Patent Publication Number: US-2021191021-A1

Title: Simultaneous phase and polarization modulation by hybrid metasurface for on-chip polarization filters

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the priority benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 62/950,930, filed on Dec. 19, 2019, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The subject matter disclosed herein relates to image sensors. More specifically, the subject matter disclosed herein relates to a multifunctional polarization filter that includes nanostructures that change the phase, amplitude and polarization of incident light based on dimensions of the nanostructures. 
     BACKGROUND 
     Polarization is a property of light that indicates the geometrical orientation of the oscillations, or vibrations, of the electromagnetic (EM) fields of the light. The EM vibrations may be directed to a specific direction using a polarizer or a polarizing filter. The general orientation of polarized light is x- or y-directed with a phase φ between the x and y axes. The general polarization of light may be in the horizontal, or x direction, or in the vertical, or y direction, with a phase ϕ between the x and y axes. By determining the amplitude of electric field in, for example, x and y directions and the relative phase between the x and y direction, a full Stokes polarization state of the light may be determined. 
       FIG. 1A  depicts unpolarized light  100  passing through a horizontally polarized filter  101 . The light  102  that passes through the horizontally polarizing filter  101  is horizontally polarized.  FIG. 1B  depicts unpolarized light  100  passing through a vertically polarization filter  103 . The light  104  that passes through the vertically polarization filter  103  is vertically polarized. The polarization filters  101  and  103  may also be referred to as linear polarizers. The polarization filters  101  and  103  may alternatively be oriented in other directions than shown in  FIGS. 1A and 1B , in which case the light passing through the polarizing filter will have an orientation corresponding to the orientation of the polarizing filter. 
     Light may also be circularly polarized as left-hand circularly polarized (LHCP) or as right-hand circularly polarized (RHCP).  FIG. 1C  depicts an example in which light  105  has been circularly LHCP polarized. If, for example, the circularly polarized light  105  passes through a quarter wave plate  106 , the light becomes linearly polarized light  107 , which then may be further filtered, or polarized, by a linear polarizer  108 .  FIG. 1D  depicts an example in which light  110  has been RHCP polarized. If, for example, the circularly polarized light passes through a quarter wave plate  111 , the light becomes linearly polarized light  112 , which then may be further filtered, or polarized, by a linear polarizer  113 . 
     Detection of the polarization of light may be used for ranging an object in poor visibility conditions, for example, in an advanced driver-assistance system (ADAS). Detection of the polarization of light may also be used to detect a specular surface, that is, whether a point on a surface is level with another point. After light has been reflected from a specular surface, light rays are oriented parallel with each other and are propagating in the same direction. Other applications of polarized light include rejecting multipath reflections of objects based on the polarization of the reflected image of an object being different from the polarization of the actual image of the object. Industrial applications of polarized light may include detecting defects of manufactured objects. 
     SUMMARY 
     An example embodiment provides a filter for an imaging device that may include a substrate and an array of phase-modulating nanostructures formed on the substrate. At least one phase-modulating nanostructure of the array of phase-modulating nanostructures may change a phase of incident light a predetermined amount based on a first width and a second width of the phase-modulating nanostructure in which the first width is perpendicular to the second width. In one embodiment, the phase-modulating nanostructure may be formed from a material having a refractive index that is greater than 1.9. In another embodiment, the phase-modulating nanostructure may be formed from at least one of silicon, silicon nitride (Si 3 N 4 ), titanium dioxide (TiO 2 ), gallium nitride (GaN), Zinc oxide (ZnO), hafnium silicate, zirconium silicate, hafnium dioxide or zirconium dioxide. In one embodiment, the phase-modulating nanostructure inelastically scatters light incident on the filter. In still another embodiment, the filter may focus light incident on the filter towards a center a pixel of an image sensor at an image plane, and a field of view of the filter may be at least 30 degrees for a normalized intensity of 1. 
     An example embodiment provides a filter for an imaging device that may include a substrate and an array of phase-modulating nanostructures formed on the substrate. At least one phase-modulating nanostructure of the array of phase-modulating nanostructures may change a phase of incident light a predetermined amount based on a first width and a second width of the phase-modulating nanostructure in which the first width is perpendicular to the second width, and the phase-modulating nanostructure may be formed from a material having a refractive index that is greater than 1.9. In one embodiment, the filter may include a quarter-wave plate. 
