Abstract:
Films for optical use, articles containing such films, methods for making such films, and systems that utilize such films, are disclosed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims priority under 35 U.S.C. §119 to U.S. Provisional Patent Application Ser. No. ______, entitled “PRECISION OPTICAL RETARDERS AND WAVEPLATES AND THE METHOD FOR MAKING THE SAME,” and filed on Apr. 15, 2004, the entire contents of which are hereby incorporated by reference. 
     
    
     TECHNICAL FIELD  
       [0002]     This invention relates to optical films and related articles, systems and methods.  
       BACKGROUND  
       [0003]     Optical devices and optical systems are commonly used where manipulation of light is desired. Examples of optical devices include lenses, polarizers, optical filters, antireflection films, retarders (e.g., quarter-waveplates), and beam splitters (e.g., polarizing and non-polarizing beam splitters).  
       SUMMARY  
       [0004]     This invention relates to films for optical use, articles containing such films, methods for making such films, and systems that utilize such films.  
         [0005]     In a first aspect, the invention features a method that includes providing an article that includes a layer of a first material, wherein the layer of the first material includes at least one trench and wherein the layer is birefringent for light of wavelength λ propagating through the layer along an axis, wherein λ is between 150 nm and 2,000 nm, and filling at least about 50% of a volume of the trench by sequentially forming a plurality of monolayers of a second material within the trench.  
         [0006]     In another aspect, the invention features a method that includes forming a layer of a material on a surface of a grating using atomic layer deposition.  
         [0007]     In another aspect, the invention features a method that includes forming an optical retardation film using atomic layer deposition.  
         [0008]     In another aspect, the invention features an article, which includes a continuous layer including rows of a first material alternating with rows of a nanolaminate material, wherein the continuous layer is birefringent for light of wavelength λ propagating through the continuous layer along an axis, wherein λ is between 150 nm and 2,000 nm.  
         [0009]     In another aspect, the invention features an article including a form birefringent optical retardation film that includes a nanolaminate material.  
         [0010]     Embodiments of the invention can include one or more of the following features.  
         [0011]     The filling can further include forming one or more monolayers of a third material within the trench, wherein the second and third materials are different. The monolayers of the second and third materials can form a nanolaminate material. At least about 80% (e.g., at least about 90%, at least about 99%) of the volume of the trench can be filled by sequentially forming the plurality of monolayers of the second material within the trench. The second material can be different from the first material. The layer of the first material and the second material can form a continuous layer. The continuous layer can be birefringent for light of wavelength λ propagating through the continuous layer along an axis, wherein λ is between 150 nm and 2,000 nm. The article can include additional trenches formed in the surface of the layer of the first material. The method can further include filling at least about 50% of a volume of each of the additional trenches by sequentially forming a plurality of monolayers of the second material within the additional trenches. The method can further include filling at least about 80% (e.g., at least about 90%, at least about 99%) of a volume of each of the additional trenches by sequentially forming a plurality of monolayers of the second material within the additional trenches. The trenches can be separated by rows of the first material. The layer of the first material can form a surface relief grating. The surface relief grating can have a grating period of about 500 nm or less (e.g., about 400 nm or less, about 300 mm or less, about 200 nm or less, about 100 nm or less).  
         [0012]     The trench can be formed by etching (e.g., reactive ion etching) a continuous layer of the first material. The trench can be formed lithographically. For example, the trench can be formed using nano-imprint lithography or holographic lithography. Where the trench is formed using nano-imprint lithography, the nano-imprint lithography can include forming a pattern in a thermoplastic material. Alternatively, or additionally, the nano-imprint lithography can include forming a pattern in a UV curable material.  
         [0013]     The method can further include forming a layer of the second material over the filled trench by sequentially forming monolayers of the second material over the trench. The layer of the second material has a surface with an arithmetic mean roughness of about 50 nm or less (e.g., about 40 nm or less, about 30 nm or less, about 20 mm or less, about 10 nm or less).  
         [0014]     The second material can be a dielectric material. In some embodiments, forming the plurality of monolayers of the second material comprises depositing a monolayer of a precursor and exposing the monolayer of the precursor to a reagent to provide a monolayer of the second material. The reagent can chemically react with the precursor to form the second material. For example, the reagent can oxidize the precursor to form the second material. Depositing the monolayer of the precursor can include introducing a first gas comprising the precursor into a chamber housing the article. A pressure of the first gas in the chamber can be about 0.01 to about 100 Torr while the monolayer of the precursor is deposited. Exposing the monolayer of the precursor to the reagent can include introducing a second gas comprising the reagent into the chamber. A pressure of the second gas in the chamber can be about 0.01 to about 100 Torr while the monolayer of the precursor is exposed to the reagent. A third gas can be introduced into the chamber after the first gas is introduced and prior to introducing the second gas. The third gas can be inert with respect to the precursor. The third gas can include at least one gas selected from the group consisting of helium, argon, nitrogen, neon, krypton, and xenon. The precursor can be selected from the group consisting of tris(tert-butoxy)silanol, (CH 3 ) 3 Al, TiCl 4 , SiCl 4 , SiH 2 Cl 2 , TaCl 3 , AlCl 3 , Hf-ethaoxide and Ta-ethaoxide.  
         [0015]     The trench can have a width of about 1,000 nm or less (e.g., about 900 mm or less, about 800 mm or less, about 700 nm or less, about 600 nm or less, about 500 m or less, about 400 mm or less, about 300 nm or less, about 200 nm or less). The trench can have a depth of about 10 nm or more (e.g., about 20 nm or more, about 30 m or more, about 40 nm or more, about 50 nm or more, about 75 m or more, about 100 mm or more, about 150 nm or more, about 200 nm or more, about 300 mm or more, about 400 nm or more, about 500 nm or more, about 1,000 or more, about 1,500 nm or more, about 2,000 or more).  
         [0016]     The method can further include forming a second birefringent layer on the layer of the first material after filling the trench. The second birefringent layer can include a plurality of trenches and forming the second birefringent layer includes filling the plurality of trenches by sequentially forming a plurality of monolayers of a third material within the trenches of the second birefringent layer. The method can also include forming additional birefringent layers on the second birefringent layer.  
         [0017]     In certain embodiments, the grating can be a surface relief grating. The grating can have a grating period of about 2,000 nm or less (e.g., about 1,500 nm or less, about 1,000 or less, about 750 nm or less, about 500 nm or less, about 300 nm or less, about 200 nm or less).  
         [0018]     The optical retardation film can be form birefringent.  
