Optical Retarders and Methods of Making the Same

TECHNICAL FIELD

This disclosure relates to optical devices, and more particularly to optical retarders.

BACKGROUND

Optical devices and optical systems are commonly used where manipulation of light is desired. Examples of optical devices include lenses, polarizers, optical filters, arnireikeCion films, retarders (e.g., quarter-wavepiates), and bean) splitters (e.g., polarizing and non-polarizing beam splitters).

SUMMARY

In general, in a first aspect, the invention features an article that includes a first layer including spaced-apart rows of a first materia], and a second layer supported by the iirsi layer, the second layer including spaced-apaxt rows of a second material, where the rows of the first layer extend along a first direction and the rows* of the second layer extend along a second direction non-parallel with the first direction, and each layer is independent Iy bireiringent for light of a wavelength λ propagating along art axis that intersects the first and second layers, where λ is in a range from about ISO mi\ to about 5,000 rim.

Embodiments of the article may include one or more of the following features and/or features of other aspects.

The first and second materials may be different.

At bast one of the first and second materials may be a dielectric material, and ihe dielectric material may be selected from a group consisting of SiO _.? . SiN _x . Si, AbO., ZrO ₃ , Ta ₂ O^, TiQ>, I lfOr, Nb ₃ O ₅ , and MgF ₂ . At least one of ihe first, and second materials may be a nanoϊaniinatε material, and may include one or more materials selected from a group consisting of Si(>>, SiN,. Si, AI ₂ Oj ₅ ZrO ₂ , Ta ₂ Os, TiO ₂ , HfO ₃ , Nb ₂ O ₅ , and MgF ₂ .

The article may further include a third layer supported by the second layer and including spaeed-apart rows of a third material extending along a third direction that is non-paraiie. with, at least one of the first and second directions, where the third layer i.s birefri agent for light of wavelength λ propagating along an axis that intersects the first second, and third layers. For example, the third direction of the rows of the third material may he parallel with one of the first and second directions, or the third direction of the rows of the third material may be non-parallel with both of the first and second directions. At least one of (he first, second, and third materials may- include a dielectric material selected from a group consisting of SiO; _. , SiN _x , Si ₅ Al ₂ O ₃ , ZrO>, Ta ₂ O ₅ , TiO ₂ , HfO ₂ . Nb ₂ O ₅ , and MgF,. Further, each of the first second, and third materials may be a nanolarninafe material independently selected from the group consisting of SiO., SiN _x . Si, AbO,, ZrO,, Ta ₂ O ₅ , TiC) ₂ , JIR) ₂ , Nb ₂ O ₅ , and MgF ₂ .

The first layer may include rows of a third material alternating with the spaeed-apart rows of the first material and extending along the first direction, the third material being different from the first material . The third material may define a substrate, the rows of the third material may be defined by walls of trenches within the substrate, and the first material maybe disposed within the trenches. The first and third materials may be dielectric materials. For example, the first material may be selected from (he group consisting of SiO;., SiN _* , Si, Al ₂ Oj, ZrO^, Ta ₃ Os, TiOz, HtDj, Nt>>P:j, and MgF;. The first material may further be a nanohmiinate material. A layer of the first material may be disposed between the rows of the first layer and the rows of ihc second layer. The layer of the first material may be contiguous with the rows of the first material of the first layer. An antireflection film may be disposed between the layer of the first materia! and the rows of the second material of the second layer. The second layer may include rows of a fourth material alternating with the spaeed-ap&ri rows of the second material and extending along the second direction, the fourth material being different from the second material. The fourth material may define a substrate, the rows of the fourth material may be defined by walls of trenches within the substrate, and the second material may be disposed within the trenches. The second and fourth materials may be dielectric materials. The first material and

second materials may include one or more materials selected from the group consisting Of SiO ₂ , SiN _x , Si, Al ₂ O ₃ , ZrOj, Ta ₂ O ₅ , TiO ₂ , HfO _2; Nb ₂ O ₃ , and MgF ₂ .

An angle ^; between the first and second directions may be at least about Kf. For example, the angle may be at least about 20°. The angle may be about 80" or less, For example, the angle may be about 70 ^' ' or less.

An angle between the first and second directions may be about SCf or less. For example, the angle may be about. 70° or less.

The fsisi layer may be a monolithic Saver, The first material of the first layer may be a nanolaminafe material. The second layer may be a monolithic layer. An arstireflecikm film may be disposed between the first and second layers.

The first and second layers may each independently have an optical retardation of at least about 1 urn for light of the wavelength λ. For example, the first and second layers may each independently have an optical retardation of at least about 5 nm for light of the wavelength λ, or the first and second layers may each independently have an optical retardation of at least about H) nm for light of the wavelength λ. or the first and second layers each independently have an optical retardation of ai least about 50 nm for light of the wavelength λ.

The wavelength X may be between about 400 nm and about 700 nm.

The wavelength λ may be between about. 1.20(J nm and about 1 ,600 nm. One of the first and second layers may have an optical retardation that is greater than the optica! retardation of the other layer, and a difference between the optical retardations of the first and second layers may be at least about 1 nm for light of the wavelength λ. The wavelength λ may be between about 400 nm and about 700 nm. One of the first and second layers may have an optical retardation that is greater than the optical retardation of the other layer, and a difference between the optical retardations of the first and second layers may be at least about 5 rim for light of the wavelength λ.

A combined thickness of the first and second layers may be about 9 microns or less. For example, the combined thickness may be about ό microns or less, or about 3 microns or less. The first and second layers may each independently have a thickness

of about 5 microns or less. For example, the first and second layers may each independently have a thickness of about 1 micron or less, or about 500 nm or less.

Centers of successive rows of the first layer may be spaced apart by about 400 n.m or less. For example, centers of successive rows of the first layer may be spaced apart by about 200 ran or less.

The first layer .may retard incident radiation, at wavelength λ by an amount l ^" _\ , the second layer may retard incident radiation at wavelength λ by an amount F->, and I ^" i and n may each be ai least about π/4. For example, at least one of T ₅ and T: may be at least about π/2. As another example, one of i "i and 1\ may be about π/4 and the other of F? ami l\ may be about π/2. A third layer may be supported by the second layer and may include spaced-apart rows of a third material extending along a third direction that is non-parallel with at least one of the first and second directions, the third layer may be birefringent for light of wavelength λ propagating along an axis that intersects the first, second, and third layers, and the third layer may retard incident radiation at wavelength λ by an amount Fj that is at least about κ/4. For example, at least one of Fj, i %, and Fj may be at least about π/3. The third direction. maybe non-parallel wiih both of the first and second directions. The article may retard incident radiation at wavelengths λ _\ and λi by respective amounts V- and F ₃ , where J λ _s - λ ₂ j may be ai least about 15 nm, and F ₅ ami \ ^' \ may be substantially equal.

^" F ^' he article may retard incident radiation at wavelengths λ; and λ; by respective amounts Fj and F^, where { λs ^■ - λi J may he ai least about 15 nm. F= and T^ may be substantially equal and both X\ and λi may be in a range from about 150 nm to about 5, {)()() nm. For example, λi - λ/> j may be at least about 30 am, or at least about 75 nm, or at least about 100 nm, or at least about 200 nm. The difference in reiardance expressed by j f\ -- i ^' % may be about 0.03π or less, for example, such as about 0.02π or less., or about 0.01 Jt or less. A system that includes the article may also include a polarizer, where the article and polarizer are configured so that during operation the polarizer substantially polarizes radiation of wavelengths λ> and λ _;> prior to the radiation being received by the article. The article may transmit radiation received by the article and the system may further include a second polarizer

configured so thai during operation the second polarizer receives radiation after the radiation is transmitted by the article.

A system that includes the article may also include a polarizer, where the article and polarizer are configured so that during operation the polarizer substantially polarizes radiation of a wavelength λ prior to the radiation being received by the article. The article may transmit radiation received by the article and the system may further include a second polarizer configured so that during operation the second polamer receives radiation after the radiation is transmitted by the article.

Iii another aspect, the invention features an article that includes a first layer including spaced- apart rows υf a first material, the centers of adjacent rows of the first material being spaced apart by about 400 nm or less, and a second layer supported by the first layer, the second layer comprising spaced -apart rows of a second material, the centers of adjacent rows of the second material being spaced apart by about 400 mil or less, where the rows of the first layer extend along a first direction and the rows of the second layer extend along a second direction non-parallel with the first direction.

Embodiments of the article may include one or more of the following features and/or features of other aspects/The article may retard incident radiation at wavelengths λj and λ ₂ by respective amounts I ^' j and IY where j λ _s - λ> j may be ai least about 15 nm, F-. and F ₂ may be substantially equal, and both λ\ and ^') ✓> may be between about ! 50 nm and about 5,000 nm. For example, j λs - A ₂ j ra&y be at least about 30 ntii. At least one of the first and second materials may include at least one dielectric material selected from a group consisting of SiQ^, SiN _x , Si, Al ₂ Ch, ZrOj, Ta ₂ Os, TiO ₂ , HK) ₂ , Nb ₂ O ₅ , and MgF ₂ . At least one of the first and second materials may be a αaπαlamrnatε material.

In another aspect, the invention features an article that includes a first layer comprising spaeed-apart rows of a first material, and a second Saver supported by the first layer, the second layer comprising spaeed-apart rows of a second material, where the rows of the first layer extend along a first direction and the rows of the second layer extend along a second direction non-parallel with the first direction, and the article retards incident radiation at wavelengths λi and λ? by respective amounts I ^' s

and I 2, where j λj - λ; \ is at least about 15 nm, Fi and ϊ\ are substantially equal and both λ _s and λ _; > are in a range .from about 150 nrn to about 5,(K)O nπs.

Embodiments of the article may include one or more of the following features and/or features of other aspects. At. least one of the first and second materials may be a nariolammaie material. At least one of the first arsd second materials may include at least one dielectric material selected from a group consisting of SiCK SiNk-, Si, AI _J O ₃ , ZrO-., Ta ₇ Os, TiO ₂ , HlO ₂ , Nb ₂ O ₅ , and MgF ₂ . in another aspect, the invention features an article that includes a form bireiringerst grating oriented along a first direction, and a second grating supported by the form birefrmgent grating and oriented along a second direction non-parallel with the first direction, where the article is birefrmgeπt for light of a wavelength λ incident on the article, where λ is in. a range from about 1.50 am to about 5,(300 nm.

Embodiments of the article may include one or more of the following features and/or features of other aspects/The form blrefringent grating can include rows formed of a dielectric material and extending along the first direction. The rows may be separated by trenches, and the trenches may be filled with a rntrsolaminate material. The second grating may be a form bircfringent grating.

The foπn bireiϋngent grating and the second grating may be spaced apart by about 2 microns or less. in ^mother aspect, the invention features an article that includes a first layer including spaced-apart rows of a naπolaminate material, the rows of nanolamύmte material extending along a first direction, and a second layer supported by the first layer, the second layer including spaced-apart rows of a second material extending along a second direction non-parallel with the first direction. Embodiments of the article may include one or more of the features of other aspects,

In another aspect, the invention features a .method that includes disposing a first layer over a second layer, the first layer including spaced-apart rows of a first material and the second layer including spaeed-apart rows of a second material, each layer being independently birefiingent for light of a wavelength λ propagating along an axis that intersects that layer, where disposing the first layer over the second layer includes disposing the rows of the first layer along a first direction and disposing the

rows of the second layer along a second direction non-parallel with, the first direction, and where λ is m a range from about 150 nro to about 5,000 mil,

Embodiments of the method may include one or more of the fallowing features and/or features of other aspects.The method may further include forming the spaced-apart rows of the second materia!. Forming the spaced-apart rows of the second material may include depositing the second material within each of multiple ■spaeed-apait trenches disposed within a substrate. The second material may be deposited using atomic layer deposition. Alternatively, depositing the second material mjiv include forming the second materia! as a narioiarøinate within the spaced- apart trenches.

The method may further include forming the spaced-apart rows of the first material ^' The substrate may be a second substrate and forming the spaced -apart rows of the first material may include depositing the first material within each of multiple spaced-apart trendies disposed within a first substrate, where the trenches of the first substrate extend along the first direction and the trenches of the second substrate extend along the second direction. The first materia! may be deposited in the trenches using atomic layer deposition. Alternatively, depositing the first materia! may include forming the first material as a nanoiaminate within the spaeed-apart trenches of the first substrate. Disposing the first layer over the second layer may include depositing the first substrate over the second layer.

The method may further include forming a second material layer of the second material prior Io disposing the first layer over the second layer, the second material layer being formed over the spaced-apart rows of the second material within the trenches, and where disposing the first layer over the second layer includes disposing the first foyer over the second materia! layer.