     An example embodiment provides a filter for an imaging device that may include a wire grid and an array of phase-modulating nanostructures formed on the wire grid. At least one phase-modulating nanostructure of the array of phase-modulating nanostructures may change a phase of incident light a predetermined amount based on a first width and a second width of the phase-modulating nanostructure in which the first width may be perpendicular to the second width. The phase-modulating nanostructure may be formed from a material having a refractive index that is greater than 1.9, and a field of view of the filter may be at least 30 degrees for a normalized intensity of 1. In one embodiment, the filter may focus light incident on the filter towards a center a pixel of an image sensor at an image plane. In another embodiment, the filter may include a quarter-wave plate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       In the following section, the aspects of the subject matter disclosed herein will be described with reference to exemplary embodiments illustrated in the figure, in which: 
         FIG. 1A  depicts unpolarized light passing through a horizontally polarized filter; 
         FIG. 1B  depicts an equivalent representation of  FIG. 1A ; 
         FIG. 1C  depicts an example in which light has been left-hand circularly polarized with respect to two orthogonal directional axes; 
         FIG. 1D  depicts an example in which light has been right-hand circularly polarized with respect to two orthogonal axes; 
         FIG. 2A  depicts an example embodiment of an arrangement of four multifunctional polarization filters with respect to four pixels that may be used to detect six polarization states according to the subject matter disclosed herein; 
         FIGS. 2B-2D  respectively depict a top view and two cross-sectional view of an enlarged portion of a polarization filter according to the subject matter disclosed herein; 
         FIG. 3A  depicts a cross-sectional view of a wire grid having a metal-insulator-metal (MIM) structure that suppresses reflection from cross-polarization according to the subject matter disclosed herein; 
         FIG. 3B  depicts a cross-sectional view of a typical wire grid having wires formed from a metal; 
         FIGS. 4A-4C  conceptually depict how the size of a particle (nanostructure) may affect scattering of light; 
         FIG. 5  shows a graph of transmission intensity as a function of Cartesian dimensions of a nanostructure according to the subject matter disclosed herein; 
         FIG. 6  conceptually depicts how changing dimensions of a nanostructure may be used to change the phase to focus incident light according to the subject matter disclosed herein; 
         FIG. 7A  is a graph of phase as a function of Cartesian dimensions of a nanostructure according to the subject matter disclosed herein; 
         FIG. 7B  is a graph of normalized intensity at a pixel as a function of the field of view angle of a polarized filter that includes nanostructures according to the subject matter disclosed herein; 
         FIGS. 8A and 8B  respective show example phase values for the transverse electric field and the transvers magnetic field for light having a wavelength of 0.8 μm for different width of x (Dx) and y dimensions (Dy) of a nanostructure according to the subject matter disclosed herein; 
         FIGS. 8C and 8D  respective show example transmission coefficient or amplitude values for the transverse electric field and the transverse magnetic field for light having a wavelength of 0.8 μm for different width of x (Dx) and y dimensions (Dy) of a nanostructure according to the subject matter disclosed herein; 
         FIG. 9  is a graph of the total transmission coefficient or amplitude values with respect to different phase values φ x  and φ y  introduced from nanostructures with width of Dx and Dy according to the subject matter disclosed herein; 
         FIG. 10 , which may be derived from  FIGS. 8A and 8B , shows the phase difference (φ x −φ y ) introduced from nanostructures with widths of Dx and Dy for different x and y dimensions according to the subject matter disclosed herein; 
         FIGS. 11A and 11B  respectively show smoothed and individual points excluding discretization errors extracted from  FIG. 10  for phase difference (φ x −φ y ) of π/2 radians; 
         FIGS. 11C and 11D  respectively show smoothed and individual points excluding discretization errors extracted from  FIG. 10  for phase difference (φ x −φ y ) of −π/2 radians; 
         FIGS. 12A and 12B  respectively show the top and side views of nanostructures for a unit cell size of the circular polarization detecting pixel according to the subject matter disclosed herein; 
         FIGS. 13A and 13B  respectively show the smooth and discrete phase maps needed to focus the light from the nanostructures to the photodiode of the sensor according to the subject matter disclosed herein; 
         FIGS. 14A and 14B  show the nanostructure dimension requirements to achieve the phase map in  FIG. 13B  for focusing light in the case of Dx=Dy and the resultant focused light on the photodiode according to the subject matter disclosed herein; 
         FIGS. 15A and 15B  show the nanostructure dimension requirements to achieve the phase map in  FIG. 13B  for focusing light in the case of Dx≠Dy according to the subject matter disclosed herein; 