         [0019]     The article can further include at least one antireflection film, wherein a surface of the article comprises a surface of the antireflection film. In some embodiments, the article also includes a layer of a third material adjacent the continuous layer. The article can include a layer of the nanolaminate material adjacent the continuous layer. The layer of the nanolaminate material adjacent the continuous layer can have a surface with an arithmetic mean roughness of about 50 nm or less (e.g., about 40 nm or less, about 30 nm or less, about 20 nm or less, about 10 nm or less). The nanolaminate material can have a refractive index of about 1.3 or more at λ (e.g., about 1.4 or more, about 1.5 or more, about 1.6 or more, about 1.7 or more, about 1.8 or more, about 1.9 or more, about 2.0 or more, about 2.1 or more). The first material can have a refractive index of about 1.3 or more at λ (e.g., about 1.4 or more, about 1.5 or more, about 1.6 or more, about 1.7 or more, about 1.8 or more, about 1.9 or more, about 2.0 or more, about 2.1 or more). The nanolaminate material can include portions of a second material and portions of a third material, wherein the second and third materials are different. In some embodiments, the first and third materials are the same.  
         [0020]     The nanolaminate material can include a dielectric material, an inorganic material, and/or a metal. The nanolaminate material can include a material selected from a group consisting of SiO 2 , SiN x , Si, Al 2 O 3 , ZrO 2 , Ta 2 O 5 , TiO 2 , HfO 2 , Nb 2 O 5 , and MgF 2 .  
         [0021]     The first material can be a dielectric material, an inorganic material, a glass, a polymer, a semiconductor, and/or a metal. In certain embodiments, the first material is selected from a group consisting of SiO 2 , SiN x , Si, Al 2 O 3 , ZrO 2 , Ta 2 O 5 , TiO 2 , HfO 2 ; Nb 2 O 5 , and MgF 2 .  
         [0022]     The continuous layer can form a grating with a grating period of about 500 nm or less (e.g., about 200 nm or less, about 100 nm or less, about 50 nm or less). The rows of the first material can have a minimum width of about 500 nm or less (about 200 nm or less, about 100 nm or less, about 50 nm or less, about 20 nm or less, about 10 nm or less). The rows of the first material can have a minimum width that is the same or different than a minimum width of the rows of the nanolaminate material. A minimum width of each of the rows of the first material can be substantially the same. Alternatively, or additionally, a minimum width of each of the rows of the nanolaminate material is substantially the same.  
         [0023]     The continuous layer has a thickness of about 15 nm or more (e.g., about 30 nm or more, about 50 nm or more, about 75 nm or more, about 100 nm or more, about 150 or more, about 200 nm or more, about 300 nm or more, about 500 nm or more, about 1,000 nm or more, about 1,500 nm or more, about 2,000 or more). In certain embodiments, the continuous layer has an optical retardation of about 1 nm or more (e.g., about 2 nm or more, about 5 nm or more, about 10 nm or more, about 20 nm or more, about 50 nm or more) for light of wavelength λ propagating through the continuous layer along an axis, wherein λ is between 150 nm and 2,000 nm. The continuous layer can have an optical retardation of about 2,000 nm or less for light of wavelength λ propagating through the composite layer along an axis, wherein λ is between 200 nm and 2,000 nm. In some embodiments, λ is between about 400 nm and about 700 m (e.g., between about 510 nm and about 570 nm). In some embodiments, the continuous layer has an optical retardation of about 4 nm or more for light of wavelength λ propagating through the continuous layer along an axis, wherein λ is between about 400 nm and about 700 nm.  
         [0024]     The article can include a second continuous layer including rows of a third material alternating with rows of a second nanolaminate material, wherein the second continuous layer is birefringent for light of wavelength λ propagating through the second continuous layer along the axis. The article can further include additional form the portion(s), thereby controlling the birefringence. As an example, one or more portions of the layer can be formed from a nanolaminate. The refractive index of the nanolaminate can be tuned by selecting the proportion of two or more different materials in the nanolaminate, which can be controlled on a monolayer by monolayer basis where the nanolaminate is formed using atomic layer deposition.  
         [0025]     Alternatively, or additionally, precisely controlling the structure of the layer can accurately control the birefringence of a form birefringent layer. For example, using lithographic techniques (e.g., electron beam lithography, nanoimprint lithography, holographic lithography) to define the structure (e.g., depth, width and profile of a grating) of a form birefringent layer can allow for precise control of the structure.  
         [0026]     In certain embodiments, the retardance of optical retarders can be precisely controlled. For example, the birefringence and/or depth of a form birefringent layer in an optical retarder can be precisely controlled to provide a desired retardance. As an example, optical retarders can include one or more layers to control the thickness of portions of a form birefringent layer in the retarder, such as one or more etch stop layers.  
         [0027]     In some embodiments, optical retarders have high transmission at wavelengths of interest. For example, optical retarders can include one or more antireflection films on one or more interfaces that reduce reflection of light at wavelengths of interest. Alternatively, or additionally, layers of optical retarders can be formed from materials with relatively low absorption at wavelengths of interest.  
         [0028]     Other features, and advantages of the invention will be apparent from the description and drawings, and from the claims. 
     
    
     DESCRIPTION OF DRAWINGS  
       [0029]      FIG. 1  is a perspective view of an embodiment of an optical retarder.  
         [0030]      FIGS. 2A-2J  show steps in the manufacture of the optical retarder shown in  FIG. 1 .  
         [0031]      FIG. 3  is a schematic diagram of an atomic layer deposition system.  
         [0032]      FIG. 4  is a flow chart showing steps for forming a nanolaminate using atomic layer deposition.  
         [0033]      FIG. 5  is a cross-sectional view of another embodiment of an optical retarder birefringent layers, wherein each of the form birefringent layers are birefringent for light of wavelength λ propagating through each form birefringent layer along the axis.  
         [0034]     Embodiments of the invention may include one or more of the following advantages.  
         [0035]     In some embodiments, the article can be a relatively robust optical retarder, that can have high transmission at wavelengths of interest, and that have a retardation that can be precisely controlled. Optical retarders can include one or more form birefringent layers. Form birefringence results from sub-wavelength structure in a medium, which can be achieved by arranging at least two difference materials (e.g., optically isotropic materials) in an alternating way. Form birefringence can result from sub-wavelength grating structures, in which a medium has a periodic modulation in its refractive index, where the period is substantially less than the wavelength of interest. Since the period is less than the wavelength of interest, substantially only zero-order diffractions occur and all higher order diffractions become evanescent (e.g., a beam at the wavelength of interest is substantially transmitted and/or reflected). While the materials composing the form birefringent media can be optically isotropic (i.e., having an isotropic index of refraction), the media itself will be optically anisotropic, giving rise to birefringence.  
         [0036]     In some embodiments, optical retarders can include one or more form birefringent layers that are formed of continuous material, as opposed to, for example, having trenches filled with a gas (e.g., air). Accordingly, the optical retarders can be more mechanically robust than optical retarders that include non-continuous layers (e.g., layers that include one or more trenches filled with air).  