The method may further include forming an arttireflection film on at least one of the first and second layers, where disposing the first layer over the second layer includes disposing the first layer over the second layer so that the antirefiectkm layer is between the first and second layers, In another aspect, the invention features a method that includes forming a first layer including spaced-apart rows of a first material using atomic layer deposition, the

rows of the first material extending along a first direction, and disposing a second layer over first layer, the second layer including spaced-apart rows of a second material extending along a second direction non-parallel with the first direction.

Embodiments of the method may include one or more of the following features and/or features of other aspects.The first materia! may be a nanokminate material.

Forming the spaced-apart rows of the first material may include depositing the first material within each of multiple spaced-aparf trenches, the trenches extending along the first direction. Forming the spaced-apart rows of the first material may further include depositing a layer of the first material that extends over at least some of the spaced-apart rows of the first material. Disposing the second layer over the rows of first material may include forming the spaced-apart rows of the second material over the first layer, and may further include forming an antircfiecUon film over the first layer prior to forming the spaced-apart rows of the second material. Forming the spaced-apan rows of the second material may include depositing the second materia! within each of multiple spaced-apart trenches that extend along the second direction. The second .materia! may be a naπolaminate material.

In another aspect,, the invention features an article that includes a first grating that is form birefrirsgerst tor light having a wavelength λ less than about 2000 ran, and a second grating positioned adjacent the first grating, the second grating also being form brrefringent for light having a wavelength λ, where the article is an achromatic retardcr for light in a range of wavelengths less than 2000 run incident on the article along a path that intersects both the first and second gratings.

Embodiments of the article may include one or more of the following features arid/or features of other aspects. in another aspect, the invention features an article that includes a first layer including spaeed-apari rows of a first materia!, and a multilayer film adjacent the first layer, where the first layer and the multilayer film arc each independently birefringeot for light of a wavelength λ propagating along an axis that intersects the first layer arsd the multilayer film, and λ is in a ranae from about 150 rim to about 5,OCK) nm.

Embodiments of the article may include one or more of the following features and/or features of other aspecls.The article may further include a substrate supporting the Orsi layer and the multilayer film. The first layer and the multilayer film may be disposed on opposite sides of the substrate. Alternatively, the Orsi layer and the multilayer film may be disposed on the same side of the substrate. The article may further include a second multilayer film disposed on an opposite side of the substrate to the first multilayer Him, the second multilayer film being birefringent for light of wavelength λ propagating along the axis that intersects the first layer and the multilayer iihn. The structures of the first and second multilayer firms may be identical.

The first layer may be supported by the multilayer film. The multilayer film may be supported by the first layer. A seeoml layer may be disposed between the first layer and the multilayer film. Rows of the first layer may define a first plane and the layers of the multilayer film may each define a respective plane parallel to and offset from the first plane.

The multilayer film may include alternating layers formed of second and third materials. At least one of the second and third materials may he a nanolanimate material. The first material and at least one of the second and third materials may be materials independently selected from a group consisting of SiO-.> ₅ SiN _x , Si, AhO;, ZrO ₂ , Ts ₂ O ₅₅ TiO ₅ , HLfO ₂ , Nh ₂ C) ₅ , and MgF..

The first layer may further include rows of a second material alternating with the spaeed-apait rows of the first material. The second material may define a substrate, the rows of the second material may be defined by wails of trenches within the substrate, and the first material may bε disposed within the trenches. The first layer may further include a layer of the first material disposed between the rows of the first layer and the multilayer film.

The multilayer film may include a total of EU least about ! 5 layers of each of second and third different materials. For example, the multilayer film may include a total of at least about 35 layers of each of the second and third materials.

The layers of the multilayer film may each be about 100 nm thick or less.

The article may farther include a second layer that includes spaeed-apari rows of a second material, and the second layer may be independent] y birefringeπt for light of a wavelength λ propagating along an axis that intersects the first and second layers and the multilayer film. The rows of the first materia! may extend along a first direction and the rows of the second layer may extend along a second direction non- parallel with the first direction. The first and second layers may be disposed on a common side of the multilayer film. Alternatively, the first and second layers may be disposed on opposite sides of the multilayer film. An angle between the first and second directions may be about 80° or less. For example, the angle may be about 70" or less. The angle between the first and second directions maybe about lϋ ^c; or more. For example, the angle may be about 20° or more. The first and second layers together may retard incident radiation at wavelengths λj and λ _; > by respective amounts Vi and r>, where j λs ~- ?o j may be at least about 15 nns. H &ftd Fs may be substantially equal, and both λj and λ ₂ maybe in a range from about 150 nm to about 5,000 nm. For example, j λ; - 1 ₂ J may be at least about 30 nm, such as at least about 75 am, or at least about 100 nm, or at least about 200 nm. The retardation difference expressed by | T ₅ - V ₂ j may be about G.03τt or less, such as about 0.02π or less, or about O.Oi ii or less. The article may further include an antireilectkm film disposed between tbe multilayer film and the first and second layers. A combined thickness of the first and second layers and the multilayer film may be about 10 microns or less. A total thickness of the multilayer film maybe about 2 microns or less.

The multilayer film may include a plurality of layers where alternating layers have different refractive indexes at λ and each of the plurality of layers m the multilayer film has a thickness in a range from about 2 nm to about 500 nm. In another aspect, the invention features an optical retarder for light having a wavelength of about 5,000 am or less, the optical retarder including a form hirefringeπt opiate for radiation at a wavelength λ, and a form birefrmgent opiate for radiation at λ, where λ is about 5,000 nm or less.

Embodiments of the optical retarder may include one or more of the following features and/or features of other aspects.

In another aspect, the invention features a method that includes using atomic layer deposition to deposit a multilayer film on a surface of a substrate, where the multilayer tlim is a form birefringent c-plate for light having a wavelength λ and λ is hi a range from about 150 nrn to about 5,000 πin. Embodiments of the method may include one or more of the following features ami/or features of other aspects.The substrate may include a form birdringαit α-platc. where the tv-plate is bireϋingent for light having wavelength λ.

The method may further include forming a form birerringerrt a-plaie on the multilayer iilm, where the α-plate is birefringent for light of wavelength λ. Embodiments of the articles may include one or more of the following advantages. For example, embodiments may includes optical retarders that are formed entirely from non-organic materials (e.g., non-organic dielectric materials). Non-organic optical retarders may be more durable than optical retarders thai, include organic materials, such as organic polymers. For example, non-organic materials are less susceptible to degradation when exposed to radiation for extended periods (e.g., to intense and/or high energy radiation, such as ultraviolet radiation). Aa a result, applications that utilize the optical retarders may display better long term performance than applications that utilize organic optica! retarders. As an example, one application that typically uses an optical retarder is a light modulators (e.g., liquid crystal displays) in a projection display system. Moreover, such light modulators are typically exposed to .intense broadband optical radiation for prolonged periods (e.g., about 10,(300 hours over the lifetime of the system). Where non-organic retarders are used in such a projection system, the system can exhibit more consistent performance over its lifetime than a system using an organic retarder. Non-organic optical retarders may also he less susceptible to environmental hazards than comparable retarders that include organic materials. For example, many organic polymeric materials are susceptible to moisture and/or organic solvents, while certain dielectric, non-organic materials are not. Accordingly, optical retarders formed exclusively from non-organic materials maybe less susceptible to moisture and/or organic solvents than optical retarders formed from organic materials.

In embodiments, optical retarders ears be used in high energy regions of the electromagnetic spectrum. For example, due to the high stability of the materials when exposed to high energy radiation., and their versatility of the manufacturing process, optical retarders can be made- for operation in the ultraviolet portion of the spectrum (e.g , from about 150 nm to about 400 nxn). As an example, optica ^] retarders can be made for use in photolithography tools which utilize radiation at, e^., about 193 nm.

Optica! retarders can include exclusively monolithic form birefrirsgeni layers (e.g., layers with optical but not physical nanostructure). Monolithic layers may be more mechanically robust than physically structured layers, and hence less susceptible to delects that adversely impact their optical performance, such as scratches.

Embodiments include optical retarders that are operative over extended wavelength ranges (e.g., about 100 ran or more, about 200 nm or more, about 300 nm or more, about 400 nm or more). For example, some optical retarders may be operative over substantially the entire visible portion of the electromagnetic spectrum. in some embodiments, optica] retarders can have a substantially constant retardation across the extended wavelength range (eg., about quarter wave retardation across the extended wavelength range).

Embodiments of optical retarders may be designed and fabricated tor operation at one or more wavelengths within a broad wavelength, range, In particular. the versatility of the manufacturing processes -used to fabricate the optical retarders in addition io the number of structural parameters of the optical retarders that can be varied allow structures to be optimized for a wavelength or wavelength band in the ultraviolet, visible, or infrared portion of {be electromagnetic spectrum. For example, the thickness, grating period, and grating duty cycle of a fonn-bireftingent _t ?-piate retardation layer can be easily varied in the fabrication process, providing .substantial flexibility for forming optical retarders with specific birefringence and/or retardation at a chosen wavelength of operation. Furthermore, a variety of different materials can be used to form optical retarders, including nanolarainate materials, which allows substantially .flexibility in the refractive index of different portions (e.g., rows or layers) of optical retarders.

Structures with relatively low mechanical stress can also be formed. For example, form birefringent opiate retardation films can be formed on opposing sides of a substrate, rather than on a single side, providing a more symmetric structure that has Sower mechanical stress than an optical retarder with comparable optical properties where the c-piate retardation iilm is formed on one side of the substrate. Layers can be sπmdtaneously deposited on opposing sides of a substrate using, for example, atomic layer deposition.

Optical reorders may be relatively thin compared to other types of optical retarders with comparable optical properties (e.g., polymer or crystalline optical retarders). For example, the birefringent retardation layers in an optical retarder can have a total thickness of about U) microns or less (e.g., about five microns or less, about two microns or less).

Optical retardation layers can be readily integrated with other components in an optical system. For example, foπn-birefringent retardation layers can be termed on substrates that are subsequently integrated into, for example, a liquid crystal display or a laser. As a result, the optical retarders can be used in optica! devices with relatively small form factors.

Optical retarders may be zero-order optical retarders. Zero-order optical retarders can have larger ranges of incident operating angles aad/or reduce wavelength sensitivity relative to non-zero-order optical retarders.

Optical retarders cars exhibit relatively small optical changes as a function of temperature over an operating temperature range, for example, optical retarders can be formed from material pairings that have complementary thermal properties, In other words, material pairings can be selected so that variations in the optica! properties of one material due to temperature changes can be offset by the variations in the optical properties of the other material

'The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent frtsm the description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FlG I A is a cross-sectional view of an embodiment of an optical retarder.

FIG I B is a perspective view of retardation layers in the optical retarder shown in PlG. I A. FiG. 2 A is a plan view of a retardation layer in the optical retarder shown in

FlG I A.

RG 28 is a plan view of a second retardation layer in the optical retarder shown in FICi LA.

FIG 3 is a cross-sectional view of another embodiment of an opticas retarder, FiG 4 is a cross-sectional view of a further embodiment of an optical retarder.

FIG 5 is a cross-sectional view of an embodiment of a retardation film with its c axis oriental parallel to the z~axis.

RG 6 is a cross-sectional view of another embodiment of an optical retarder.

FIG 7 A is a cross-sectional view of a further embodiment of an. optical retarder,

FiG. 7 B is a cross-sectional view of another embodiment of an optical retarder.

FϊG. 8A-8J are schematic diagrams showing various steps m a process lor fabricating retardation layers in an optical retarder.

FIG 9 is a schematic view of an apparatus for atomic layer deposition. FIG 10 js a flow chart showing steps in an implementation of atomic layer deposition.

FIG 1 1 is a cross-sectional view of an embodiment of a circular polarizer that includes an optical retarder,

FiG 12 is a schematic diagram of an embodiment of an optical pickup thai includes an optical retarder,

FIG 13 is a cross-sectional schematic diagram of an embodiment of a liquid crystal display that includes a pair of optical retarders.