         FIG. 16  depicts an example arrangement of a wire grid and nanostructures for the multifunctional horizontally polarization filter in  FIG. 2A  according to the subject matter disclosed herein; 
         FIG. 17  depicts an example arrangement of a wire grid and nanostructure for the multifunctional diagonal polarization filter of  FIG. 2A  according to the subject matter disclosed herein; 
         FIG. 18  depicts an example arrangement of a wire grid and nanostructure for the multifunctional left-hand circular polarized polarization filter of  FIG. 2A  according to the subject matter disclosed herein; 
         FIG. 19  depicts an example embodiment of a multifunctional polarization filter for a unit-cell pixel according to the subject matter disclosed herein; 
         FIGS. 20A-20E  depict a cross-sectional view of an example sequence of forming different spectral filters on an array of photodiodes according to the subject matter disclosed herein; 
         FIG. 21  depicts a top view of an example embodiment of an array of polarizing filters and different spectral filters that may be used with an image sensor to provide on-chip simultaneous full Stokes polarization parameters and multi/hyper spectral imaging according to the subject matter disclosed herein; 
         FIG. 22  depicts an imaging system that may include polarizing filters and spectral filters that provide on-chip simultaneous full Stokes polarization parameters (both linear and circular polarization) and multi/hyper spectral imaging according to the subject matter disclosed herein; and 
         FIG. 23  depicts an electronic device that includes an image sensor having one or more multifunctional polarization filters according to the subject matter disclosed herein. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the disclosure. It will be understood, however, by those skilled in the art that the disclosed aspects may be practiced without these specific details. In other instances, well-known methods, procedures, components and circuits have not been described in detail not to obscure the subject matter disclosed herein. 
     Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment disclosed herein. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” or “according to one embodiment” (or other phrases having similar import) in various places throughout this specification may not be necessarily all referring to the same embodiment. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. In this regard, as used herein, the word “exemplary” means “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not to be construed as necessarily preferred or advantageous over other embodiments. Additionally, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Also, depending on the context of discussion herein, a singular term may include the corresponding plural forms and a plural term may include the corresponding singular form. Similarly, a hyphenated term (e.g., “two-dimensional,” “pre-determined,” “pixel-specific,” etc.) may be occasionally interchangeably used with a corresponding non-hyphenated version (e.g., “two dimensional,” “predetermined,” “pixel specific,” etc.), and a capitalized entry (e.g., “Counter Clock,” “Row Select,” “PIXOUT,” etc.) may be interchangeably used with a corresponding non-capitalized version (e.g., “counter clock,” “row select,” “pixout,” etc.). Such occasional interchangeable uses shall not be considered inconsistent with each other. 
     Also, depending on the context of discussion herein, a singular term may include the corresponding plural forms and a plural term may include the corresponding singular form. It is further noted that various figures (including component diagrams) shown and discussed herein are for illustrative purpose only, and are not drawn to scale. Similarly, various waveforms and timing diagrams are shown for illustrative purpose only. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, if considered appropriate, reference numerals have been repeated among the figures to indicate corresponding and/or analogous elements. 
     The terminology used herein is for the purpose of describing some example embodiments only and is not intended to be limiting of the claimed subject matter. As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The terms “first,” “second,” etc., as used herein, are used as labels for nouns that they precede, and do not imply any type of ordering (e.g., spatial, temporal, logical, etc.) unless explicitly defined as such. Furthermore, the same reference numerals may be used across two or more figures to refer to parts, components, blocks, circuits, units, or modules having the same or similar functionality. Such usage is, however, for simplicity of illustration and ease of discussion only; it does not imply that the construction or architectural details of such components or units are the same across all embodiments or such commonly-referenced parts/modules are the only way to implement some of the example embodiments disclosed herein. 