         [0037]     In certain embodiments, continuous form birefringent layers can be formed having relatively high aspect ratios between the width and thickness of portions of the layers. As an example, high aspect ratio trenches can be etched into a layer, and the trenches subsequently filled using a conformal coating method (e.g., atomic layer deposition) to provide a continuous form birefringent layer having a relatively high aspect ratio.  
         [0038]     The birefringence of optical retarders can be precisely controlled. To achieve this, the refractive index of one or more portions of a form birefringent layer in an optical retarder can, for example, be tuned to a desired value by controlling the composition of  
         [0039]      FIG. 6  is a cross-sectional view of an embodiment of an optical retarder including multiple retardation layers.  
         [0040]      FIG. 7  is a cross-sectional view of a polarizer incorporating an optical retarder.  
         [0041]      FIG. 8  is a cross-sectional view of a liquid crystal display incorporating an optical retarder.  
         [0042]      FIG. 9A  is a scanning electron micrograph of a sub-wavelength grating prior to trench filling.  
         [0043]      FIG. 9B  is a scanning electron micrograph of the sub-wavelength grating shown in  FIG. 9A  after trench filling. 
     
    
       [0044]     Like reference symbols in the various drawings indicate like elements.  
       DETAILED DESCRIPTION  
       [0045]     Referring to  FIG. 1 , an embodiment of an optical retarder  100  includes a retardation layer  110  and two antireflection films  150  and  160 . Optical retarder  100  also includes a substrate  140 , an etch stop layer  130 , and a cap layer  120 . Retardation layer  110  is in the form of a grating and includes portions  111  having a first refractive index and portions  112  having second refractive index. Retardation layer  110  is birefringent for light of wavelength λ propagating along an axis  101 , parallel to the z-axis of the Cartesian coordinate system shown in  FIG. 1 . In general, λ is between about 150 nm and about 5,000 nm. In certain embodiments, λ corresponds to a wavelength within the visible portion of the electromagnetic spectrum (e.g., from about 400 nm to about 700 nm).  
         [0046]     Portions  111  and  112  extend along the y-direction, forming a periodic structure consisting of a series of alternating rows having different indices of refraction. The rows corresponding to portions  111  have a width Λ 111  in the x-direction, while the rows corresponding to portions  112  have a width Λ 112  in the x-direction. The widths of the rows are smaller than λ, resulting in retardation layer  110  being form birefringent for light of wavelength λ without encountering significant high-order diffraction. Optical waves with different polarization states propagate through retardation layer  110  with different phase shifts, which depend on the thickness of retardation layer  110 , the index of refraction of portions  111  and  112 , and Λ 111  and Λ 112 . Accordingly, these parameters can be selected to provide a desired amount of retardation to polarized light at λ.  
         [0047]     Retardation layer  110  has a birefringence, Δn, which corresponds to n e -n o , where n e , and n o  are the effective extraordinary and ordinary indices of refraction for layer  110 , respectively. For retardation layer  110 , n e  and n o  are given by:  
                 n   o   2     =           Λ   111         Λ   111     +     Λ   112         ⁢     n   111   2       +         Λ   112         Λ   111     +     Λ   112         ⁢     n   112   2           ⁢     
     ⁢       1     n   e   2       =           Λ   111         Λ   111     +     Λ   112         ⁢     1     n   111   2         +         Λ   112         Λ   111     +     Λ   112         ⁢       1     n   112   2       .                   (   1   )             
 
 In Eq. (1), n 111  and n 112  and Λ 111  and Λ 112  refer to the refractive indices and thickness (along the x-direction) of portions  111  and  112  respectively. In general, the values of ne and n 0  depend on n 111 , n 112 , Λ 111  and Λ 112 , and are between n 111  and n 112 . Λ 111  and Λ 112  can be selected to provide a desired value of Δn based on the values for n e  and n o  given by Eq. (1). Moreover, the refractive indices n 111  and n 112 , which depend on the respective compositions of portions  111  and  112 , can be selected to provide a desired value of Δn. In some embodiments, Δn is relatively large (e.g., about 0.1 or more, about 0.15 or more, about 0.2 or more, about 0.3 or more, about 0.5 or more, about 1.0 or more, about 1.5 or more, about 2.0 or more). Alternatively, in other embodiments, Δn 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 less, about 0.005 or less, about 0.002 or less, 0.001 or less). 
 
         [0048]     In general, the refractive index of portions  111  can be about 1.3 or more (e.g., about 1.4 or more, about 1.5 or more, about 1.6 or more, about 1.7 or more, about 1.8 or more, about 1.9 or more, about 2.0 or more, about 2.1 or more, about 2.2 or more). Furthermore, in general, the refractive index of portions  112  can be about 1.3 or more (e.g., about 1.4 or more, about 1.5 or more, about 1.6 or more, about 1.7 or more, about 1.8 or more, about 1.9 or more, about 2.0 or more, about 2.1 or more, about 2.2 or more).  
         [0049]     In general, Λ 111  can be about 0.2 λ or less (e.g., about 0.1 λ or less, about 0.05 λ or less, about 0.04 λ or less, about 0.03 λ or less, about 0.02 λ or less, 0.01 λ or less). For example, in some embodiments, Λ 111  is about 200 nm or less (e.g., about 150 nm or less, about 100 nm or less, about 80 nm or less, about 70 nm or less, about 60 nm or less, about 50 nm or less, about 40 m or less, about 30 nm or less). Similarly, Λ 112  can be about 0.2 λ or less (e.g., about 0.1 λ or less, about 0.05 λ or less, about 0.04 λ or less, about 0.03 λ or less, about 0.02 λ or less, 0.01 λ or less). For example, in some embodiments, Λ 112  is about 200 nm or less (e.g., about 150 nm or less, about 100 nm or less, about 80 nm or less, about 70 nm or less, about 60 nm or less, about 50 nm or less, about 40 nm or less, about 30 m or less). Λ 111  and Λ 112  can be the same as each other or different.  
         [0050]     Along the x-axis, the refractive index of retardation layer  110  is periodic, with a period, Λ, corresponding to Λ 111 +Λ 112 . In general, Λ is less than λ, such as about 0.5 λ or less (e.g., about 0.3 λ or less, about 0.2 λ or less, about 0.1 λ or less, about 0.08 λ or less, about 0.05 λ or less, about 0.04 λ or less, about 0.03 λ or less, about 0.02 λ or less, 0.01 λ or less). In some embodiments, Λ is about 500 nm or less (e.g., about 300 nm or less, about 200 m or less, about 100 nm or less, about 80 nm or less, about 60 m or less, about 50 nm or less, about 40 nm or less).  