Like reference symbols in the various drawings indicate like elements,

DETAILED DESCRIPTION

Referring to FIG, 1 A, an optical retarder 100 includes a first retardation layer 110 and a second retardation layer 120. Both retardation layers 110 and 120 are hire frhi gent for incident radiation at a wavelength λ. In general, λ cars be m the ultraviolet (e.g., from about 100 am to about 400 nrn), optical (e.g., from about 400 πϊTS to about 700 nm), or infrared portions (e.g., from about 700 nm to about 20,000 mi)) of the electromagnetic spectrum. A substrate 130 supports first and second retardation layers HO and 120. A Cartesian, co-ordinate system is provided for reference and optical retarder K)O extends in the x-y plane, Referring also to FiG. 18, FIG 2A, and FIG. 2B, first retardation layer HO includes a series of spaced-apart rows ! 1 1 of a first material separated by a aeries of spaeed-apart rows 1 12 of a material different from the first material Rows 1 11 and 112 both extend substantially parallel to the>>-d?reciion. Second retardation layer 120 also includes a series of spaeed-apart rows 121 of a second material separated by a spaced apart-rows 122 of a material different from the second material, ^[ lows 121 and 122 both extend along a direction at an angle φ with respect to the >-direetioB, a.rκ! form a grating that is periodic in a direction that is at angle φ with respect to thex- diredion.

Rows 1 1 ! and 112 have widths λj j j and λ, ;; in the x-direction, respectively, Rows 111 and 1 1.2 form a periodic grating in layer 1 SO. The grating in layer 1 K ⁾ lias a grating period λπo _> which is equal to λ> π + Am- Similarly, rows 121 and 122 have widths As _{?. !} and λ;r>, respectively, forming a periodic grating in layer 120. The grating in layer 120 has a period λ _t2< > which is equal to λm ⁺ A _t2 τ. Layer 100 and layer 120 have thicknesses d and f/'iπ the ^-direction, respectively. Layers 1 10 and 120 are form hirefriπgent. for radiation having wavelengths greater than λ;κ _> . hi other words, even though the materials composing layers ϊ 10 and ! 20 are optically isotropic at λ, the structure of the layers (e.g., the alternating spaoed-apart rows) result, in each layer being birefringent for radiation at λ. Accordingly, different polarization states of radiation having wavelength λ propagate through layers 110 and 120 with different phase shifts. For each layer, the phase shift

between the orthogonal polarization states depend on the thickness of the respective layer (e.g., d for layer 1 10 and d' for layer 120), the index of refraction at λ of each portion in the layer, the grating period in each layer and ihe grating's duty cycle. Accordingly, for each layer, these parameters can be selected to provide a desired amount of retardation of optical retarder 100 to polarized light ai a wavelength λ.

Each retardation layer can he thought of as an effective uniaxial optical material having a birefringence, An(λ), at wavelength λ, which corresponds to \π _c - « _; J, where n _? and «„ are the effective extraordinary and effective ordinary indexes of refraction, respectively; for that retardation layer. The effective extraordinary axis corresponds to the refractive index of the layer foτ radiation polarized parallel to the optica! ax is of the effective uniaxial optica! materia!, in retardation layer 1 ! O ₅ for example, the optica! axis of the layer is parallel to the y-axis. Accordingly, for this layer, the effective ordinary index of refraction is the index of refraction experienced by radiation having its electric field polarized parallel to the A-- axis, while the effective extraordinary index is the index of retraction experienced by radiation having its electric polarized parallel to the v-axis. In retardation layer 120, the optica! axis is at an angle ^ with respect to the y-axis, parallel to portions 121 and 122. Retardation layers 1 10 and 120 are examples of so called α-plates, ^" having their optical axes in the plane of the respective layers, the x-y plane. In general, the values of n _c and n _o depend on the indexes of refraction of the portions in each layer, the width of each portion in the layer, and on the radiation wavelength, λ. Without wishing to be bound by theory, the ordinary and extraordinary index for each retardation layer can be determined according to the oαisatioπs;

where a and β respectively correspond to Am and λ _} ;;< i'br layer 110 and to λκ>f and λ _r > ₂ for layer 120. « ₃ and m correspond to n»jj and m^ respectively; for layer UO and to Tiyjt and nπ>, respectively, for layer 120. hi some embodiments, 4/?(so and/or An _i2ϋ are relatively large (e.g., about 0,1 or more, about 0. i 5 or more, about 0.2 or more, about 0.3 or more, about 0.4 or more, about 0.5 or more, about 0.6 or more, about 0,7 or more, about QM or more, about 0 9 or more, about 1 .0 or more), A relatively large birefringence can be desirable in embodiments where a high retardation and/or phase retardation are desired (sue below), or where a relatively thin retardation layei is desired. In certain embodiments, δ«; _J < _J and/or An ^i are relatively small (e.g., about 0.05 or less, about 0.04 or less, about 0.03 or less, about 0.02 or less, about 0.01 or less, about 0.005 or less, about 0.002 or less, 0.001 or less). A relatively small birefrio.gen.ee may be desirable in embodiments where a low retardation or phase retardation are desired, and/or where relatively low sensitivity of the retardation and/or phase retardation to variations in the thickness of retardation layer 110 is desired. δHΉO ami/or δJJπO can also be between about 0.05 and about 0.1 (e.g., about 0.06, about 0.07. about 0.08, about 0,09).

IB general, the ratio of Anna to Anno can vary. In some embodiments, λϊJUO is approximately equal to AH^ ₀ , For example, the ratio δλ MO/ λ»i2c> can be *n a range from about 0.5 to about two (e.g., about 0.75 to about 1.5, such as about one). Ir? certain embodiments, however, δR _πO can be relatively large, while δλ'KϊO can be relatively small. For example, the ratio δ«us/ An uo can be more than about two (e.g., about three or more, about four or more, about five or more, about six or more, about eight or snore, about 10 c?r more). Alternatively, λ«oo can be relatively small, while δtfii' _ϋ is relatively large. For example, the ratio An^ψ An^o can be less than about 0.S (e.g., about 0.4 or less, about 0.3 or less, about 0,2 or less, about 0,1 or less, about 0.05 or less).

The retardation of eaeh retardation layer at λ is the product of the layer's thickness and its birefringence at λ. By selecting appropriate values for Anna and the d and/or δ«πo and <f the retardation of layers 110 and i 20, respectively; can vary

as desired. in some embodiments, the retardation of retardation layers 1 I O and/or layer 120 is about 50 nm or more (e.g., about 75 nm or more, about 100 mil or more, about 125 nm or more, about 150 am or more, about 200 nm or more, about 250 urn or more, about 300 nm or more, about 400 nm or more, about SOO nm or more, about 1 ,000 or more, such as about 2,000 nm). Ln certain embodiments, the retardation of layers i 10 and/or 120 is about 40 nm or less (e.g., about 30 nm or less, about 20 nrn or less, about 10 nm or less, about 5 ran or less, about 2 nm or less),

In general, the relative retardation of layers I K) and 120 can vary. In some embodiments, the retardation of layer 110 can be about the same as the retardation of layer 120 at λ. For example, the ratio [δκπo(λ}α ^r |/lδf?s;ϊθ(λ)ώ ⁱ '] can in a range from about 0.5 to about 1 .5 (e.g., from about 0.75 to about 1 .25, such as about one). However, is certain embodiments, the retardation of layer 110 can be relatively large compared to the retardation oflayer 120. For example, me ratio δ/η loiXjd/AnmiA)^ can be more than about 1 ,5 (e.g., about three or more, about four or more, about five or more, about six or more, about eight or more, about IO or more). Alternatively, the retardation of layer 1 ! 0 can be relatively small compared to the retardation of layer 120. For example, the ratio Afi _\ u0.}df&ni2oQS)ϋ' can be less than about 0.5 (eg., about 0.4 or less, about 0.3 or less, about 0.2 or less, about 0.1 or less, about 0.05 or less), In some embodiments, the retardation oflayer 110 and/or layer 120 corresponds to λ/4 or λ/2.

Retardation layers 1 10 and 120 also have respective phase retardations, H so and ϊ ^" _ϊ2 « _J at wavelength λ, which can be determined according to the equation;

where /) is d for layer 1 30 and d' for layer 120.

Quarter wave phase retardation is given, for example, by F ^::: Jϊ?'2 _S while half wave phase retardation is given by F ^::: π. In general, phase retardation for a layer may vary as desired, and is generally selected based on the desired end use

application of optical retarder 100. In. some embodiments, phase retardation for layers 1 ! 0 and/or 120 may be about 2;τor less (e.g., about ?r or less, about 0.8 # or less, about 0.7/τor less, about 0.6?ro.r less, about 0.5s- or less, about 0.4 r or less, about 0.2 π of less, 0.2,τor less, about 0.1 jr or less, about 0,05 JT or less, 0,01 /tor less). In certain embodiments, phase retardation of retardation layers i 10 and/or 120 can be more than 2/T (e.g., about 3 ?ror more, about 4;τor more, about 5πoτ more).

In some embodiments, one of the retardation layers 110 and 120 has half-wave retardation at λ, while the other retardation layer has quarter-wave retardation at λ. hi general, the dispersion of retardation layer 110 can be the same or different as the dispersion of retardation 120, Dispersion, of a layer refers to the dependence of n _< ; and n _e on wavelength. The dispersion of each retardation layer depends on the dispersion of the materials used to form the layers (i.e., the materials used to form rows 111 and i 12 in layer 110, and the materials used to form 121 and 122 in layer 120) and on the dimensions of the structures forming the layers, in general, the dispersion of an optical retarder can be measured using methods known in the an. For example, a Mueller Matrix SpeetroPolarimeter (e.g., from Axoractries Inc., 51 5 Sparkmars Dr., Huntsvϊlle, AL ₅ 358.16) that includes an arc lamp light source and a scanning monochromator can be used to measure a complete set of polarization properties for a selected sample in ϊt spectral range from about 450 tun to about 800 n.rn. The dispersion or retardan.ee for an optical retarder can, for example, be measured for any wavelength in the above range, yielding a retardanee dispersion curve for the retarder. Alternatively, or additionally, the dispersion, or retardanee for each material used in the optical retarder can separately be measured for any wavelength in the above range to yield separate retardanee dispersion curves for each of the materials. Ttie retardanee dispersion curves for the materials can then be used, together with knowledge of the structural parameters of the optical retarder, to calculate the optical retarder 's dispersion according to effective medium theory, for example. In some eases, both of these methods are used concurrently and the results are compared.

Alternatively; or additionally, dispersion of an optical retarder and/or retardation layer can be determined using theoretical models to calculate the

birefringence of the optical retarder and/or retardation layer at different wavelengths. For such calculations, the values of the optical constants of the materials at different wavelengths can be found, for example, in the Handbook of Optical Constants of Solids, 1 st edition, edited by Lkhvard D. Paiik, Academic Press, (1997). Widths Au u λn _? , λ^ _b and Au2 and grating periods Aπo and λuo and dirty cycles art; selected based on the desired optical, characteristics of retardation layers ϊ 10 and 120, respectively. Typically, periods λ; io and Ana are k'$s than λ, so that retardation layers HQ mά 120 are form bireftmgent for radiation at λ. For example, λπo and/or λii _< ) can be about 0.8λ or less (e.g., about 0.6λ or less, about θ.Sλ or leas, about 0.4λ or less, about 0.3λ or less, about 0,2λ or less, about 0.1 λ or less).

In some embodiments, λm and/or A _J2 o is in a range from about 20 am to about 500 nm. For example, where optical retarder 100 is designed to operate in the visible- and/or ultraviolet portions of the electromagnetic spectrum, λ _{S )} « and/or A ^ may be in this range. Aw, can be, for example, about 40 nm or more (e.g., about 50 sim or more, about 75 nm or more, about 100 mn or more, about 125 nm or more, about 150 nm or more, about 175 nm or more, about 200 nm or more). A. m and/or As j _. o can be about 450 nm or less (e.g., about 425 mrs or less, about 400 nm or less, about 375 nm or less, about 350 nm or less, about 325 ran or less, about 300 .am or less, about 275 rs.ro or less, about 250 rim or less, about 225 nm or less). !.π certain embodiments, A _{} H5} and/or λ^o can larger than 500 nm. λπo and/or A- _: >o can be in a range from about. 600 nm to about 2,000 nm when, for example, optical retarder is designed to operate in. the mfrarα? portion of electromagnetic spectrum.. For example, λ _{} }} « and/or λπs ean be about 800 nm or more (e.g., about 1,000 nm or snore, about 1 JOO urn or more, about 1 ,200 nm or more). Ann and/or λj-.>o can be about 1,800 rtm or less (e.g. , about 1 ,600 nm or less, about 1 ,500 nm or less, about 1 ,400 nm or less, about 1,300 ran or less, about 1,200 nm or less}.