     It will be understood that when an element or layer is referred to as being on, “connected to” or “coupled to” another element or layer, it can be directly on, connected or coupled to the other element or layer or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to” or “directly coupled to” another element or layer, there are no intervening elements or layers present. Like numerals refer to like elements throughout. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     The terms “first,” “second,” etc., as used herein, are used as labels for nouns that they precede, and do not imply any type of ordering (e.g., spatial, temporal, logical, etc.) unless explicitly defined as such. Furthermore, the same reference numerals may be used across two or more figures to refer to parts, components, blocks, circuits, units, or modules having the same or similar functionality. Such usage is, however, for simplicity of illustration and ease of discussion only; it does not imply that the construction or architectural details of such components or units are the same across all embodiments or such commonly-referenced parts/modules are the only way to implement some of the example embodiments disclosed herein. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this subject matter belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     The subject matter disclosed herein provides a multifunctional polarization filter that includes nanostructures that change the phase of incident light a predetermined amount based on dimensions of the nanostructures. In one embodiment, the dimensions of the nanostructures include a first width and a second width that is perpendicular to the first width. 
     A multifunctional polarization filter may be formed that includes a wire grid and the nanostructures to provide both simultaneous polarization and phase modulation of incident light to focus the light toward the center of a pixel of an image sensor and to reduce angle dependency and crosstalk and 0-th order effect between pixels (and between N×N unit-cell pixels) of the image sensor. No microlens is needed at the pixel because the multifunctional polarization filters can focus the incident light. 
     In one embodiment, the multifunctional polarization filter disclosed herein may provide full Stokes imaging for detecting both linear and circular polarization for near infrared (NIR) light (700 nm-900 nm) for an N×N unit-cell pixel. The multifunctional polarization filter disclosed herein may be designed for other wavelengths of light. The multifunctional polarization filter may also provide high QE efficiency (greater than 95% transmission for certain polarizations) for each N×N unit-cell pixel of an image sensor, thereby making the image sensor less angle-dependent in comparison to traditional image sensors. 
     In one embodiment, the multifunctional polarization filter disclosed herein provides a high-efficiency on-chip polarization filter that provides complete polarization-state detection and may be used for multifunctional purposes, such as, but not limited to, ADAS, industrial and healthcare applications. 
       FIG. 2A  depicts an example embodiment of an arrangement  200  of four multifunctional polarization filters  201   a - 201   d  with respect to four pixels  205 - 208  that may be used to detect six polarization states according to the subject matter disclosed herein. The four multifunctional polarization filters  201   a - 201   d  respectively correspond to the four pixels  205 - 208 . The four pixels  205 - 208  form an N×N unit-cell pixel. (For this example, N equals 2.) Each respective pixel  205 - 208  includes a photodetector (not shown). The filter  201   a  (H) horizontally polarizes light passing through the filter  201   a . The filter  201   b  (V) vertically polarizes light. The filter  201   c  (D) diagonally polarizes light, and the filter  201   d  (L) circularly polarizes light. In an alternative embodiment, six polarization filters and six pixels may be used. The additional two polarization filters in the alternative embodiment would be an anti-diagonally (A) polarization filter and a circularly (R) polarization filter that would polarize light in the opposite circular direction from the circularly polarization filter  201   d.    
     Additional details of the polarization filter  201  are depicted at  201 ′, which shows a top view of the polarization filter  201   a . The polarization filter  201   a  includes a wire grid  210 , of which only one wire of the wire grid is indicated, and one or more phase-modulating nanostructures, or metasurfaces,  211 , of which only one nanostructure is indicated. 
     The orientation of the wire grid  210  may be selected to control, or modulate, the polarization of light provided by a polarization filter  201 . For example, the wire grid  210  horizontally polarizes the light passing through the polarization filter  201   a , and the nanostructures  211  change, or modulate, the phase of the light that passes through the polarization filter  201   a . The other polarization filters  201   b - 201   d  also include a wire grid (not shown) that may have a series of metal-insulator-metal (MIM) structure and one or more nanostructures (also not shown). 
     The wires of the wire grid may include a series of metal-insulator-metal (MIM) structures that suppresses reflection from cross-polarization. The metal portion of a wire may be formed from any metal or doped semiconductor, such as, but not limited to, aluminum (Al), gold (Au), silver (Ag), titanium (Ti), tungsten (W), copper (Cu), palladium (Pd), tantalum (Ta), tantalum nitride (TaN), Niobium (Nb) and p-doped silicon (p-Si). The insulator portion of a wire may be formed from any dielectric material like oxides, such as, but not limited to, aluminum oxide (Al 2 O 3 ), silicon dioxide (SiO 2 ), silicon nitride (Si 3 N 4 ), titanium dioxide (TiO 2 ), zinc oxide (ZnO), hafnium silicate (HfSiO 4 ), zirconium silicate (ZrSiO 4 ), hafnium dioxide (HfO 2 ), and zirconium dioxide (ZrO 2 ) and/or semiconductors, like silicon (a-Si, p-Si). In one embodiment, a thickness t of the insulator layer may range from about a few nanometers to a few hundred nanometers. 