         [0051]     While retardation layer  110  is shown as having 19 portions, in general, the number of portions in a retardation layer may vary as desired. The number of portions depends on the period, A, and the area required by the retarder&#39;s end use application. In some embodiments, retardation layer  110  can have about 50 or more portions (e.g., about 100 or more portions, about 500 or more portions, about 1,000 or more portions, about 5,000 or more portions, about 10,000 or more portions, about 50,000 or more portions, about 100,000 or more portions, about 500,000 more portions).  
         [0052]     The thickness, d, of retardation layer  110  measured along the z-axis can vary as desired. In general, the thickness of layer  110  is selected based on the refractive indices of portions  111  and  112  and the desired retardation of retardation layer  110  at λ. In some embodiments, d can be about 50 nm or more (e.g., about 75 nm or more, about 100 nm or more, about 125 nm or more, about 150 nm or more, about 200 nm or more, about 250 nm or more, about 300 nm or more, about 400 m or more, about 500 nm or more, about 1,000 or more, such as about 2,000 nm).  
         [0053]     The aspect ratio of retardation layer thickness, d, to Λ 111  and/or d to Λ 112  can be relatively high. For example d:Λ 111  and/or d:Λ 112  can be 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).  
         [0054]     The retardation of retardation layer  110  corresponds to the product of the thickness of retardation layer  110 , d, and Δn. By selecting appropriate values for Δn and the layers thickness, the retardation can vary as desired. In some embodiments, the retardation of retardation layer  110  is about 50 nm or more (e.g., about 75 nm or more, about 100 nm or more, about 125 nm 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 1,000 or more, such as about 2,000 nm). Alternatively, in other embodiments, the retardation is about 40 nm or less (e.g., about 30 nm or less, about 20 nm or less, about 10 nm or less, about 5 m or less, about 2 nm or less). In some embodiments, the retardation corresponds to λ/4 or λ/2.  
         [0055]     Retardation can also be expressed as a phase retardation, Γ, where  
             Γ   =         2   ⁢   π     λ     ⁢   Δ   ⁢           ⁢     nd   .               (   2   )             
 
 For example, quarter wave retardation corresponds to Γ=π/2, while half wave retardation corresponds to Γ=π. In general, phase retardation may vary as desired. In some embodiments, phase retardation may be about 2π or less (e.g., about 0.8 π or less, about 0.7π or less, about 0.6π or less, about 0.5π or less, about 0.4π or less, about 0.2π or less, 0.2π or less, about 0.1π or less, about 0.05π or less, 0.1π or less). Alternatively, in other embodiments, phase retardation of retardation layer  110  can be more than 2 π (e.g., about 3π or more, about 4π or more, about 5π or more). 
 
         [0056]     In general, the composition of portions  111  and  112  can vary as desired. Portions  111  and/or  112  can include inorganic and/or organic materials. Examples of inorganic materials include metals, semiconductors, and inorganic dielectric materials (e.g., glass). Examples of organic materials include polymers.  
         [0057]     In some embodiments, portions  111  and/or portions  112  include 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 SiO 2 , Al 2 O 3 , Nb 2 O 5 , TiO 2 , ZrO 2 , HfO 2 , SnO 2 , ZnO, ErO 2 , Sc 2 O 3 , and Ta 2 O 5 . Examples of fluorides include MgF 2 . Other examples include ZnS, SiN x , SiO y N x , AlN, TiN, and HfN.  
         [0058]     The compositions of portions  111  and  112  are typically selected based on their optical properties and their compatibility with the processes used to manufacture optical retarder  100  and their compatibility with the materials used to form other layers of optical retarder  100 . The composition of portions  111  and/or portions  112  can be selected to have particular refractive indices at λ. In general, the refractive index of portion  111  is different from the refractive index or portion  112  at λ. In some embodiments, portions  111  or portions  112  are formed from a material that has a relatively high index of refraction, such as TiO 2 , which has a refractive index of about 2.35 at 632 nm, or Ta 2 O 5 , which has a refractive index of 2.15 at 632 nm. Alternatively, portions  111  or portions  112  can be formed from a material that has a relatively low index of refraction. Examples of low index materials include SiO 2  and Al 2 O 3 , which have refractive indices of 1.45 and 1.65 at 632 nm, respectively.  
         [0059]     In some embodiments, the composition of portions  111  and/or portions  112  have a relatively low absorption at λ, so that retardation layer  110  has a relatively low absorption at λ. For example, retardation layer  110  can absorb about 5% or less of radiation at λ propagating along axis  101  (e.g., about 3% or less, about 2% or less, about 1% or less, about 0.5% or less, about 0.2% or less, about 0.1% or less).  
         [0060]     Portions  111  and/or portions  112  can be formed from a single material or from multiple different materials. In some embodiments, one or both of portions  111  and  112  are formed from a nanolaminate material, which refers to materials that are composed of layers of at least two different materials and the layers of at least one of the materials are extremely thin (e.g., between one and about 10 monolayers thick). Optically, nanolaminate materials have a locally homogeneous index of refraction that depends on the refractive index of its constituent materials. Varying the amount of each constituent material can vary the refractive index of a nanolaminate. Examples of nanolaminate portions include portions composed of SiO 2  monolayers and TiO 2  monolayers, SiO 2  monolayers and Ta 2 O 5  monolayers, or Al 2 O 3  monolayers and TiO 2  mono layers.  
         [0061]     Portions  111  and/or portions  112  can include crystalline, semi-crystalline, and/or amorphous portions. Typically, an amorphous material is optically isotropic and may transmit light better than portions that are partially or mostly crystalline. As an example, in some embodiments, both portions  111  and  112  are formed from amorphous materials, such as amorphous dielectric materials (e.g., amorphous TiO 2  or SiO 2 ). Alternatively, in certain embodiments, portions  111  are formed from a crystalline or semi-crystalline material (e.g., crystalline or semi-crystalline Si), while portions  112  are formed from an amorphous material (e.g., an amorphous dielectric material, such as TiO 2  or SiO 2 ).  
         [0062]     Referring now to other layers in optical retarder  100 , in general, substrate  140  provides mechanical support to optical retarder  100 . In certain embodiments, substrate  140  is transparent to light at wavelength λ, transmitting substantially all light impinging thereon at wavelength λ (e.g., about 90% or more, about 95% or more, about 97% or more, about 99% or more, about 99.5% or more).  
         [0063]     In general, substrate  140  can be formed from any material compatible with the manufacturing processes used to produce retarder  100  that can support the other layers. In certain embodiments, substrate  140  is formed from a glass, such as BK7 (available from Abrisa Corporation), borosilicate glass (e.g., pyrex available from Corning), aluminosilicate glass (e.g., C1737 available from Corning), or quartz/fused silica. In some embodiments, substrate  140  can be formed from a crystalline material, such as a non-linear optical 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  140  can also be formed from an inorganic material, such as a polymer (e.g., a plastic).  
