FIG>, the recessed areas <NUM> and the non-recessed areas <NUM> are each considered features <NUM>, similar or equivalent to features <NUM> of <FIG>. Each feature <NUM> has a circular shaped cross section if formed with any of the patterns discussed with respect to <FIG>. Furthermore, each feature <NUM> has a diameter, or characteristic dimension, suited for a particular wavelength of an optical signal to be propagated through the particular feature <NUM>. The features <NUM> 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 <NUM>. The features <NUM> may also be larger than the wavelength of the light incident to, emerging from, and/or transmitted by the features. The features <NUM>, either alone or in conjunction with neighboring features <NUM> generate a specific phase delay or transformation to the light that is propagated through that particular feature <NUM>.

Any particular feature <NUM> includes either the dielectric material <NUM> having refractive index n<NUM>, or the optical medium <NUM> (<FIG>) having a refractive index n<NUM>. However, in the examples shown, a feature <NUM> does not include both (excluding portions of optical medium <NUM> above the transmissive layer <NUM> (<FIG>).

In some embodiments, a feature <NUM> is a discrete, circumscribed non-recessed area <NUM> surrounded by a recessed area <NUM>. In other embodiments, a feature <NUM> is a circumscribed post, column, pillar, or wall surrounded by a recessed area <NUM>. Yet in other embodiments, a feature <NUM> is a discrete, circumscribed recessed areas <NUM> surrounded by a non-recessed area <NUM>. A non-recessed area <NUM> may be a circumscribed hole, elongated region, or other shape surrounded by a recessed area <NUM>. In should be noted that a single embodiment of an optical device <NUM> may contain features <NUM> that are non-recessed areas <NUM> and other features <NUM> that are recessed areas <NUM>.

In some embodiments, the recessed areas <NUM> are filled with air, vacuum, or a material with a refractive index differing from the refractive index of the non-recessed areas <NUM>, e.g., of dielectric <NUM> layer. Alteration of the dimension of the features <NUM> changes the phase delay / phase function experienced by an electromagnetic or light wave propagating through the respective features <NUM>.

In one example, the height D of the dielectric layer <NUM> and the diameters of the features <NUM> are dimensioned such that, when an optical wave, with a particular wavelength, travels through the optical device <NUM>, the optical wave experiences a differential phase delay in a range <NUM> 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 <NUM> 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 <NUM> 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 <NUM> are sized and positioned irregularly, randomly, or pseudo-randomly. In other embodiments, the features <NUM> are arranged in a regular two-dimensional transverse lattice pattern across the optical device <NUM>. In some embodiments, the features <NUM> 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 <NUM> can delay a light wave such that the phase of the light wave changes.

The pixel features <NUM> can likewise be arranged in several types of unit cells <NUM> of an optical device <NUM>, <NUM>. For example, <FIG> schematically illustrates several examples of unit cells <NUM> having none, one, or multiple circumscribed pixel features <NUM> (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 <NUM> is arranged so that, within each unit cell <NUM>, a single simply connected volume of the first optical medium is surrounded by the second optical medium, or vice versa. For example, <FIG> schematically illustrates several examples of unit cells <NUM> having only a single circumscribed pixel feature <NUM> (i.e., areal region of post or hole) of varying sizes.

Accordingly, each unit cell <NUM> of a non-empty subset of the grid pattern can have pixel features <NUM> arranged as one or more discrete, circumscribed non-recessed areal regions <NUM> surrounded by a recessed areal region <NUM> (i.e., circumscribed posts, columns, pillars, or walls surrounded by recessed areas) shown within unit cell 600A of unit cells <NUM>. Alternatively, each unit cell <NUM> of a non-empty subset of the grid pattern can have pixel features <NUM> arranged as one or more discrete, circumscribed recessed areal regions <NUM> surrounded by a non-recessed areal region <NUM> (i.e., circumscribed holes or trenches surrounded by non-recessed areas) shown, for example within unit cell 600B of unit cells <NUM>. Any given grid-based example can contain at least a subset of unit cells <NUM> of the post type (e.g. non-recessed areas <NUM>) or at least a subset of unit cells <NUM> of the hole type (e.g. recessed areas <NUM>); in some examples both types can be present. In addition to post-type or hole-type unit cells <NUM> (or both), some grid-based examples can also include a subset of unit cells <NUM> that are entirely recessed, a subset of unit cells <NUM> that are entirely non-recessed, or both. An example of such a cell <NUM> is shown as cell 600C (although this view does not show whether the cell 600C is entirely recessed or non-recessed). The pixel features <NUM> and or unit cells <NUM> can be arranged in two-dimensional spatial patterns to approximate a desired phase function. <FIG> schematically illustrate a density distribution of pixel features <NUM> of a transmission layer <NUM> 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 <NUM> 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.

Claim 1:
A method of fabricating an optical device (<NUM>,<NUM>), the method comprising:
- applying a resist layer (<NUM>) to a dielectric layer (<NUM>) for the optical device(<NUM>,<NUM>) having a thickness;
- producing a set of first features (<NUM>, <NUM>) in the resist layer (<NUM>) using a first mask, the first features (<NUM>, <NUM>) arranged in a period in a patterned grid and having one or more first characteristic dimensions;
- producing at least one set of additional features (<NUM>, <NUM>) in the patterned grid in the resist layer (<NUM>) using at least one additional mask offset at a fraction of the period in at least one planar dimension from the first features (<NUM>, <NUM>), the additional features (<NUM>, <NUM>) having one or more additional characteristic dimensions, wherein the at least one set of additional features is discrete from the set of first features; and
- producing the patterned grid of the first features (<NUM>, <NUM>) and the additional features (<NUM>, <NUM>) in the dielectric layer (<NUM>);
- wherein the set of first features and the at least one set of additional features combine, based on the thickness, the period, the fraction of the period, the one or more first characteristic dimensions and the one or more additional characteristic dimension to impart a differential phase delay in a range <NUM> to 2π or multiple of 2π radians to an optical signal incident onto the optical device.