The period of the grating in layer 120, λ|> _t >, can be the same or different as the period of the grating in layer I iO, λπo- m certain embodiments, Am-. is approximately equal to Am-- For example, the ratio λπo/Aiio can be in a range from about 0.9 to about 1.! (e.g., from about 0.95 to about 1.05, such as about one). In

some embodiments, λπι; is larger than λ _{t t} o- For example, λuo/λuo can be about 1.1 or more {e.g., about 1.2 or more, about 1.3 or more, about i .4 or more, about 1.5 or more, about 1 .8 or more, about two or more). Alternatively, in certain embodiments, λo _1} is smaller than λi so. For example, λ^A no can be less than about 0.9 (e.g., about 0.8 or less, about 0.7 or less, about 0.6 or less, about 0.5 or less, about 0,4 or less, about 0.3 or less, about 0.2 or less, about 0. \ or less).

The grating in layers HO and 120 have doty cycles λ _U >/λJ JO and λjWλrø, respectively. In. general the duty cycle of the grating in layers i 10 and ! 20 may vary- as desired. In some embodiments, the duty cycles of the gratings in layers 110 and/or 120 arc in a range from about 0.2 to about 0.8 (e.g., about 0.3 or more, about 0.4 or more, about 0.5 or more, or about 0.7 or less, about 0.6 or less).

¹ IHc duty cycle of the grating in layer 120 can be the same or different as the duty cycle of the grating in layer 110. For example, the ratio of the duly cycle of the grating in layer 110 can be about 0.1 or more (e.g., about 0.2 or more, about 0.3 or more, about 0.4 or more, about 0.5 or more, about 0.6 or more, about 0.7 or more, about 0.S or more, about 0.9 or more, about, one or more, about 1 ,1 or more, about 1.2 or more, about 1 .3 or more, about ! .4 or more, about 1 .5 or more, about 1.8 or more. about two or more, about three or more, about four or more, about five or more, about six or more, about eight or more, about 10 or more) times the duty cycle of the grating in layer 120.

Ln general, thickness d ear? be the same or different as thickness d '. d and/or d ^f can be leas than or greater than λ. For example, ά and/or ,</'can be about 0.1 λ or more (e.g., about 0.2 λ or more, about 0.3 λ or more, about 0.5 λ or more, about 0.8 λ or more, about λ or more, about 1 ,5 λ or more, such as about 2 X or more). In certain embodiments, d can be about 50 am or more (e.g., about 75 nm or more, about 100 urn or more, about ! 25 τim or more, about 150 nm or more, about 200 nm or more, about 250 nm or more, about 300 nm or more, about 400 nm or more, about 500 nm or more, about 750 π.m or more, such as about 1 ,000 nm). In some embodiments. d ^f can be about 50 nm or more (e.g., about 75 nm or more, about 100 nm or more, about ! 25 nm or more, about 150 nm or more, about 200 nm or more, about 250 am or

more, about 300 am or more, about 400 am or more, about 500 mil or more, about 750 rmi or more, such as about Ii)OO urn). hi general the relative thickness of layer 120 to layer 11.0 can vary as desired. In some embodiments, layers i 10 and 120 have approximately (he same thickness. For example, did' can be in a range from about 0,5 to about 1 .5 (e.g.. from about 0.75 to about L25, such as about one). In certain embodiments, layer 1 10 is notably thicker than layer 120. For example, did ¹ can greater than about 1.5 (e.g., about 1.75 or more, about two or more, about three or more, about four or more, about live or more, about eight or more, about 30 or more). Alternatively, in some embodiments, layer 1 K) is notably thinner than layer 120. For example, did' can be less than about 0.5 (e.g., about 0.4 or less, about 0,3 or less, about 0.2 or less, about 0.1 or less).

In some embodiments, the combined thickness of retardation layers 1 10 and 120 can vary as desired. Generally, the combined thickness of the retardation layers refers to the thickness of the retardation layers along the z-axis from the lower surface of the lowest retardation layer to the upper surface of the top-most retardation layer. For optics! retarder 100, the combined thickness of the retardation layers is equal to d + d'. In certain embodiments, the combined thickness of the retardation layers in an. optical retarder ears be relatively small. For example, the combined thickness can be about five microns or less (e.g., about four microns or less, about three microns or less, about two microns or less, about one micron or less, about 0.5 microns or less). A relatively small combined thickness may be advantageous because it can provide optical retard ers with relatively compact form factors.

The aspect ratio of retardation layer gratings can be relatively high. Aspect ratio refers to the thickness of the respective layer (e.g., d for retardation layer 110 and a' for layer 120) to the width of one of the portions in the layer (e.g., A . π in retardation layer 110 and λ _{J ?} j in retardation layer 120}. For example, d\Am and/or d':Am can he about 2: 1 or more (e.g., about 3: 1 or more, about 4:1 or more, about 5: 1 or more, about 8: 1 or more, about 10: 1 or more).

Relative orientation angle φ may vary, φ is typically selected based on the desired optical characteristics of optical retarder 100, φ can be determined using theoretical models (see discussion infra) and/or by empirical studies, hi certain

embodiments, φ is relatively small. For example, φ can be about 2(F or less (e.g., about 18* or less, about 15° or less, about 12° or less, about 10° or less, about 8° or less, about (f or less, about 5° or less, about 4 ^C ' or less, about.3° or less, about 2° or less). Alternatively, in some embodiments, f can be larger than 20*. For example, φ can be about 25° or more, about 30° or more, about 35 ^' ' or more, about 40° or more, about 45* or more, about 50° or more, about 55° or more, about 6(F or more, about 65' ^J or more, about 70 ^fJ or more, about 75° or more). IB certain embodiments, the rows in retardation layer 120 ears be close to perpendicular to the rows in retardation layer UO, For example _. , φ can be about 80° or more (e.g., about SS ⁰ or more, such as about 9(F').

Io embodiments, the orientation angle φ, is selected based on the retardation uϊ retardation layers 1 K) and 120 at one or more wavelengths so that the retardation of optical reiarder at those wavelengths is at or close to a desired value. For example, in some embodiments, φ. r _U a and V ^o can be selected so that optica! retarder 100 has a retardation Hoc, that is substantially equal at two different wavelengths, λ< and λ>.

ID other words, at λ _{! 5} optical retaxder 100 has a phase retardation F ₅ , while at A.;, optica! retarder 1 C)O has a phase retardation F ₂ . where F, ~ F ₂ . For example, in some embodiments, \l ^" _\ - T ₂ ] is about 0.05π or less, about 0.03 Jϊ or less, about O. ^Q 2τ. or less, about 0.01 π or less, about 0.005π or less, 0.00 in or less. In certain embodiments, Fi and 1% vary by about 10% or less (e.g., about 8% or less, aboul 5% or less, about. 4% or less, about 3% or less, about 2% or less, about 1% or less).

Moreover, values of fjoo tor wavelengths in a range of wavelengths λλ are substantially constant. For example, V _m for any wavelength λ' in the range Aλ can vary lrom P ₅ by about 0,05π or less, about 0.03π or less, about ( ⁾ .02π or less, about 0.01 TT or less, about 0,005π or less, 0.001 Tt or less, in sonic embodiments, F varies by about 10% or less over the range λλ (e.g.. by about S ⁵ Ji or less, by about 5% or less, by about 4% or less, by about 3% or less, by about 2% or less, by about 1% or less) for a range of wavelengths that is about 20 nro or more (e.g., about 30 nm or more, about 40 nm or more, about 50 nm or more, about 60 πm or more, about 70 nrti or more, about 100 mi> or more, about.200 nm or more, about 300 rmi or more, about

500 rim or more, about LOOO nm or more). Optical retarders where i ^' lyo is substantially constant over a relatively large range of wavelengths {e.g., shout HK) run or more) is referred to as an achromatic retarder.

The location of δλ in the electromagnetic spectrum can be designated by a central wavelength, λ _ts which is given by ^ι δ{λι + λ.>j, hi general, λ, can vary as desired, and is typically selected based on the end use application of optical retarder 100. For example, in telecommunication applications that use infrared radiation, λ, _; cars be between about SOO nni and about 2,000 mn (e.g., between about 900 nm and aboυi 1 ,000 nm, or from about 1,300 nm and about !,60O nm}, As another example, where optical retarder ICK) is used in an optical memory device (e.g., a compact disc (CDs or digital versatile disc (DVD) device), λ _c can be in the visible portion or near- inirared portion of the electromagnetic spectrum (e.g., from about 400 nni to about 850 nni). As another example, where optica! retarder 100 is used as a component in a liihography exposure apparatus, λ _c is typically in the ultraviolet portion of the spectrum (e.g., from about 150 nm to about 4(K) nm).

Various metrics can be used to characterize the phase retardation spectrum of an optical retarder, including, for example, the spectral Harness and integrated spectral flatness of the spectrum, and the dispersion slope of the phase retardation spectrum. Spectral flatness, λ, of a retarder is given by;

and is related to the variation of a retarder's phase retardation at λ _λ and X ₂ , In some embodiments, δ can be relatively small. For example, δ can be about 10% or less (e.g., about 8% or less, about 5% or less, about 3% or less, about, 2% or less) for U; - λ _? \ of about 20 nm or more (e.g., about 50 nm or more, about 100 nm or more, about 200 nm or more).

Integrated spectral flatness, a is given by

where

Integrated spectral flatness is related to the variation of an optical retarder's phase retardation over the range of wavelengths from λ\ to λ%. In certain embodiments, σ ears be relatively small. For example, σcan be about 10% or less (e.g., about 8% or less, about 5% or less, about 3% or less, about 2% or less) for U; ^■ - /Uj of about 20 ran or more (e.g.. about 50 røπ or more, about 100 run or more, about 200 ran or more).

Another parameter that can be used to characterize an optica! retarder from its phase retardation spectrum is the dispersion si ape, ko, which is related to a linear component of the retarder's phase retardation spectrum over a spectral range defϊtied by λι and A ₂ . kn van be determined as a fit parameter B for a minimum value of r; givers by the equation

where

">S

and C ϊs another fitting parameter. A small value of kn can be indicative of a high degree of achrottiaticity in the retarders performance over the spectral range from to A ₂ .

The linearity of an optical retarder's phase retardation spectrum ϊS related to £ when λ'is minimized. A value of // close to unity indicates a substantially linear phase retardation over the range λJ to λz, while a valise of f close to zero indicates substantial non-linearity, hi some embodiments, £ can be about 0.8 or more (e.g., about 0.9 or more, about 0,95 or more, about 0.9? or more, about 0.98 or more, about 0.99 or more) for \λ _\ - λ>i of about 20 nm or more (e.g., about 50 am or more, about ! 00 run or more, about 200 πm or more).

In general, the thickness of retardation layer S K) and retardation. layer 120, widths λπu λ _H2 , A : _?J and A ₁ ^, and the refractive indexes of the materials forming layers 1 10 and 120, and orientation angle φ are selected to provide desired retardation over wavelength range for one or more wavelengths in the range δλ. The value for each of these parameters can be determined using computer modeling techniques. Far example, in some embodiments, the structure of retardation layers 110 and/or 120 can be determined using a computer-implemented algorithm that varies one or more of the grating parameters until the grating design provides the desired retardation values at the wavelengths of interest. One model that can he used is referred to as "rigorous coupled-wave analysis" (RfWA), which solves the governing Maxwell equations of the gratings, RCWA can he implemented in a number of ways. For example, one may use commercial software, such as G Solver, from Grating Development Company (GDC) (Alien, TX) ₁ to evaluate and the grating structure for transmissions and reflections. Alternatively, or additionally, RCWA can be implemented to calculate the relative phase shift among different polarization states. One or more optimization techniques such as, for example, direct-binary search (DBS), simulated annealing (SA), constrained global optimization (CGO), simplex/multiplex, may be used in comhination with the RCWA to determine the structure of retardation layers I H ⁾ and ] 20 that will provide desired optica! performance for each layer and for optical retarder H)O, Optimization techniques are described, for example, in Chapter 10 of

"Numerical Recipes in C, the Art of Scientific Computing," by W. H, Press et aL,

University of Cambridge Press, 2"° Ed. (1992). Examples of implementations of RCWA are described by L. IJ in "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,." J. Opt. Soc. Am. A. Vol. 10, No. 12. p. 25S 1 ( ! 993) and by T, K. Gaylord and M. G. Moharam in "Analysis and applications of optica] diffraction gratings," Proc, JEEE, Vol. 73, No. 5 ( 1985),

Alternatively, or additionally, effective media theory (EMT) can be used to determine the approximate phase of radiation at various wavelengths that traverses retardation layers 130 and 120 for different, values of parameters associated with the structure of retardation layers 110 and 120, Implementations of HMT are described, for example, by H, Kikirta et al., in "Achromatic quarter- wave plates using the dispersion of form birefringence," ApplieiiClgtics, Vol. 3(S, No, 7, pp. 1566- 1572 (1997), by CW. Haggans et al., in 'εffective-medium theory of zeroth order lamellar gratings in conical mountings," J- QpI- SOe- Am- A, Vol. 10, pp 2217-2225 (1993}, and by H. Kikuta et aL in "Ability and limitations of effective medium theory for subwavelervgth gratings;' Oρ_L__Rεv., Vol. 2, pp. 92-99 ( 1995), in general, the materials used to form the spaced-apart rows in each retardation layer can van/. Materials are usually selected based on their retractive index at the wavcleπgtli(s) of interest. Typically, the material forming rows 11 1 will have a different refractive index from the material forming rows 112 at one or more wavelengths of interest. Similarly, the material forming rows 121 will typically have a different, refractive index from the material forming rows 122 at one or more wavelengths of interest.