         [0064]     Etch stop layer  130  is formed from a material resistant to etching processes used to etch the material(s) from which portions  112  are formed (see discussion below). The material(s) forming etch stop layer  130  should also be compatible with substrate  140  and with the materials forming retardation layer  110 . Examples of materials that can form etch stop layer  130  include HfO 2 , SiO 2 , Ta 2 O 5 , TiO 2 , SiN x , or metals (e.g., Cr, Ti, Ni).  
         [0065]     The thickness of etch stop layer  130  can be varied as desired. Typically, etch stop layer  130  is sufficiently thick to prevent significant etching of substrate  140 , but should not be so thick as to adversely impact the optical performance of optical retarder  100 . In some embodiments, etch stop layer is about 500 nm or less (e.g., about 250 nm or less, about 100 nm or less, about 75 nm or less, about 50 nm or less, about 40 nm or less, about 30 nm or less, about 20 nm or less).  
         [0066]     Cap layer  120  is typically formed from the same material(s) as portions  111  of retardation layer  110  and provides a surface  121  onto which additional layers, such as the layers forming antireflection film  150 , can be deposited. Surface  121  can be substantially planar.  
         [0067]     Antireflection films  150  and  160  can reduce the reflectance of light of wavelength λ impinging on and exiting optical retarder  100 . Antireflection film  150  and  160  generally include one or more layers of different refractive index. As an example, one or both of antireflection films  150  and  160  can be formed from four alternating high and low index layers. The high index layers can be formed from TiO 2  or Ta 2 O 5  and the low index layers can be formed from SiO 2  or MgF 2 . The antireflection films can be broadband antireflection films or narrowband antireflection films.  
         [0068]     In some embodiments, optical retarder  100  has a reflectance of about 5% or less of light impinging thereon at wavelength 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  100  can have high transmission of light of wavelength λ. For example, optical retarder can transmit about 95% or more of light impinging thereon at wavelength λ (e.g., about 98% or more, about 99% or more, about 99.5% or more).  
         [0069]     In general, optical retarder  100  can be prepared as desired.  FIGS. 2A-2J  show different phases of an example of a preparation process. Initially, substrate  140  is provided, as shown in  FIG. 2A . Surface  141  of substrate  140  can be polished and/or cleaned (e.g., by exposing the substrate to one or more solvents, acids, and/or baking the substrate).  
         [0070]     Referring to  FIG. 2B , etch stop layer  130  is deposited on surface  141  of substrate  140 . The material forming etch stop layer  130  can be formed using one of a variety of techniques, including sputtering (e.g., radio frequency sputtering), evaporating (e.g., electron beam evaporation, ion assisted deposition (LAD) electron beam evaporation), or chemical vapor deposition (CVD) such as plasma enhanced CVD (PECVD), ALD, or by oxidization. As an example, a layer of HfO 2  can be deposited on substrate  140  by _IAD electron beam evaporation.  
         [0071]     Referring to  FIG. 2C , an intermediate layer  210  is then deposited on surface  131  of etch stop layer  130 . Portions  112  are etched from intermediate layer  210 , so intermediation layer  210  is formed from the material used for portions  112 . The material forming intermediate layer  210  can be deposited using one of a variety of techniques, including sputtering (e.g., radio frequency sputtering), evaporating (e.g., election beam evaporation), or chemical vapor deposition (CVD) (e.g., plasma enhanced CVD). As an example, a layer of SiO 2  can be deposited on etch stop layer  130  by sputtering (e.g., radio frequency sputtering), CVD (e.g., plasma enhanced CVD), or electron beam evaporation (e.g., LAD electron beam deposition). The thickness of intermediate layer  210  is selected based on the desired thickness of retardation layer  110 .  
         [0072]     Intermediate layer  210  is processed to provide portions  112  of retardation layer  110  using lithographic techniques. For example, portions  112  can be formed from intermediate layer  210  using electron beam lithography or photolithograpy (e.g., using a photomask or using holographic techniques). In some embodiments, portions  112  are formed using nano-imprint lithography. Referring to  FIG. 2D , nano-imprint lithography includes forming a layer  220  of a resist on surface  211  of intermediate layer  210 . The resist can be polymethylmethacrylate (PMMA) or polystyrene (PS), for example. Referring to  FIG. 2E , a pattern is impressed into resist layer  220  using a mold. The patterned resist layer  220  includes thin portions  221  and thick portions  222 . Patterned resist layer  220  is then etched (e.g., by oxygen reactive ion etching (RIE)), removing thin portions  221  to expose portions  224  of surface  211  of intermediate layer  210 , as shown in  FIG. 2F . Thick portions  222  are also etched, but are not completely removed. Accordingly, portions  223  of resist remain on surface  211  after etching.  
         [0073]     Referring to  FIG. 2G , the exposed portions of intermediate layer  210  are subsequently etched, forming trenches  212  in intermediate layer  210 . The unetched portions of intermediate layer  210  correspond to portions  112  of retardation layer  110 . Intermediate layer  210  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  210  are etched down to etch stop layer  130 , which is formed from a material resistant to the etching method. Accordingly, the depth of trenches  212  formed by etching is the same as the thickness of portions  112 . After etching trenches  212 , residual resist  223  is removed from portions  112 . Resist can be removed by rinsing the article in a solvent (e.g., an organic solvent, such as acetone or alcohol), by O 2  plasma ashing, O 2  RIE, or ozone cleaning.  
         [0074]     Referring to  FIG. 2I , after removing residual resist, material is deposited onto the article, filling trenches  212  and forming cap layer  120 . The filled trenches correspond to portions  111  of retardation layer  110 . Material 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 cap layer  120  is formed and trenches  212  are filled during the same deposition step, portions  111  and cap layer  120  are formed from a continuous portion of material.  
         [0075]     Finally, antireflection films  150  and  160  are deposited onto surface  121  of cap layer  120  and surface  142  of substrate  140 , respectively: Materials forming the antireflection films can be deposited onto the article by sputtering, electron beam evaporation, or ALD, for example.  
         [0076]     As mentioned previously, in some embodiments, portions  111  of retardation layer  110 , cap layer  120 , and/or one or both of antireflection films  150  and  160  are prepared using atomic layer deposition (ALD). For example, referring to  FIG. 3 , an ALD system  300  is used to fill trenches  212  of an intermediate article  301  (composed of substrate  140 , cap layer  130 , and portions  112 ) with a nanolaminate multilayer film, forming portions  111  and cap layer  120 . 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 are introduced into the chamber and are adsorbed onto exposed surfaces of portions  112 , etch stop layer surface  131  or previously deposited monolayers adjacent these surfaces. Subsequently, a reactant is introduced into the 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  110 . Accordingly, the layers of the nanolaminate film conform to the shape of the trenches of intermediate article  301 .  