     The pattern of light that is generated by the polarization filter  201   a  and that is focused at the pixel  205  is depicted at  212 . The size and shape of the nanostructures  211  may control, or modulate, the phase of light passing through a polarization filter  201  to focus the light at the pixel  205 . Additionally, the nanostructures  211  may affect how light passing through a polarization filter  201  may be scattered, may also reduce the backscattering of the incident light, and may also help detect circular polarization. The nanostructures of the circularly polarization filter  201   d  provide a 90-degree phase shift so that the circularly polarization filter operates as a quarter wave plate. The nanostructures  211  may be formed from a high dielectric index material, such as amorphous silicon (a-Si), crystalline silicon (c-Si), p-Si, silicon nitride (Si 3 N 4 ), titanium dioxide (TiO 2 ), gallium nitride (GaN), Zinc oxide (ZnO), hafnium silicate, zirconium silicate, hafnium dioxide and zirconium dioxide. In one embodiment, the nanostructures  211  may be formed from a material having a refractive index that is greater than 1.9 at the desired wavelength. 
       FIGS. 2B-2D  respectively depicts a top view and two cross-sectional views of an enlarged portion  201 ″ of the polarization filter  201   a  according to the subject matter disclosed herein.  FIG. 2B  depicts a top view of the enlarged portion  201 ″ of the polarization filter.  FIG. 2C  is a cross-sectional view of the enlarged portion  201 ″ taken along line A-A′ in  FIG. 2B , and  FIG. 2D  is a cross-sectional view taken along line B-B′ in  FIG. 2B . As depicted in  FIGS. 2B-2D , the polarization filter  201   a  includes a wire grid (of which only one wire  210  is depicted) that is formed on a surface  215  of a detector substrate  216 . The wire  210  may include an MIM structure. The surrounding medium of the wire-grids can be air or empty or low-refractive index medium. Otherwise, a capping layer  217  of a dielectric or a polymer, such as: aluminum oxide (Al 2 O 3 ), silicon dioxide (SiO 2 ), silicon nitride (Si 3 N 4 ), silicon oxynitride (Si x N y O z ), silicon oxide (SiO), photoresists, epoxy resins and/or other materials. The dielectric layer  217  may be formed on the wire grid and the surface  215  of the detector substrate  216 . The dielectric layer  217  may be substantially optically transparent, and may be formed by chemical vapor deposition (CVD), plasma enhanced CVD (PECVD), physical vapor deposition (PVD), atomic layer deposition (ALD), evaporation, spin-on coating, and/or other processes. A plurality of nanostructures  211  (of which only one nanostructure is depicted) may be formed on the capping polymer  217  in vertical coincidence with a wire  210 . 
       FIG. 3A  depicts a cross-sectional view of a wire grid  300  having a metal-insulator-metal (MIM) structure that suppresses reflection from cross-polarization according to the subject matter disclosed herein.  FIG. 3B  depicts a cross-sectional view of a typical wire grid  350  that does not include an MIM structure and does not suppress reflections. The MIM structure of the wire grid  300  of  FIG. 3A  includes a first metal wire layer  301 , a dielectric layer  302 , and a second metal wire layer  303 . A phase-modulating nanostructure  304  is shown formed on the wire grid  300 . Although only a single MIM structure is depicted in  FIG. 3A , in alternative embodiments multiple MIM structures may be used that are stacked on each other. For example, if two MIM structures were to be stacked on each other, the resulting structure would be an MIMMIM structure. The two middle M layers could be formed from the same metal material or from different metal materials. 
     The first and second wire layers  301  and  303  may be formed from any metal or doped semiconductor, such as, but not limited to, aluminum (Al), gold (Au), silver (Ag), titanium (Ti), tungsen (W), copper (Cu), palladium (Pd), tantalum (Ta), tantalum nitride (TaN), niobium (Nb) and p-doped silicon (p-Si). The dielectric layer  402  may be formed from any dielectric material like oxides, such as, but not limited to, aluminum oxide (Al 2 O 3 ), silicon dioxide (SiO 2 ), silicon nitride (Si 3 N 4 ), titanium dioxide (TiO 2 ), zinc oxide (ZnO), hafnium silicate (HfSiO 4 ), zirconium silicate (ZrSiO 4 ), hafnium dioxide (HfO 2 ), and zirconium dioxide (ZrO 2 ) and/or semiconductors, like silicon (a-Si, p-Si). In one embodiment, the thickness t of the dielectric layer  302  may range from about a few nanometers to a few hundred nanometers.  FIG. 3B  depicts a cross-sectional view of a typical wire grid  350  having wires  351  formed from a metal, such as aluminum. 
     Tables 1 and 2 below respectively set forth transmission (T), reflection (R) and absorption (A) characteristics of the wire grid  300  in  FIG. 3A  at a wavelength of 800 nm, and for the typical wire grid  350  in  FIG. 3B . In Tables 1 and 2, both the wire grid  300  and the typical wire grid  350  are oriented for horizontal polarization. Similar characteristics may be obtained for wire grids oriented for vertical or diagonal polarization. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Polarization 
                 T (%) 
                 R (%) 
                 A (%) 
               