In some embodiments, materials with a relatively high refractive index arc used to form one or more of the spaeed-apart rows. For example, materials can have a refractive index of about 1.8 or more (e.g., about i .9 or more, about 2,0 or more, about 2. 1 or more, about 2.2 or more, about 2.3 or more). Examples of materials with a relatively high refractive index include TiCb, which has a refractive index of about 2.35 at 632 nra, or la^Os, which has a refractive index of 2,15 at 632 πm.

Alternatively, or additionally, rows can be formed from materials with a relatively low refractive index (e.g., about 1 ,7 or less, about 1.6 or less, about i ,5 or less). Examples of low index materials include MgF^, SiO:-. and Al ₂ O-^ which have

refractive indexes of about ! .37, L45 and 1.65 at 632 mil, respectively. Various polymers can also have relatively low refractive index (e.g., from about 1 ,4 to about 1.7}

In some embodiments, the material(s) mcύ to form the rows have a relatively low absorption at wavelengths of interest, so thai retardation layer 1 10 and/or retardation layer ! 20 has a relatively low absorption at those wavelengths. For example, retardation layer i i 0 and/or retardation layer 120 can absorb about 5% or less (e.g., about 3% or less, about 2% or less, about 1% or less, about 0.5% or iess, about ϋ.2% or less, about 0.1% or less) of incident radiation at wavelengths in the range άλ propagating parallel to the >axis.

In general, ihe materials forming rows 11 1, 1 12, 121, and/or 122 can include inorganic and/or organic materials. Examples of inorganic materials include metals, semiconductors, and inorganic dielectric materials (e.g., glass, SiN _x ). Examples of organic materials include organic polymers. In embodiments, rows 111, 112, 121, and/or 122 are formed from one or more dielectric materials, such as dielectric oxides (e.g., metal oxides), fluorides (e.g.. metal fluorides), sulphides, and/or nitrides (e.g., metal nitrides). Examples of oxides include SKh, AbO _. ,, Nb>0 ₃ , TiO ₂ , ZrO ₂ , HiO ₂ , SnO ₂ , ZnO, ErO ₂ , Se ₂ CK, and Ta ₂ O ₅ . Examples of fluorides include MgF->, Other examples include ZnS ₅ SiN _x , SiOyN _x , AlN ₅ TiN, and HiK.

Rows l i t, 112, 121, and/or 122 can be formed from a single material or from multiple different materials (e.g., composite materials, such as naαocorapαsite materials).

Rows 1 11, 112, 121 , and/or 122 can include crystalline, semi-crystalline, and/or amorphous portions. Typically, an amorphous material is optically isotropic arid may transrn.it light better than portions that are partially or mostly crystalline. As an example, in some embodiments, rows 11 1 and 1 12 are formed from amorphous materials, such as amorphous dielectric materials (e.g., amorphous TiO ₂ or SiO ₂ , respectively). Alternatively, in certain embodiments, rows 1 1 1 are formed from a crystalline or semi-crystalline material (e.g., crystalline or semi-cr ^y stalline Si), while

layers 1 12 are formed fro.ro an amorphous material (e.g., an amorphous dielectric material, such as ^" HOj or SiOi),

Ln certain embodiments, the materials used to form rows 111 and 1 12 arc selected so that retardation layer 1 10 has a certain birefringence at λ. Similarly; in some embodiments, the materials used to form rows 12 ! and 122 are selected so that retardation layer 120 has a certain birefringence at λ. In general, where a relatively large birefringence for a retardation layer is obtained by using materials in adjacent rows having substantially different refractive indexes;, As an example, adjacent rows can be formed using SiO ₂ and MgFj., which have refractive indexes of 1 ,45 and 1 ,37 at 632 3im, respectively. Conversely, where a retardation layer having a relatively small birefringence is desired, adjacent rows can be farmed using materials having similar refractive indexes. As an example, adjacent rows can be formed using SiO.? and TiO;, which has a refractive index of 235 at 632 nra. Possible values for birefringence of retardation layers 1 10 and 120 are presented supra. Referring now to other layers in optical retardcr 100, in general, substrate 130 provides mechanical support to optical retarder 100. In certain embodiments, substrate 130 is transparent to light at wavelength λj and λj, transmitting substantially ail light krspirigirig thereon at wavelengths λ.j and λ; (e.g., about 90% or more, about 95% or more, about 97% or more, about 99% or more, about 99.5% or more). In general, substrate 130 can be formed from any material compatible with the manufacturing processes used to produce retarder 100 that cars support the other layers. In certain embodiments, substrate 130 is formed from a glass, such as BK ^" (available from Abrisa Corporation), borosilicate glass (e.g., pyrex available from Coming}, alurmnosiikate glass (e.g., C 173? available from Coming), or quartz/feed silica. Irs some embodiments, substrate 120 can be formed from a crystalline materia!. such as a non-linear optica! crystal {e.g., LiNbO ₃ or a magneto-optical rotator, such as garnett) or a crystalline (or semicrystalline) semiconductor (e.g., Si, InP, or GaAs). Substrate 130 can also be formed from an inorganic material, such as a polymer (e.g., a plastic). Substrates can also be a metal or metal-coated substrate. In some embodiments, one of the retardation layers can be formed in a surface of the substrate. For example, referring to PIG. 3, an optica! retarder 300 includes a

retardation layer 320, where the fømvbirefringent structure in the retardation layer Ls formed in a surface 331 of a substrate 330. In particular, surface 331 includes a Tusmber of irench.es 321 (three of the trenches are ^' labeled in FIG, 3) filled with a material with a different refractive index from substrate 330. Retardation layer 320 has a thickness in the z-direetion of α', corresponding to the depth of trenches 321. Retardation layer 1 H) is formed on top of retardation layer 320.

Embodiments of optical retarders can include one or more additional layers. For example, embodiments of optical retarders can include more than two retardation layers (e.g., three retardation layers, four retardation layers, five retardation layers or more). In general, the relative orientation between the rows in each adjacent layer can vary and can be optimized so that the optical retarder provides desired optical characteristics for one or more wavelengths. As an example, an optical retarder can include a retardation layer having half-wave retardation at λ disposed between two quarter-wave retardation layers. The quarter-wave retardation layers include spaeeά- apart rows extending parallel to the v-axis, while the half-wave layer has rows extending at angle φ with respect to the _y-aχis. φ is selected so that ύrc three layers function as an achromatic quarter-wave retarder for a range of wavelengths, as described by S. Pancharavnatn in "Achromatic Combinations of Birefringent Plates/ ¹ i , pp. 136- 144 {1955}, for example. In embodiments, optical retarders can. include one or more layers on a substrate in addition to the retardation layers. For example, referring to FiG. 4, in addition first retardation layer 110, second retardation layer 120, and substrate 130, an optical retarder 400 includes an etch stop layer 410, cap layers 420 and 440, and antirefleetion films 430, 450, and 460, Hi eh stop layer 410 is formed from a material resistant to etching processes used to etch the material (s) from which rows 112 are formed (see discussion below). The τnaterial(s) forming etch stop layer 410 should also be compatible with substrate 130 and with the materials forming retardation layer 1 K ⁾ . Examples of materials that can form etch stop layer 410 include HfO;, SiO ₂ , AbO?, Ta ₂ O ₅ , TiO ₂ , SiN _x . or metals (e.g., Cr, Ti, Ni).

The thickness of etch stop layer 410 in the r-direction cars vary as desired. Typically, etch stop layer 410 is sufficiently thick to prevent significant etching of substrate 130, but should not be so thick as to adversely impact the optical performance of optical retard er 400. In some embodiments, etch stop layer is about 500 nm or less thick (e.g., about 250 nm or less, about 100 nni or less, about 75 rtro or less, about 50 nm or less, about 40 nm or less, about 30 am or less, about 20 nm or

Cap layers 420 and 440 cover layers 12(J and 110, respectively, and provide smooth surfaces 421 and 441 onto which antirefleαion films 430 and 450 can be respectively deposited, In general, the thickness along the ^-direction and composition of cap layers 420 and 440 can vary as desired, and are typically selected so that the layers provide their mechanical function without substantially adversely aftectiBg the optical performance of retarder 400. In some embodiments, cap layer 420 and/or cap layer 440 are about 50 nm or more thick {e.g., about 70 nm or more thick, about 100 nm or more thick, about 150 nm or more thick, about 300 am or more thick}. Cap layers can be formed from dielectric materials, such as dielectric oxides (e.g., metal, oxides), fluorides (e.g., metal fluorides), sulphides, and/or nitrides (e.g., metal nitrides), such as those listed above.

In optical relarder 400, retardation layer 110 and retardation layer 120 are separated by a distance s. In general s can vary, and depends on the thickness layers disposed between the retardation layers (e.g., cap layer 420 and etch stop layer 430 in optical retarder 400). Typically, s is about K) nm or more (e.g., about 20 nm or more, about 50 nm or more, about 100 nm or more, about 200 nm or more), s can be relatively small (e.g., about 1 ,000 nm or less, about 800 nm or less, about 6Of ⁾ nm or less, about 500 no or less, about 400 nni or less, about 300 nm or less),

As a result, the combined thickness, t. of retardation layers 1 10 and 120 in optical retarder 400 can be relatively small (e.g., about 10 microns or less, about eight microns or less, about six microns or less, about five microns or less, about four microns or less, about three microns or iess, about two microns or less). Moreover, the combined thickness, 71 of the all the layers on the skis of the substrate that the retardation layers are disposed can be relatively small. For example,

T can be about 15 microns or less, about 12 microtis or less (e.g., about 10 microns or less, about eight microns or less, about, six microns or less, about five microns or less, about four microns or less).

Aπtireflection Films 430, 450, and 460 can reduce the reflectance of radiation at one or more wavelengths of interest impinging on and exiting optical retarder 400. Ami reflection -films generally include one or more layers of different refractive index. As an example, one or more of antireflection films 430. 450, and 460 can be formed irom four alternating high and low index layers. The high index layers can be formed from TiO;? orTajO* and the low index layers can be formed from SiO ₂ or MgFi- The antireflection films can be broadband antireflection films or .narrowband antireflection films.

In some embodiments, optical retarders, such as optical retarder 400, have a reflectance of about 5% or less of light impinging thereon at wavelength λj and/or λ _; ? (e.g., about 3% or less, about 2% or less, about 1% or less, about 0.5% or less, about 0.2% or less). Furthermore, optical, retarder 400 can have high transmission of light of wavelength λ; and/or /<>. For example, optical retarder can transmit about 95% or more of Mghi impinging thereon at wavelength λj and/or ^' I ₂ (e.g., about 96% or more, about 97% or more, about 98% or more, about 99% or more, about 99.5% or more). Moreover, while the gratings forming the retardation layers m the foregoing embodiments have a rectangular profile, in genera!, the grating can have other profiles. For example, the grating may have a sinusoidal, triangular, trapezoidal (e.g., tapered), or sawtooth profile.

While the foregoing optical retarders include retardation layers thai are have properties corresponding to effective uniaxial, optical materials with the optical axis oriented in the plane of the retarder (i.e., a~plat.es), embodiments can inchxle other types of retardation layer. For example, embodiments can include form bireifingent f-plates, which are form birefringent media having an optical axis substantially perpendicular to the plane of the retarder. An example of a form birefringent opiate is retardation film 500 shown in FIG. 5, Retardation film 500 includes alternating layers 510 and 520 having different refractive indexes at λ.

Because the optical axis is oriented substantially parallel to thcz-axis, radiation incident on retarder 500 along this direction propagates as ordinary rays regardless of the radiation's polarization stale. However, for radiation incident, at a non-πoππai angie, 0, the layers effective refractive index varies depending on θ and S on the polarization state of the incident radiation.