         [0077]     ALD system  300  includes a reaction chamber  310 , which is connected to sources  350 ,  360 ,  370 ,  380 , and  390  via a manifold  330 . Sources  350 ,  360 ,  370 ,  380 , and  390  are connected to manifold  330  via supply lines  351 ,  361 ,  371 ,  381 , and  391 , respectively. Valves  352 ,  362 ,  372 ,  382 , and  392  regulate the flow of gases from sources  350 ,  360 ,  370 ,  380 , and  390 , respectively. Sources  350  and  380  contain a first and second precursor, respectively, while sources  360  and  390  include a first reagent and second reagent, respectively. Source  370  contains a carrier gas, which is constantly flowed through chamber  310  during the deposition process transporting precursors and reagents to article  301 , while transporting reaction byproducts away from the substrate. Precursors and reagents are introduced into chamber  310  by mixing with the carrier gas in manifold  330 . Gases are exhausted from chamber  310  via an exit port  345 . A pump  340  exhausts gases from chamber  310  via an exit port  345 . Pump  340  is connected to exit port  345  via a tube  346 .  
         [0078]     ALD system  300  includes a temperature controller  395 , which controls the temperature of chamber  310 . During deposition, temperature controller  395  elevates the temperature of article  301  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. In some embodiments, the temperature of article  301  can be about 500° C. or less (e.g., about 400° C. or less, about 300° C. or less, about 200° C. or less, about 150° C. or less, about 125° C. or less, about 100° C. or less).  
         [0079]     Typically, the temperature should not vary significantly between different portions of article  301 . 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 and/or morphology of the deposited layers. In some embodiments, the temperature between different portions of the deposition surfaces can vary by about 40° C. or less (e.g., about 30° C. or less, about 20° C. or less, about 10° C. or less, about 5° C. or less).  
         [0080]     Deposition process parameters are controlled and synchronized by an electronic controller  399 . Electronic controller  399  is in communication with temperature controller  395 ; pump  340 ; and valves  352 ,  362 ,  372 ,  382 , and  392 . Electronic controller  399  also includes a user interface, from which an operator can set deposition process parameters, monitor the deposition process, and otherwise interact with system  300 .  
         [0081]     Referring to  FIG. 4 , the ALD process is started ( 410 ) when system  300  introduces the first precursor from source  350  into chamber  310  by mixing it with carrier gas from source  370  ( 420 ). A monolayer of the first precursor is adsorbed onto exposed surfaces of article  301 , and residual precursor is purged from chamber  310  by the continuous flow of carrier gas through the chamber ( 430 ). Next, the system introduces a first reagent from source  360  into chamber  310  via manifold  330  ( 440 ). The first reagent reacts with the monolayer of the first precursor, forming a monolayer of the first material. As for the first precursor, the flow of carrier gas purges residual reagent from the chamber ( 450 ). Steps  420  through  460  are repeated until the layer of the first material reaches a desired thickness ( 460 ).  
         [0082]     In embodiments where the films are a single layer of material, the process ceases once the layer of first material reaches the desired thickness ( 470 ). However, for a nanolaminate film, the system introduces a second precursor into chamber  310  through manifold  330  ( 380 ). A monolayer of the second precursor is adsorbed onto the exposed surfaces of the deposited layer of first material and carrier gas purges the chamber of residual precursor ( 490 ). The system then introduces the second reagent from source  380  into chamber  310  via manifold  330 . The second reagent reacts with the monolayer of the second precursor, forming a monolayer of the second material ( 500 ). Flow of carrier gas through the chamber purges residual reagent ( 510 ). Steps  580  through  510  are repeated until the layer of the second material reaches a desired thickness ( 520 ).  
         [0083]     Additional layers of the first and second materials are deposited by repeating steps  520  through  530 . 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 ( 540 ), and the coated article is removed from chamber  310 .  
         [0084]     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. For example, where the bonding energy between the precursor and the surface is higher than the bonding 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.  
         [0085]     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 material being deposited. Materials composed of larger molecules may result in thicker monolayers compared to materials composed of smaller molecules.  
         [0086]     The temperature of the article can also affect the monolayer thickness. For example, for 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.  
         [0087]     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.  
         [0088]     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, and possible effects from the byproducts on the deposited material. An example of where the byproducts affect the film thickness are where a byproduct etches the deposited material. For example, HCl is a byproduct when depositing TiO 2  using a TiCl 4  precursor and water as a reagent. HCl can etch the deposited TiO 2  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).  
         [0089]     Typically, monolayer thickness is between about 0.1 nm and about five nm. For example, the thickness of one or more of the deposited monolayers can be about 0.2 nm or more (e.g., about 0.3 nm or more, about 0.5 nm 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 one nm or less, about 0.8 nm or less, about 0.5 nm or less).  
         [0090]     The average deposited monolayer thickness may be determined by depositing a preset number of monolayers on a substrate to provide a layer of a material. Subsequently, the thickness of the deposited layer is measured (e.g., by ellipsometry, 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 of a molecule composing the monolayer, which can be calculated from the material&#39;s bulk density and the molecules molecular weight. For example, an estimate of the monolayer thickness for SiO 2  is ˜0.37 nm. The thickness is estimated as the cube root of a formula unit of amorphous SiO 2  with density of 2.0 grams per cubic centimeter.  
         [0091]     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 thickness, about 0.8 of the theoretical monolayer thickness, about 0.9 of the theoretical monolayer thickness). Alternatively, the average deposited monolayer thickness can correspond to 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).  
         [0092]     During the deposition process, the pressure in chamber  310  can be 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 be sufficiently high to allow the precursor to saturate the surface with chemisorbed 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 and/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 high as to hinder the removal of the reaction products generated by the reaction of the precursor and reagent. Residual 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 Torr and about 100 Torr (e.g., between about 0.1 Torr and about 20 Torr, between about 0.5 Torr and 10 Torr, such as about 1 Torr).  
         [0093]     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.  
         [0094]     The amount of precursor and/or reagent introduced during each cycle can be controlled by the timing of the opening and closing of valves  352 ,  362 ,  382 , and  392 . 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 all 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. In some embodiments, the precursor dose corresponds to opening the appropriate valve for between about 0.1 seconds and about five 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 0.1 seconds and about five 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).  
         [0095]     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 0.1 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 1.5 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).  
         [0096]     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 10 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.  