               
                   
                   
               
             
            
               
                   
                 X 
                 ~96  
                 ~1 
                 ~3.5  
               
               
                   
                 Y 
                 ~0.5 
                 ~4 
                 ~95.5 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Polarization 
                 T (%) 
                 R (%) 
                 A (%) 
               
               
                   
                   
               
             
            
               
                   
                 X 
                 ~96 
                 ~4  
                 ~0 
               
               
                   
                 Y 
                 ~1  
                 ~90 
                 ~9 
               
               
                   
                   
               
            
           
         
       
     
     Both Tables 1 and 2 show that the percentage transmission of horizontally polarized light (i.e., in the X direction) is about 96%, whereas the percentage of transmission of vertically polarized light (i.e., in the Y direction) is small (i.e., about 0.5% and about 1%). The percentage reflection of the horizontally polarized light is about 1% for the wire grid  300 , and is about 4% for the typical wire grid  350 . The percentage reflection is about 4% for the wire grid  300  having an MIM structure, whereas the percentage reflection for the typical wire grid  350  is about 90%. Thus, the MIM structure significantly reduces the amount of reflection in comparison to a typical wire grid. Further, the percentage absorption of light for the wire grid  300  having the MIM structure is about 3.5% in the X direction and about 95.5% in the Y direction. In contrast, the typical wire grid  350  exhibits virtually no absorption of light in the X direction and only about 9% in the Y direction. The significant reduction in reflection and the increase is absorption provided by the MIM structure may significantly reduce ghosting in a captured image. 
     Returning to  FIG. 2A , the arrangement  200  of the four polarization filters  201   a - 201   d  and the four pixels  205 - 208  may be used to generate the following six polarization states for incident light. 
         I   H   =I   H   (1)
 
         I   V   =I   V   (2)
 
         I   D   =I   D   (3)
 
         I   A   =I   H   +I   V   −I   D   (4)
 
         I   R   =I   H   +I   V   −I   L   (5)
 
         I   L   =I   L   (6)
 
     in which I H  is the light intensity parameter of horizontally polarized light (H) measured at pixel  205 , I V  is the light intensity parameter of the vertically polarized light (V) measured at pixel  206 , I D  is the light intensity parameter of the diagonally polarized light (D) measured at pixel  207 , I A  is the intensity parameter of the anti-diagonally polarized light, I R  is the intensity parameter of the right-hand circularly polarized light, and I L  is the light intensity parameter of the left-hand circularly polarized light (LHCP) measured at pixel  208 . 
     Using the intensity parameters of Eqs. (1)-(6), the Stokes parameters S 0 , S 1 , S 2  and S 3  may be calculated as follows. 
     
       
         
           
             
               
                 
                   
                     S 
                     0 
                   
                   = 
                   
                     
                       I 
                       H 
                     
                     + 
                     
                       I 
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     1 
                   
                   = 
                   
                     
                       I 
                       H 
                     
                     - 
                     
                       I 
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     2 
                   
                   = 
                   
                     
                       2 
                       * 
                       
                         I 
                         D 
                       
                     
                     - 
                     
                       S 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                     3 
                   
                   = 
                   
                     
                       2 
                       * 
                       
                         I 
                         L 
                       
                     
                     - 
                     
                       S 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   DoLP 
                   = 
                   
                     
                       
                         
                           s 
                           1 
                           2 
                         
                         + 
                         
                           s 
                           2 
                           2 
                         
                       
                     
                     
                       s 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   AoLP 
                   = 
                   