Layers 510 and 520 have thicknesses duo an.d <hκ _h respectively, hi general, d _. si _f ) and a _& n are selected so that retardation film 500 has a desired birefringence. <h\<> and djiij arc approximately the same. For example, in some embodiments, the ratio <hv/thx _> is in a range from about 0.8 to about 1.2 (e.g., in a range from about 0.9 to D about 1.1 , such as about one). In certain embodiments, dim is larger than d\ ₂ (h For example, the ratio dsuJd _& a can be more than about 1 .2 (e.g., about 1.3 or more, about 1.4 or more, about 1 ,5 or more, about 1 .8 or more, about two or more, about 2.5 or more, about three or more, about four or more, about five or more), hi certain embodiments, chin and/or d$?c _> is about 5 lira or more (e.g., about 10 nm or more, 5 about 15 am or more, about 20 nm or more, about 30 nm or more, about 40 nm or more, about 50 nm or more, about 60 nm or more, about 70 nm or more, about 80 nrn or more, about 90 nm or more, about 100 rmi or more).

Layers 510 and 520 are formed from materials having refractive indexes ϊi _Sffi and ns ₂ i; at λ, respectively. In general, n$v _> is different from n^y. The material and 0 refractive index of layers 510 and 520 can be the same as those listed with respect to rows 11 1 , 1 12, 121, arid 122 described supra with respect to optical retarder 100. in some embodiments, one or both of layers 510 and 520 are formed from a nanolaminaie material .

The effective ordinary and extraordinary indexes of refraction are given by Eq, 5 (1 a) and (1 b), respectively, a and β correspond to dy.o and dsj _h respectively, n _x and β> correspond to n^o and n^h respectively.

Retardation Him 500 lias a birefringence δrtsoo ^~ ^- ™ «a- Ui some embodiments, λ??jo _f > is relatively large (e.g., about 0.1 or more, about 0. ! 5 or more, about 0.2 or more, about 0.3 or more, about 0.4 or more, about 0.5 or more, about 0.6 0 o.r more, about 0.7 or more, about 0.8 or more, about 0.9 or more, about 1 X) or more). A relatively large birefringence can be desirable in embodiments where a high

retardation and/or phase retardation are desired, and/or where a relatively thin retardation layer is desired. Ln certain embodiments, An^o is relatively small (e.g., about 0.05 or less, about 0.04 or less, about 0.03 or less, about 0.02 or less, about 0,01 or leas, about 0.005 or less, about 0.002 or less, 0.001 or less), A relatively small birefringence may be desirable m embodiments where a low retardation or phase retardation are desired, and/or where relatively Sow sensitivity of the retardation and/or phase retardation to variations in the thickness of retardation film 500 is desired. λ^oy can also be between about 0.05 and about 0.1 (e.g., about 0.06, about 0.07, about 0.08, about 0.09). In certain embodiments, λ«. _WJ is negative. For example, ά«seo can be about negative with JδH _JOO J being about 0,005 or more (e.g., about 0.01 or more, about 0,02 or more, about 0.03 or more, about 004 or more, about 0.05 or more, about 0.07 or more, about 0. ! or more, about 0.12 or more, about 0.15 or more, about 0.2 or more, about 0.3 or more, about 0.4 or more, about 0.5 or more). As an example, optical retarder 500 can include alternating layers of SiO2 and TiO2 with layer thickness of about 20 nm each. For visible light, the refractive index of SiO? is about 1.53 while the refractive index OfTiO ₂ is about 2.13. Thus, based on equations (1 a) and (Ib). supra, in this ease Any^ is about -0.1.

Film 500 has thickness d". in general, d" is selected so that retardation film retards radiation at λ incident at #hy a desired amount, ϊn some embodiments, d" can be relatively thin. For example, d" can be about five microns or less (e.g., about four ^■ microns or less, about three microns or less, about two microns or less, about one micron or less, about 0,8 microns or less, about 0.6 microns or less, about 0.5 microns or less, about 0,4 microns or less, about 0.3 microns or less, about 0.2 microns or less, about O.I microns or leas) thick.

While retardation film 500 is shown as including nine layers, in general the number of layers in a form hirefringent c-plates can vary as desired. Typically, torn. birefπngent c-piates include about 10 to about 200 layers (e.g., about 15 or more layers, about 20 or more layers, about 30 or more layers, about 40 or more layers, about 50 or more layers, about 60 or more layers, about 70 or more layers) (e.g., about

180 or fewer layers, about 150 or fewer layers, about 120 or fewer layers, about 100 or fewer layers, about 90 or fewer layers, about 80 or fewer layers).

Moreover, retardation film 500 can include one or more additional layers having thicknesses different from d$ιo and α ^J s>o and/or layers formed from materials with refractive indexes different from n^ and n^o- ϊn general, the structure of retardation film 500 can be based on theoretical models, and can be optimized to provide a desired amount of retardation at one or more wavelengths based on the theoretical models.

Examples of form birefdngent e-plates are described by M. KJtagawa and M. Tateda in "Form birefringence of SiCWI a^O^ periodic multilayers,' ^* Appi Opt.. Vol. 24, Na. 2O ₅ pp. 3359-3362 (1985).

An example of an optica! retarder that includes both α-plate retardation layers and opiate retardation layers is shown in FICt, 6, The structure of optical retarder 600 corresponds to the structure of optical retarder 400, except that a c-platc retardation film 620, rather than antirefleetion film 450 is disposed on top of cap layer 440. An antirelleeiion fslra 620 is disposed on retardation film 610.

The combined thickness t' of optical retardation layers 110 and 120 and optical retardation film 610 can be relatively small. Fur example, /' can be about I S microns or less, about 12 microns or less (e.g., about 10 microns or less, about eight microns or less, about six microns or less, about live microns or less, about four microns or

In general the respective location of the retardation layers in optica: retarder 600 can vary as desired. For example, while both α-plate retardation layer 120 and a- plate retardation. layer 1 i 0 are both positioned between c-plate retardation iiim 610 and substrate 130, in some embodiments, a c-plate retardation film can be positioned between two α-plaie retardation layers or between the substrate and the α-piafe retardation layers. Moreover, optical retarders can, in general, include more or fewer ϊϊ-pjatε retardation layers or more c-plate retardation films.

The foregoing retarders include period arrangements of different materials. However, more general Iy, optical retarders (e.g., « -plate optical retarders, c-plate optica! retarders} can include non-periodic arrangements of different materials in

additional, or as alternative to, periodic arrangements. For example, a-piaie optical retard crs can include regions of periodicity variation (e.g., chirped grating structures). Optical retarders of e-plate type can also include non-periodic arrangements of different materials. As an example, a opiate optical retarder can be fabricated having alternating layers of a high index material and a low index material (referred to as biiayers). the high index layers having thicknesses of about 10 am and the low index layers having thicknesses of about 15 nm. A stack of about 90 bi layers can be produced. Atop the stack, an alternating sequence of high and low index layers can be deposited, the high and low index layers having variable thicknesses to provide a non- periodic portion of the overall structure. For example, the thicknesses of the layers can be selected to vary in a regular manner to provide a chirped variation in index of refraction.

While the foregoing optical retarders include retardation layers on one side of a substrate, embodiments can include retardation layers on opposite sides of a substrate. For example, referring to FlG. 7 A, and optical reiarder 700 includes a first retardation film 720 and a second retardation film 730 on opposing sides; of a substrate 710. Retardation film 720 and/or 730 cars, include one or more retardation layers (e.g., opiate retardation layers or layers forming a c-plate optical retardation film). Sm some embodiments, retardation layers and/or retardation films can be pix dialed. In other words, the retardation layers and/or retardation films can include portions with structure thai differs from other portions. The portions are referred to as pixels. For example, a pixeliated α-plaie can include portions with where the spaced apart rows of material are oriented along different directions. The spaced apart rows of different portions can be, for example, oriented at about 45" or at about 9Cr ^' with respect to each other. Alternatively, or additionally, a pixeliated ff-plaie can include pixels with different grating periods. opiate retardation films can also be pixeliated. For example, a pixellated c- plate can include pixels with differing layer structure, providing differing retardation properties.

Referring to FIG 7B, an example of a pixellatecl optica! retarder 7000 is shown. Optical retarder includes a substrate 7001, and two pixellated retardation layers 7010 and 7020. Retardation layer 70 ! 0 includes pixels 7011 , 7012, 7013, 7014, and 70! S ₅ while retardation layer 7020 includes pixels 7021 , 7022, 7023. 7024, and 7025. Pixels 70 !.1 , 7012, 7013, ^" 014, and 7015 are registered with pixels 7021 , 7022, 7023, 7024, and 7025, respectively. Although layers 7010 and 7020 are depicted as including only five pixels each, more generally, the number of pixels in each layer can vary as desired, hi some embodiments, for example, layers can include thousands to millions of pixels, Ln general pixels can be arranged in a one-dimensional array or a two- dimensional array. The pixel size, number and density can he selected to correspond to the pixel size, number, and density of a pixellated device, such as a detector array (e.g., for a digital camera) or a display device (e.g., a liquid crystal display device). While the pixels m retardation layers 7010 and 7020 are the same area (in the x-y plane), in some embodiments, pixels in different layers can have different areas. In certain embodiments, the pixel area in one layer ca.o correspond to an integer number of pixels (e.g., two pixels, three pixels, four pixels, five or more pixels) in another layer. hi certain embodiments, one of. retardation layers can be pixellatcd, while the other layer is not pixellated. A non pixellated layer JS referred to as a single pixel layer.

Lo general, optical retarders can be fabricated using a variety of methods. Optical retard ers can be Conned using methods commonly used to fabricate microelectronic components, including a variety of deposition and lithographic patterning techniques, FϊGs, 8A - SJ show different phases of an example of a preparation process. Initially, a substrate 840 is provided, as shown in FlCl. 2BA, A surface 841 of substrate 840 can be polished and/or cleaned (e.g.. by exposing the substrate to one or more solvents, acids, and/or baking the substrate).

Referring to FiG. SB, an etch stop layer 830 is deposited on surface 841 of substrate 840. The material forming etch stop layer 830 can he formed using one of a variety of techniques, including sputtering (e.g., radio frequency sputtering), evaporating (e.g., electron beam evaporation, ion assisted deposition (IAD) electron

bearn evaporation), or chemical vapor deposition (CVD) such as plasma enhanced CVD (PECVD), ALD, or by oxidization. A.s an example, a layer of HfG? can be deposited on substrate 140 by IAD electron beam evaporation.

Referring to FlG. SC, an intermediate layer 801 is then deposited on a surface 831 of etch stop layer 830. Portions 812 are etched from intermediate layer 810, so intermediation layer 801 is formed from the material used for portions Si 2. The ^• material forming intermediate layer 801 can be deposited using one of a variety of techniques, including sputtering (e.g., radio frequency sputtering), evaporation (e.g., election beam evaporation), or chemical vapor deposition (CVD) (e.g., plasma enhanced CVD).

In certain embodiments intermediate layer 801 is formed from a dielectric. such as SiO;;- Dielectric layers can be formed by using, for example, vapor deposition methods, (e.g., CVD, such as plasma enhanced CVD) ₅ evaporation methods (e.g., electron beam or thermal evaporation methods), sputtering, or atomic layer deposition (ALD).

In general, the thickness of intermediate layer 801 is selected based on the desired thickness of the retardation layer that will he formed from intermediate layer 801 .

Intermediate layer 801 is processed to provide portions 812 of a subsequent retardation layer using lithographic techniques. For example, portions 812 can be formed from intermediate layer 801 using electron beam lithography or photolithography (e.g., using a photomask or using holographic techniques).

Ui some embodiments, portions 812 are formed using nanα-iπi print lithography. Referring to FIG. 8D ₅ nano-imprint lithography includes forming a layer 820 of a resist on surface 81 1 of intermediate layer 801 . The resist can he polymethylmethacrylate (PMMA) or polystyrene (PS), for example. Referring to FIG. 8E, u pattern is impressed into resist layer 820 using a mold. The patterned resist layer 820 includes thin portions 821 and thick portions 822. Patterned resist layer 820 is then etched (e.g., by oxygen reactive ion etching (RIE)), removing thin portions 821 to expose portions S24 of surface 81 1 of intermediate layer 801 , as

shown in FEG. SF. Thick, portions 822 are also etched, but are not completely removed. Accordingly, portions 823 of resist remain on surface SU after etching, deferring to FfO. &G, the exposed portions of intermediate layer 801 are subsequently etched, forming trenches 812 m intermediate layer SOL The unetchcd portions of intermediate layer 801 correspond to portions SI2 of retardation layer S 10. Intermediate layer 801 can be etched using, for example, reactive ion etching, ion beam etching, sputtering etching, chemical assisted ion beam etching (CAIBE), or wet etching. The exposed portions of intermediate layer SOl are etched down to etch stop layer 830, which is formed from a material resistant to the etching method. Accordingly, the depth of trenches 813 formed by etching is the same as the thickness of portions 812. After etching trenches 813, residua! resist 823 is removed from portions 812. Resist can be removed by rinsing the article in a solvent (e.g., an organic solvent, such as acetone or alcohol), by Oj. plasma ashing, O> RlE, or ozone cleaning. Etching can be performed using commercially-available equipment, such as a

TCP* ^' 96(M)DFM (available from Lam Research, Fremont, CA).