         [0097]     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 be compatible with the material on which they are deposited (e.g., with the substrate material or the material forming the previously deposited layer). Examples of precursors include chlorides (e.g., metal chlorides), such as TiCl 4 , SiCl 4 , SiH 2 Cl 2 , TaCl 3 , HfCl 4 , InCl 3  and AlCl 3 . In some embodiments, organic compounds can be used as a precursor (e.g., Ti-ethaOxide, Ta-ethaOxide, Nb-ethaOxide). Another example of an organic compound precursor is (CH 3 ) 3 Al.  
         [0098]     The reagents are also generally selected to be compatible with the ALD 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 3 ) 3 Al, and various alcohols (e.g., Ethyl alcohol CH 3 OH). Water, for example, is a suitable reagent for oxidizing precursors such as TiCl 4  to obtain TiO 2 , AlCl 3  to obtain Al 2 O 3 , and Ta-ethaoxide to obtain Ta 2 O 5 , Nb-ethaoxide to obtain Nb 2 O 5 , HfCl 4  to obtain HfO 2 , ZrCl 4  to obtain ZrO 2 , and InCl 3  to obtain In 2 O 3 . In each case, HCl is produced as a byproduct. In some embodiments, (CH 3 ) 3 Al can be used to oxidize silanol to provide SiO 2 .  
         [0099]     While certain embodiments have been described, the invention, in general, is not so limited. For example, while optical retarder  100  (see  FIG. 1 ) shows a specific configuration of different layers, other embodiments can include additional or fewer layers. For example, in certain embodiments optical retarders need not include one or both of antireflection films  150  and  160 . In some embodiments, optical retarders can include additional antireflection films (e.g., between substrate layer  140  and etch stop layer  130 ). Embodiments can also include protective layers, such as hardcoat layers (e.g., hardcoat polymers) on one or both of antireflection films  150  and  160 . In certain embodiments, optical retarders need not include a cap layer. For example, the cap layer, which forms while filling trenches between portions  112 , can be removed once portions  111  are formed. The cap layer can be removed by, e.g., chemical mechanical polishing or etching.  
         [0100]     Referring to  FIG. 5 , in some embodiments, an optical retarder  600  is formed by partially etching trenches directly into a substrate layer, and subsequently filling the trenches to provide a continuous retardation layer  610 . Optical retarder  600  also includes a cap layer  620 , and a base layer  630 , which corresponds to an unetched portion of the original substrate layer. An antireflection film  640  is deposited on surface  621  of cap layer  602 , and a second antireflection film  650  is deposited on surface  631  of base layer  630 .  
         [0101]     In certain embodiments, optical retarders can be formed from more than one retardation layer. For example, referring to  FIG. 6 , an optical retarder  800  includes four retardation layers  810 ,  820 ,  830 , and  840 . Optical retarder  800  also includes a substrate layer  801 , an etch stop layer  805 , and cap layers  811 ,  821 ,  831 , and  841 .  
         [0102]     Retardation layers  810 ,  820 ,  830 , and  840  can have the same retardation for a beam of light having wavelength λ, or can have different retardations.  
         [0103]     Optical retarder  800  can be prepared using methods disclosed herein. For example, each retardation layer and its corresponding cap layer can be formed by depositing and etching an intermediate layer either on etch stop layer  805  (e.g., retardation layer  810 ) or on the previously deposited cap layer (e.g., retardation layers  820 ,  830 , and  840 ), and then depositing materials to fill the etched trenches and form the cap layers.  
         [0104]     In some embodiments, additional etch stop layers can be deposited onto a cap layer prior to forming a subsequent retardation layer. Of course, other layers may also be included, such as antireflection films, for example.  
         [0105]     In general, the thickness of retardation layers  810 ,  820 ,  830 , and  840  along the z-direction, the width of their portions (along the x-direction), and the materials used to form them may vary as desired. In some embodiments, retardation layers  810 ,  820 ,  830 , and  840  are identical, while in other embodiments, one or more of the retardation layers can be different (e.g., composed of one or more different materials to the other retardation layers, have a different thickness, and/or have a different birefringence).  
         [0106]     Moreover, while optical retarder  800  has four retardation layers, in general, embodiments can include more than or less than four retardation layers. Optical retarders can include two retardation layers, three retardation layers, or five or more retardation layers (e.g., about 10 or more retardation layers, about 20 or more retardation layers, about 30 or more retardation layers, about 100 or more retardation layers, about 1000 or more retardation layers).  
         [0107]     The total phase retardation for light of wavelength λ propagating through an optical retarder having more than one retardation layer can be relatively large. For example, an optical retarder can have a phase retardation of about 2π or more at λ (e.g., about 3π or more, about 4π or more, about 5π or more, about 8π or more, about 10π or more, about 12π or more, about 15π or more, about 20π or more, about 30π or more.  
         [0108]     The total thickness (along the z-direction) of optical retarders than include more than one retardation layer can be about 200 μm or more (e.g., about 500 μm or more, about 800 μm or more, about 1,000 μm or more, about 1,500 μm or more, about 2,000 μm or more, about 5,000 μm or more).  
         [0109]     In certain embodiments, optical retarders can be used as an optical walk-off crystal, which splits non-normally incident light (i.e., light not propagating along the z-direction) into an ordinary and an extraordinary ray, which exit the retarder along different paths. Such optical walk-off crystals can be re-cut and polished into a wedge. Walk-off crystals can be used in numerous applications, such as in telecom isolators, circulators, or interleavers, and/or in consumer applications, such as optical low pass filters, for example.  
         [0110]     Although embodiments of optical retarders have been described that include form birefringent layers that have a rectangular grating profile, other embodiments are also possible. For example, in some embodiments, the grating profile of a form birefringent layer can be curved, such as having a sinusoidal shape. In another example, the grating can have a triangular or sawtooth profile.  
         [0111]     Furthermore, while the grating period in the form birefringent layers of optical retarders has been described as constant, in certain embodiments the grating period may vary. In some embodiments, portions of form birefringent layers can be non-periodically arranged.  
         [0112]     Optical retarders such as those described herein can be incorporated into optical devices, including passive optical devices (e.g., polarizers) and active optical devices (e.g., liquid crystal displays). Optical retarders can be integrated into the device, providing a monolithic device, or can be arranged separately from other components of the device.  
         [0113]     Referring to  FIG. 7 , an example of a passive optical device incorporating an optical retarder is a polarizer  660 . Polarizer  660  includes a polarizing film  670  and an optical retarder  680 . Polarizing film  670  can be a sheet polarizer (e.g., iodine-stained polyvinyl alcohol) or a nano-structured polarizer, such as is disclosed in U.S. patent application Ser. No. 10/644,643, entitled “MULTILAYER STRUCTURES FOR POLARIZATION AND BEAM CONTROL,” and PCT Patent Application Serial No. PCT/US03/26024, entitled “METHOD AND SYSTEM FOR PROVIDING BEAM FOR POLARIZATION,” the contents both of which are hereby incorporated by reference in their entirety.  