                     
                       1 
                       2 
                     
                      
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                      
                     
                       
                         S 
                         2 
                       
                       
                         S 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     in which S 0  is the total intensity of a light beam, DoLP is the degree of linear polarization, and AoLP is the angle of linear polarization, E 0x  is the magnitude of the electric field of the light in the x direction, E 0x  is the magnitude of the electric field of the light in the y direction, and δ is the angle of inclination of the electric field of the light with respect to the x-axis. 
     The size of the nanostructures  211  may affect how light passing through a polarization filter  201  may be scattered.  FIGS. 4A-4C  conceptually depict how the size of a particle (nanostructure) may affect scattering of light.  FIG. 4A  shows that if the size of a nanostructure is less than 0.10 of the wavelength λ of incident laser light (i.e., 0.1λ), the scattering of the light is Rayleigh scattering, which is elastic and is not angle dependent.  FIG. 4B  shows that if the size of a particle is greater than 0.10 of the wavelength λ (i.e., &gt;0.1λ), the scattering of the light is Mie scattering, which is inelastic scattering and is angle dependent.  FIG. 4C  shows that as the size of a particle increases, the angle dependency of the Mie scattering increases. 
       FIG. 5  shows a graph  500  of transmission intensity as a function of Cartesian dimensions of a nanostructure according to the subject matter disclosed herein. For a wide range of nanostructure dimensions, transmission intensity (curve  501 ) remains greater than 90% (i.e., greater than 0.9) for one linear polarization orientation, and less than 5% (i.e., less than 0.5) for the perpendicular polarization orientation (curve  502 ). Thus, for a wide range of nanostructure dimensions, scattering of light caused by the nanostructures  211  does not appreciably affect transmission of light through a polarization filter  201 . 
     The size and shape of the nanostructures  211  may be used to control, or modulate, the phase of light passing through a polarization filter  201 .  FIG. 6  conceptually depicts how changing dimensions of a nanostructure may be used to change the phase to focus incident light according to the subject matter disclosed herein. At  601 , a baseline depiction of light having an example wavelength of λ=1 μm is shown as propagating in air in the direction indicated by the arrow. The light and dark gray areas along the path of propagation represent peaks and troughs of a wave model of the light. White areas represent zero crossings of the wave model. At  602 , a change in phase of the light is shown that is caused by an array of square nanostructures  602   a  having a width W equal to w 1 . The centers of the nanostructures  602   a  are positioned λ/2 of the light from each other. At  602   b , the nanostructures are shown as being hollow to more clearly shown the phase of the light changes. It should be understood that the nanostructures are solid, as shown at  502   a . The change of phase caused by the nanostructures  502   a  with respect to the baseline depiction  601  is indicated at  601   c.    
     At  603 , a change in phase of the light is shown that is caused by an array of square nanostructures  603   a  having a width W equal to w 2  in which w 2 &gt;w 1 . The centers of the nanostructures  603   a  are positioned λ/2 of the light from each other. At  603   b , the nanostructures are shown as being hollow to more clearly shown the phase of the light changes. It should be understood that the nanostructures are solid, as shown at  603   a . The change of phase caused by the nanostructures  503   a  with respect to the phase change of the nanostructures  602  is indicated at  603   c.    
     At  604 , the change in phase of the light is shown that is caused by an array of square nanostructures  604   a  having a width W equal to w 3  in which w 3 &gt;w 2 &gt;w 1 . The centers of the nanostructures  604   a  are positioned λ/2 of the light from each other. At  604   b , the nanostructures are shown as being hollow to more clearly shown the phase of the light changes. It should be understood that the nanostructures are solid, as shown at  604   a . The change of phase caused by the nanostructures  604   a  with respect to the phase of the nanostructures  603   a  is indicated at  604   c.    
     The changes in phase provided by conceptual depictions at  601 - 604  may be used to focus the incident light. For example, at  605  a change in phase of the light is shown that is caused by an array of square nanostructures  605   a  having widths W equal to w 1 , w 2  and w 3  and arranged as shown. At  605   b , the nanostructures are shown as being hollow to more clearly shown the phase of the light changes. It should be understood that the nanostructures are solid, as shown at  605   a . The change in phase caused by a nanostructure of a given size is depicted as discrete changes in phase at  605   c  for illustrative purposes. 
     At  606 , a change in phase of the light is shown that is caused by an array of square nanostructures  606   a  having widths W equal to w 1 , w 2  and w 3  arranged as shown. At  606   b , the nanostructures are shown as being hollow to more clearly shown the phase of the light changes. It should be understood that the nanostructures are solid, as shown at  606   a . The change in phase caused by a nanostructure of a given size (W=w 1 , w 2  or w 3 ) is depicted as continuous changes in phase at  606   c.    
       FIG. 7A  is a graph  700  of phase as a function of Cartesian dimensions of a nanostructure  211  according to the subject matter disclosed herein. The abscissa of graph  700  is the dimensions of a nanostructure in nm (also referred to a post dimensions). Phase for both horizontal (i.e., x) and vertical (i.e., y) dimensions are plotted. The ordinate of graph  700  is phase is in arbitrary units (a.u.). By changing the dimensions of the nanostructures, a full 2π phase shift may be obtained to change, or modulate, the wave front of the light for focusing purposes and for increasing angle-independence properties of a polarizing filter, thereby resulting in a greater efficiency of the pixels of an image sensor. 
       FIG. 7B  is a graph  750  of normalized intensity at a pixel as a function of the field of view (FOV) angle of a polarized filter that includes nanostructures according to the subject matter disclosed herein. The abscissa of graph  750  is FOV angle in degrees and the ordinate is normalized intensity. The curve  751  represents the normalized intensity at a pixel, such as pixel  205 , as a function of FOV angle of a polarized filter, such as polarization filter  201 , which includes the nanostructures  211  that change, or modulate, the phase of the light to focus the light at the pixel. As can be seen, the curve  751  has a FOV of ±15 degrees, that is, a total FOV of 30 degrees, whereas as a comparison, curve  752  represents the normalized intensity at a pixel that is provided by a typical polarized filter that does not include phase-modulating nanostructures  211 . 
       FIGS. 8A and 8B  respective show example phase values for the TE field and the TM field for light having a wavelength of 0.8 μm for different x and y dimensions of a nanostructure according to the subject matter disclosed herein. The abscissas of  FIGS. 8A and 8B  are the x dimension of a nanostructure (in μm), and the ordinates are the y dimension of a nanostructure (in μm). The normalized phase with respect to 2π radians is indicated as a shade of gray. The term “Llattice=0.37778 indicates the pitch of single nanostructure is 0.37778 μm for the simulations shown in  FIGS. 8A and 8B . If, for example, the pixel size is 3.4 μm, then there will be 9×9 nanostructures in one pixel, and 9 times 0.37778 μm equals 3.4 μm. 
       FIGS. 8C and 8D  respective show example transmission intensity values for the TE field and the TM field for light having a wavelength of 0.8 μm for different x and y dimensions of a nanostructure according to the subject matter disclosed herein. The abscissas of  FIGS. 8C and 8D  are the x dimension of a nanostructure (in μm), and the ordinates are the y dimension of a nanostructure (in μm). Intensity values are indicated by shades of gray. 
       FIG. 9  is a graph of the total transmission coefficient values in the φ x  and the φ y  plane. In  FIG. 9 , the coefficient values for the total transmission T are determined as 
     