More than one etch step can be used. For example, in some embodiments, a two-step etch is used. An example of a two step etching process is as follows. A substrate such as a blank .fused silica substrate, or a glass substrate having a layer of SiOi of thickness about 1000 nm deposited thereon, is cleaned and prepared for deposition. An aluminum layer of thickness approximately 150 nm is deposited thereon using a high vacuum electron-beam deposition process. Atop the aluminum layer, a thin layer of SiO; having a thickness of about 30 nm is deposited using an ion-assisted deposition electron-beam deposition process. Subsequently, a process of nanoimprirti lithography is initiated. Firstly, a resist layer of thickness about 180 nm is applied atop the SiO _.? layer by a spin coating process. Secondly, a moid having a thickness or depth of about 120 nra and a period of about 200 nm or about 150 nm, is pressed into the resist layer and then separated therefrom to form a pattern profile. An oxygon reactive ion etching process is then used to etch the residual (recessed) resist and expose the SiO ₂ layer underneath. Next, a reactive ion etching process using

CHF _.? is used to etch the 30 am SiOs layer using the remaining resist as a mask. Following this process, the remaining resist is removed by an oxygen ashing process. In a subsequent, step, the SiCb layer is used as a mask to preferentially etch the 150 πm aluminum layer using a chemical etching process based on CJ _^ . Following this process of aluminum removal SiO _? is deep-etched using the remaining aluminum as a mask. It. is possible to etch to a depth of up to about 800 πrn in SiC) ₂ using the 150 nm aluminum mask. In a final step, the aluminum mask is removed using either a dry (Cb) or wet chemical process.

Referring to FIG. SI, alter removing residual resist, material is deposited onto the article, filling trenches 813 and forming cap layer 820. The filled trenches correspond to portions 814 of retardation layer 810. Materia! can be deposited onto the article in a variety of ways, including sputtering, electron beam evaporation, CVD (e.g., high density CVD) or atomic layer deposition (ALD). Note that where eap layer 820 is formed and trenches 813 are filled during the same deposition step, portions 813 and cap layer 820 are formed from a continuous portion of materia! .

Finally, additional layers 150 and 160, such as antirefieetie-n films are deposited onto surface 821 of cap layer 820 and surface 842 of substrate 840, respectively. Additional layers maybe formed on layers 150 and/or 160. For example, the process described above for fabricating retardation layer 810 may be repeating Io fabricate a second retardation layer on a surface of the artiele.

Alternatively, or additionally, a opiate retardation film can be formed on one or more surfaces of the article. Materials forming the additional layers can be deposited onto the article by sputtering, electron beam evaporation, or ALU, tor example.

Additional fabrication steps can be used at various points during .he described process. For example, surfaces can be planarized and/or layers can be reduced in thickness by polishing (e.g., chemical mechanical polishing) or milling (e.g., using an ion beam), for example, hi sonic embodiments, multiple optical retarders can be prepared simultaneously by forming a relatively large retardation layer on a single substrate, which is then diced into individual units. For example, a retardation layer can be forma.! on 3 substrate that has a single-side surface area about 10 square inches or more (e.g., a four inch, six inch, or eight inch diameter substrate). Alter loaning

the grating layer, the substrate can be diced into multiple units of smaller size (e.g., having a single-side surface area of about one square inch or less).

As discussed previously, in some embodiments, holographic lithography techniques can be used to form a pattern in a layer of resist material on intermediate layer 801. In these techniques, a photosensitive resist layer is exposed to an interference pattern formed by overlapping two or more coherence beams of radiation, usually derived from a laser light source. The varying light intensity of the interference pattern is transferred Io the resist material, which can be developed after exposure io provide a patterned resist layer. Holographic lithography can be used to generate a period intensity pattern by interfering two coherent beams of similar intensity. The technique is particularly versatile as the period of the intensity pattern can be varied by varying tlie angle at which the two beams interfere.

Theoretically, the period of the intensity pattern, i ^' \ is given by the equation:

where λ. _b is the wavelength of the interfering radiation, n h the refractive index of the medium in which the beams interfere, and ψ Ls half the angle subtended by the interfering beams. Since V is proportional to /^, interference patterns having relatively short periods (e.g., about 300 ran or less) can be formed by selecting a light source with a relatively short wavelength (e.g., an argon laser having output at 351 nm). Furthermore, the interference pattern period can be reduced by interfering the two beams at relatively large angles- (e.g., φ about 45 degrees or more). For example, the resist can be exposed to two 351 nm beams with φ at about 6! degrees- to provide a grating having a period of about 200 mil.

In some embodiments, holographic lithography can be performed while immersing the substrate and resist in a medium having a refractive index higher than the refractive index of air. For example, the resist surface cars be immersed in a liquid

such as water (which has a refractive index of about 1.33) or an organic liquid (e.g., glycerin, which has a refractive index of about 1 ,5)

As mentioned previously, in some embodiments, layers of optical retarders can be prepared using atomic layer deposition (ALD), For example, referring to FlG. 9, an ALD system 900 is used to fill trenches 912 of an intermediate article 901 (e.g., composed of a substrate, a cap layer, and a layer of a series of spaced- apart rows) with a nanoiarfiinaie multilayer film. Deposition of the nanolaminate multilayer film occurs monolayer by monolayer, providing substantial control over the composition and thickness of the films. During deposition of a monolayer, vapors of a precursor arc introduced into the chamber and are adsorbed onto exposed surfaces of portions 912, the exposed surface of the etch stop layer or previously deposited monolayers adjacent these surfaces. Subsequently, a reaetant is introduced into fee chamber that reacts chemically with the adsorbed precursor, forming a monolayer of a desired material The self-limiting nature of the chemical reaction on the surface can provide precise control of film thickness and large-area uniformity of the deposited layer. Moreover, the non-directional adsorption of precursor onto each exposed surface provides for uniform deposition of material onto the exposed surfaces, regardless of the orientation of the surface relative to chamber 910, Accordingly, the layers of the nanoiaminate Him conform to the shape of the trenches of intermediate article 901. ALD system 900 includes a reaction chamber 91 CX which is connected to sources 950, 960, 970. 980. and 990 via a manifold 930, Sources 950, 960, 970, 980, and 990 are connected to manifold 930 via supply lines 951 , 961 , 971 , 981 , and 99 ! , respectively. Valves 952, 962, 972. 982, and 992 regulate the flow of gases from sources 950, 9(SO, 970, 980, and 990, respectively. Sources 950 and 980 contain a first and second precursor, respectively, while sources 960 and 990 include a first reagent and second reagent, respectively. Scarce 970 contains a carrier gas, which is constantly flowed through chamber 910 during the deposition process transporting precursors and reagents to article 901, while transporting reaction byproducts away irons the substrate. Precursors and reagents are introduced into chamber 910 by mixing with the carrier gas in manifold 930. Gases are exhausted from chamber 910

via an exit post 945, λ pump 940 exhausts gases from chamber 910 via an exit port 945. Pump 940 is connected to exit port 945 via a tube 946,

ALD system 900 includes a temperature controller 995, which controls the temperature of chamber 9!C). During deposition, temperature controller 995 elevates the temperature of article 901 above room temperature. In general the temperature should be sufficiently high to facilitate a .rapid reaction between precursors and reagents, but should not damage the substrate, hi some embodiments, the temperature of article 901 can be about 500°C or less (e.g., about 400 ^c C or leys, about 3OG ⁰ C or less, about 200 ⁰ C or less, about 150 ⁶ C or less, about 1.25 ^' - ¹ C or less, about HKFC or less).

Typically, the temperature should not vary significantly between, different portions of article 901. Large temperature variations can cause variations in the reaction rate between the precursors and reagents at different portions of the substrate, which can cause variations in the thickness aπ.d/or morphology of the deposited layers, In some embodiments, the temperature between different portions of the deposition surfaces can vary by about 40 ^t: C or less (e.g., about 3 ⁽ FC or less, about 20"C or less, about 10 ^c C or less, about 5 ^'1 C or less).

Deposition process parameters are controlled and synchronized by an electronic controller 999. Electronic controller 999 is in communication with temperature controller 995; pump 940: and valves 952, 962, 972, 982. and 992.

Electronic controller 999 also includes a user interface, from which an operator can set deposition process parameters, monitor the deposition process, and otherwise interact with system 900.

Referring to FIG. Ii), the ALD process is started (1005) when system 900 introduces the first precursor from source 950 into chamber 910 by mixing it with carrier gas from source 970 { 1010). A monolayer off-he first precursor is adsorbed onto exposed surfaces of article 901 , and residual precursor is purged from chamber 9 ! 0 by the continuous How of carrier gas through the chamber ( 1015), Next, the system introduces a first reagent from source 960 into chamber 910 via manifold ^c >30 f 102(3). The first reagent reacts with the monolayer of the first precursor, forming a monolayer of the first materia!. As tor the first precursor, the flow of carrier gas

purges residua) reagent from the chamber (1025). Steps 1010 through HBO are repeated until the layer of the first material reaches a desired thickness (1030).

In embodiments where the films are a single layer of material the process ceases once the layer of first material reaches the desired thickness (1035). However, for a tianolaminaie film, the system introduces a second precursor into chamber 910 through manifold 930 (1040), A monolayer of die second precursor is adsorbed onto the exposed surfaces of the deposited layer of first material and carrier gas purges the chamber of residual precursor (1045). The system then introduces the second reagent from source 1040 into chamber 1005 via manifold 1015, The second reagent reacts with the monolayer of the second precursor, forming a monolayer of the second material ( 1050), Flow of carrier gas through the chamber purges residual reagent (1055). Steps 1040 through 1055 are repeated until the layer of the second materia! reaches a desired thickness (1060).

Additional layers of the first and second materials are deposited by repeating steps 1060 through 1065. Once the desired number of layers are formed (e,g., the trenches are filled and-'Or cap layer has a desired thickness), the process terminates ( 1070), and the coated article is removed from chamber 910.

Although the precursor is introduced into the chamber before the reagent during each cycle in the process described above, in other examples the reagent can be introduced before the precursor. ^' The order in which the precursor and reagent are introduced can be selected based on their interactions with the exposed surfaces. Par example, where the bonding energy between the precursor and the surface is higher than the hoπάmg energy between the reagent and the surface, the precursor can be introduced before the reagent. Alternatively, if the binding energy of the reagent is higher, the reagent can be introduced before the precursor.

The thickness of each monolayer generally depends on a number of factors. For example, the thickness of each monolayer can depend on the type of materia! being deposited. Materials composed of larger molecules may result In thicker monolayers compared to materials composed of smaller molecules. The temperature of the article can also affect the monolayer thickness. For example, ibr some precursors, a higher temperate can reduce adsorption of a precursor

onto a surface during a deposition cycle, resulting in a thinner monolayer than would be formed if the substrate temperature were lower.

The type or precursor and type of reagent, as well as the precursor and reagent dosing can also affect monolayer thickness. In some embodiments, monolayers of a material can be deposited with a particular precursor, but with different reagents, resulting in different monolayer thickness for each combination. Similarly, monolayers of a material formed from different precursors can result in different ^■ monolayer thickness for the different precursors.

Examples of other factors which may affect monolayer thickness include purge duration, residence time of the precursor at the coated surface, pressure in the reactor, physical geometry of the reactor, aid possible effects from the byproducts on the deposited material. An example of where the byproducts aiϊeet the film thickness are where a byproduct etches the deposited material. For example, HO .is a byproduct when depositing TiCK using a ^" FiCl ₄ precursor and water as a reagent. I ItI can etch the deposited TiO; before it is exhausted. Etching will reduce the thickness of the deposited monolayer, and can result, in a varying monolayer thickness across the substrate if certain portions of the substrate are exposed to HCl longer than other portions (e.g., portions of the substrate closer to the exhaust may be exposed to byproducts longer than portions of the substrate further from the exhaust). Typically, monolayer thickness is between about 0.1 nra and about five nra.

For example, the thickness of one or more of the deposited monolayers can be about 0.2 am or more (e.g., about 03 nm or more, about 0.5 nni or more). In some embodiments, the thickness of one or more of the deposited monolayers can be about three nm or less (e.g., about two nm, about ons nm or less, about 0.8 nm or less, about 0.5 nm υx less).