         [0114]     Polarizing film  670  linearly polarizes light incident on polarizer  660  propagating along axis  661 . Optical retarder  680  then retards the linearly polarized light, providing polarized light with a desired ellipticity exiting polarizer  660 . The ellipticity of the exiting light can vary as desired by choosing the parameters associated with the retardation layer of optical retarder  680  to provide a desired amount of retardation. For example, the exiting light can be circularly polarized or elliptically polarized.  
         [0115]     Referring to  FIG. 8 , an example of an active optical device incorporating an optical retarder is a liquid crystal display  700 , which includes a substrate  710  (e.g., a silicon substrate), a reflective electrode  720 , a layer  730  of a liquid crystal (e.g., a nematic or ferroelectric liquid crystal), a transparent electrode  740  (e.g., formed from indium tin oxide), an optical retarder  750 , and a polarizing film  760 . Optical retarder  750  retards polarized light transmitted through polarizing film  760 . This light reflects from electrode  720 , propagating through liquid crystal layer  730  twice. The reflected light is again retarded by optical retarder  760  before impinging on polarizing film  760  a second time. Depending on the voltage applied across electrodes  720  and  740 , the reflected light is either absorbed or transmitted by polarizing film  760 , corresponding to a dark or bright pixel, respectively. Optionally, LCD  700  includes color filters that absorb certain wavelengths in the visible spectrum providing a colored image. While LCD  700  is a reflective display, the optical retarders disclosed herein can be used in other types of display, such as transmissive displays or transflective displays.  
         [0116]     The following examples are illustrative and not intended as limiting.  
       EXAMPLES  
       [0117]     Optical retarders were prepared as follows. A 0.5 mm thick BK7 wafer (four inches in diameter), obtained from Abrisa Corporation (Santa Paula, Calif.), was cleaned by removing insoluble organic contaminants with a H 2 O:H 2 O 2 :NH 4 OH solution, and removing ionic and heavy metal atomic contaminants using a H 2 O:H 2 O 2 :HCl solution. Thereafter, the wafer was rinsed with isopropyl alcohol and deionized water, and spin dried.  
         [0118]     A sub-wavelength grating was etched into the BK7 wafer as follows. The BK7 wafer was spin coated with a thin layer (˜180 nm) of PMMA (molecular weight of 15 K purchased from Sigma-Aldrich, St. Louis, Mo.), which was baked on a hot plate at about 115° C. for about one hour. After baking, the resist was imprinted with a grating mold having a period of 200 nm and depth of about 110 nm, and a grating linewidth of about 100 nm. The mold included a patterned SiO 2  layer (about 200 nm thick) on a 0.5 mm thick silicon substrate. The mold was prepared using methods disclosed by J. Wang, Z. Yu, and S. Y. Chou, in  J. Vac. Sci. Technol ., B17, 2957 (1999). After imprinting, the deformed UV curable resist was fully cured by exposing to UV light through the BK7 substrate side. The mold was then separated from the resist, leaving a mask with a negative pattern of the mold profile. The mask was etched by O 2  RIE until the BK7 wafer was exposed in the recessed portions of the mask. This etch was performed using a plasma-therm  790  (available from Unaxis, Inc., St. Petersburg, Fla.). The pressure during etching was 4 mtorr. The power was set to 70 W and the oxygen flow rate during the etching was 10 sccm. The total thickness of resist etched to expose the BK7 wafer was about 120 nm.  
         [0119]     After etching the mask, about 50 nm of Cr was deposited on the remaining resist/exposed BK7 wafer by e-beam evaporation at high vacuum (i.e., less than about 5×10 −6  torr) at an oblique angle from the wafer normal. The oblique angle was about 65 degrees. Cr was deposited on the top and sidewall of the remaining mask lines, providing a hard mask for etching of BK7. After Cr deposition, O 2  RIE was used again to etch any exposed resist that was not covered by the Cr. CHF 3  RIE was then used to etch exposed portions of the BK7 wafer surface to form a subwavelength grating in the wafer. The BK7 was etched using a plasma-term  720 . The chamber pressure was about 5 mtorr, the power was about 100 W, and flow rate of 10 sccm and 1 sccm of CHF 3  and O 2  were used, respectively. 100 nm wide trenches having a depth of about 630 m were etched into the BK7 wafer. After etching the BK7, the Cr was removed by immersing the wafer into CR-7 Cr etchant (obtained from Cyantek, Fremont, Calif.) for about 30 minutes. Residual resist was subsequently removed by O 2  RIE.  
         [0120]     The trenches were filled with a nanolaminate material composed of TiO 2  and SiO 2 . The nanolaminate material was deposited by ALD, which was performed using a P-400A ALD apparatus, obtained from Planar Systems, Inc. (Beaverton, Oreg.). Prior to depositing the nanolaminate, the etched wafer was heated to 300° C. inside the ALD chamber for about three hours. The chamber was flushed with nitrogen gas, flowed at about 2 SLM, maintaining the chamber pressure at about 0.75 Torr. The TiO 2  precursor was Ti-ethaoxide, which was heated to about 140° C. The SiO 2  precursor was silanol, heated to about 110° C. For both precursors, the reagent used was water, which was maintained at about 13° C. The Ti-ethaoxide and silanol were 99.999% grade purity, obtained from Sigma-Aldrich (St. Louis, Mo.). The nanolaminate was formed by repeating a cycle in which 10 monolayers of TiO 2  were deposited, followed by a single monolayer of SiO 2 . To deposit a TiO 2  monolayer, water was introduced to the chamber for two seconds, followed by a two second nitrogen purge. Then Ti-ethaoxide was introduced to the chamber, followed by another two second nitrogen purge. SiO 2  monolayers were deposited by introducing water to the ALD chamber for one second, followed by a two second nitrogen purge. Silanol was then introduced for one second. The chamber was then purged for three seconds with nitrogen before the next pulse of reagent. The refractive index of the nanolaminate was estimated to be approximately 1.88 at 632 nm, as determined from measurements of a nanolaminate film similarly prepared on a flat glass substrate.  
         [0121]     The retardation of an optical retarder was measured using an M-2000V® Spectroscopic Ellipsometer (commercially available from J.A. Woollam Co., Inc., Lincoln, Nebr.) to be 23.85 nm at a wavelength of 551 nm.  
         [0122]     Unfilled and filled gratings were studied using scanning electron microscopy, which was performed using a LEO thermo-emission scanning electron microscope. To perform this study, a sample was cleaved and coated with a thin layer of Au. The cross section of the cleaved interface was then viewed.  FIGS. 9A and 9B  show SEM micrographs of a grating prior to and after trench filling, respectively.  
         [0123]     Other embodiments are in the following claims.