The average deposited monolayer thickness may be determined by depositing a preset number of monolayers on a substrate to provide a layer of a materia ⁾ . Subsequently, the thickness of the deposited layer is measured (e.g., by eilipsometry, electron microscopy, or some other method). The average deposited monolayer thickness can then be determined as the measured layer thickness divided by the number of deposition cycles. The average deposited monolayer thickness may

correspond to a theoretical monolayer thickness. The theoretical monolayer thickness refers to a characteristic dimension oϊa. molecule composing the monolayer, which can be calculated from the material's bulk density and the molecules molecular weight. For example, an estimate of the monolayer thickness for Si<>> is - 0,37 urn. The thickness is estimated as the cube root of a foraiuia unit of amorphous SiO? with density of 2.0 grams per cubic centimeter.

In some embodiments, average deposited monolayer thickness can correspond to a fraction of a theoretical monolayer thickness (e.g., about 0,2 of the theoretical monolayer thickness, about 0.3 of the theoretical monolayer thickness, about 0.4 of the theoretical monolayer thickness, about 0.5 of the theoretical monolayer thickness, about. 0.6 of the theoretical -monolayer thickness, about 0,7 of the theoretical monolayer ihkkntss, about 0.8 of the theoretical monolayer thickness, about 0,9 of the theoretical monolayer thickness). Alternatively, the average deposited monolayer thickness can correspond k> more than one theoretical monolayer thickness up to about 30 times the theoretical monolayer thickness (e.g., about twice or more than the theoretical monolayer thickness, about three time or more than the theoretical monolayer thickness, about five times or more than the theoretical monolayer thickness, about eight times or more than the theoretical monolayer thickness, about 10 times or more than the theoretical monolayer thickness, about 20 times or more than the theoretical monolayer thickness).

During the deposition process, the pressure in chamber 910 can he maintained at substantially constant pressure, or can vary. Controlling the flow rate of carrier gas through the chamber generally controls the pressure, In general, the pressure should he sufficiently high to allow the precursor to saturate the surface with ohemisorbed species, the reagent to react completely with the surface species left by the precursor and leave behind reactive sites for the next cycle of the precursor. If the chamber pressure is too low. which may occur if the dosing of precursor arsd/or reagent is too low. and/or if the pump rate is too high, the surfaces may not be saturated by the precursors and the reactions may not be self limited. ^' This can result in an uneven thickness in the deposited layers. Furthermore, the chamber pressure should not be so hi ^h as to hinder the removal of the reaction products generated by the reaction of the

precursor and reagent. Residua! byproducts may interfere with the saturation of the surface when the next dose of precursor is introduced into the chamber, in some embodiments, the chamber pressure is .maintained between about 0.01 Ton ^* and about 100 Ton- (e.g., between about 0.1 Toiτ and about 20 Torr, between about 0.5 Torr and 10 Torr, such as about 1 Torr),

Generally, the amount of precursor and/or reagent introduced during each cycle can be selected according to the size of the chamber, the area of the exposed substrate surfaces, and/or the chamber pressure. The amount of precursor and/or reagent introduced during each cycle can be determined empirically. The amount of precursor and/or reagent introduced during each cycle can be controlled by the timing of the opening and closing of valves 952, 962, 982, and 992. The amount of precursor or reagent introduced corresponds to the amount of time each valve is open each cycle. ^' The valves should open for sufficiently long to introduce enough precursor to provide adequate monolayer coverage of the substrate surfaces. Similarly, the amount of reagent introduced during each cycle should be sufficient to react with substantially ail precursor deposited on the exposed surfaces, introducing more precursor and/or reagent than is necessary can extend the cycle time and/or waste precursor and/or reagent. Irs some embodiments, the precursor dose corresponds to opening the appropriate valve for between about 0.1 seconds and about live seconds each cycle (e.g.. about 0,2 seconds or more, about 0.3 seconds or more, about 0.4 seconds or more, about 0.5 seconds or more, about 0.6 seconds or more. about 0.8 seconds or more, about one second or more}. Similarly, the reagent dose can correspond to opening the appropriate valve for between about CU seconds and about live seconds each cycle {e.g., about 0.2 seconds or more, about 0.3 seconds or more, about 0.4 seconds or more, about 0.5 seconds or more, about 0.6 seconds or more, about 0,8 seconds or more, about one second or more).

The time between precursor and reagent doses corresponds to the purge. The duration of each purge should be sufficiently long to remove residual precursor or reagent from the chamber, but if it is longer than this it can increase the cycle time without benefit. The duration of different purges in each cycle can be the same or can vary. In some embodiments, the duration of a purge is about OJ seconds or more

(e.g., about 0,2 seconds or more, about 0.3 seconds or more, about 0.4 seconds or more, about 0,5 seconds or more, about 0.6 seconds or more, about 0,8 seconds or more, about one second or more, about L5 seconds or more, about two seconds or more). Generally, the duration of a purge is about 10 seconds or less (e.g., about eight seconds or less, about five seconds or less, about four seconds or less, about three seconds or less).

The time between introducing successive doses of precursor corresponds to the cycle time. The cycle time can be the same or different for cycles depositing monolayers of different materials. Moreover, the cycle time can be the same or different for cycles depositing monolayers of the same material but using different precursors and/or different reagents, In some embodiments, the cycle time can be about 20 seconds or less (e.g., about 15 seconds or less, about 12 seconds or less, about H) seconds or less, about 8 seconds or less, about 7 seconds or less, about 6 seconds or less, about 5 seconds or less, about 4 seconds or less, about 3 seconds or less). Reducing the cycle time can reduce the time of the deposition process.

The precursors are generally selected to be compatible with the ALD process, and to provide the desired deposition materials upon reaction with a reagent, in addition, the precursors and materials should he compatible with the material on which they are deposited (e.g., with the substrate material or the materia ^] forming the previously deposited layer). Examples of precursors include chlorides (.e.g., metal chlorides), such as HCI ₄ , SiCl ₄ , SiH ₂ CI ₃ , TaCb, HfCl ₄ , InCJ ₃ and AiCl,. hi some embodiments, organic compounds can be used as a precursor (e.g., Ti-ethaOxidε, Ta- ethaOxide, Nb-ethaOxide), Another example of an organic compound precursor is (CHshAi F» ^r SiO ₂ deposition, for example, suitable precursors include Tris{tert- butoxy}, Tris{tt;jrt-pentoxy) silanol, or tetraethoxysiiaue (TEOS).

The reagents are also generally selected to be compatible with the ALT ⁾ process, and are selected based on the chemistry of the precursor and material For example, where the material is an oxide, the reagent can be an oxidizing agent. Examples of suitable oxidizing agents include water, hydrogen peroxide, oxygen, ozone. (CH^AL and various alcohols (e.g., Ethyl alcohol CM ₃ OH), Water, for example, is a suitable reagent for oxidizing precursors such as Ti(T ₄ to obtain TiO?.

AlCI _? to obtain AiaO*, and Ta-ethaoxide to obtain Ta ₂ O ₅ , Nb-ethaoxicie to obtain Nb _, ->Q ₅ , MfCl ₄ to obtain HfO ₂ , ZrCl ₄ to obtain ZiO ₂ , and LoCb to obtain irbCH. In each case, JHCl is produced as a byproduct !π. some embodiments, (ChbbAl can be used to oxidize silanol to provide SiO^. Irs same embodiments, an optical retard er can be combined with a linear polarizing film to provide a polarizer that delivers light of a certain non-linear polarization (e.g., circularly polarized light or a specific elliptical polarization state). An example of such a device is polarizer 1100, shown in FfG. ! 1. Polarizer 1 100 includes polarizing film 11 IO (e.g., an absorptive polarizing film, such as iodinesunned polyvinyl alcohol, or a reflective polarizer) and optical retarder 1.120. Film 1 \ 10 linearly polarizes incident isotropic light propagating along axis 11 10. Subsequently, optical retarder 620 retards the polarized light exiting polarizing film 1 1 10, resulting in polarized light having a specific ellipttoity and orientation of the elliptical axes. Alternatively, optical retarder [120 can be designed to rotate the electric field direction of the linearly polarized light exiting film 11 i 0, Polarizer 1 100 can be included in a variety of optical systems, such as, for example, a liquid crystal display (LCD) (e.g., a Liquid Crystal on Silicon (LCoS) LCD),

As another example, referring to FIG 12, in some embodiments, an optical retarder 1210 can be included in an optical pickup 1201 used for reading and/or writing to an optical storage medium 1220 (e.g., a CD or DVD). In addition to optica! retarder 1210, optical pickup 1201 also includes a light source 1230 (e.g., one or snore laser diodes), a polarizing beam splitter 1240, and a detector 1250, In some embodiments, optical retarder has quarter wave retardation at wavelengths λ( and λ;j (e.g., about 660 nm and about 785 ran, respectively). Alternatively, or additionally, in certain embodiments, optical retarder can also have quarter-wave retardation at other wavelengths, such as about 405 nm for example. During operation, light source 1230 illuminates a surface of medium 1220 with linearly polarized radiation at λj and/or X% as the medium spins (indicated by arrow 122! }. The polarized radiation passes through polarizing beam splitter (PBS) 1240. Optical retarder 1210 retards the polarized radiation, changing it from linearly polarized radiation to substantially circularly polarized radiation. The circularly polarized radiation changes handedness

upon reflectϊOω from medium 1220, and is converted back to linearly polarized radiation upon its second pass through optical retarder 1210. At beam splitter 1240, the reflected radiation is polarized orthogonally relative to the original polarization stale of the radiation emitted from light source 1230. Accordingly; polarizing beam splitter reflects the radiation returning from medium 1220, directed it to detector 1250. The retarder can be integrated with the PBS in this device. The PBS can be a metal wire-grid polarizer. in some embodiments, optical retarders can be used as components in a liquid crystal display (LCD). For example, optica! retarders can be used to improve the viewing angle characteristics of LCDs. The transmission properties of an LCD generally depends on the angle of viewing for many modes of operation based on a thin film of liquid crystal material, including, for example, twisted nematic (TN) LCDs, vertically-aligned (VA) LCDs, bend aligned (BA) LCDs, and super-twisteά- nematic (STN) LCDs. Optical retarders can be used to improve the viewing angle characteristics of LCDs by, for example, introducing compensatory retardation of off- axis light relative to on-axis light.

As an example, refernng FlG 13, an LCD 1300 includes, among other components, im LC Him 1310, optical retarders 1320 and 1330, a polarizer 1340 and an analyzer 1342. Optica) retarder 1320 includes an «-platc retardation layer 132 ! and a e-plate retardation film 1322. Optical retarder 1330 includes an c-piaie retardation layer 1331 and a opiate retardation film 1332.

The substrate surfaces (not shown in FlG. 13} of adjacent LC layer 13 I ^Q arc treated so that the LC molecules align substantially parallel to the x~axis and .y-axis adjacent retardation layers 1330 and 1332, respectively. The optica! axis of α-piate retardation layer 1330 is substantially parallel to the jf-axis and the optical axis of a- piale retardation layer 1332 is substantially parallel Io the v-axis. The polarizer and analyzer arc configured so that the display appears bright when BO voltage is applied across the LC film (i.e., the display is normally white).

The fi-phui* retardation layers are employed to reduce the phase retardation due to the LC regions near the surfaces of the LC film. The optic axes of the #-p!aies are aligned substantially parallel to the rubbing directions of the adjacent surfaces,

The e-plate retardation films are aligned with their optic axes substantially parallel to the --axis. The opiate retardation films compensate for the effect ofhomeotropic LC molecules m the middle of the LC film when a voltage is applied to the film. In general, the retardation of the each υf the retardation films and retardation layers are selected based, on the retardation of the LC film. The retardation of each film/layer can be determined from tbeoretiea! modeling and/or empirically.

Viewing angle compensation of LCDs is discussed further by P. YeH and C. Gu m "Optics of Liquid Crystal Displays," John Wiley & Sons, Inc., New York ( 1999), for example. Compensators are also described in Yeh et aL in U.S. Patent No. 5, 196.953.

Furthermore, while the foregoing examples of LCD compensators are in relation to iraπsmissive LCDs, more generally, optical retarders can also be used to compensate other types of LCD. For example, optical retarders can be used to compensate reflective LCDs, such as liquid crystal on silicon (LCX)S) LCDs. In certain embodiments, optical retarders can he used in applications that utilize ultraviolet radiation. Optical retarders may he relatively stable when exposed to UV radiation, for example, when they do not include any organic materials. Accordingly; optical retarders can be used as retarders in UV lasers and systems that use UV lasers, such as lithography tools. Other embodiments are in the claims.