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       1 
                       2 
                     
                      
                     
                       ( 
                       
                         
                           T 
                           TE 
                           2 
                         
                         + 
                         
                           T 
                           TM 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     in which T TE  is the transmission coefficient for the TE field and T TM  is the transmission coefficient for the TM field. The total transmission coefficient values are indicated by shades of gray. In  FIG. 9 , the line of equal phase is indicated at  901 , and the lines for a 90° phase shift for a QWP are indicated at  902 . 
     Two types of QWPs may be designed using the nanostructures disclosed herein for respectively detecting right and left circularly polarized light. In the first type of QWP design, the phase of the TE field leads to the phase of the TM field by π/2 radians. In the second type of QWP design, the phase of the TE field lags the phase to the TM field by π/2 radians.  FIG. 10  shows the phase difference for different x and y dimensions of a nanostructure. The abscissa of  FIG. 10  is D x  in μm, and the ordinate of  FIG. 10  is D y  in μm. The phase difference normalized with 2π radians is indicated by a shade of gray. 
     A tolerance may be expected in finding the values for π/2.  FIGS. 11A and 11B  respectively show smoothed and individual points excluding discretization errors for the TM field for the first type of QWP design in which the phase of the TE field leads to the phase of the TM field by π/2 radians to determine the Dx and Dy values.  FIGS. 11C and 11D  respectively show smoothed and individual points excluding discretization errors for the TE field for the first type of QWP design in which the phase of the TE field lags to the phase of the TM field by π/2 radians. The magnitude of the discretization error is indicated by a shade of gray. 
       FIGS. 12A and 12B  respectively depict top and side views of a unit cell example nanostructure  1200  together with metal wire grids and phase modulating metasurface for a 9×9 arrangement of nanostructures designed to operate as simultaneously a QWP, a focusing lens and linear polarization detection according to the subject matter disclosed herein. The unit cell nanostructure  1200  includes a wire grid  1201 , a metasurface  1202  and a capping layer  1203 . The dimension of the metasurface nanostructures for unit cell Dx may be selected to be 2×106 nm, and the dimension Dy was selected to be 2×68.9 nm, which may be extracted from  FIG. 11D . Table 3 shows the simulated transmission and reflection properties of the example nanostructure for RHCP light and LHCP light. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Polarization 
                 Transmission 
                 Reflection 
               
               
                   
               
             
            
               
                 RHCP 
                 0.841  
                 0.129 
               
               
                 LHCP 
                 0.0235 
                 0.684 
               
               
                   
               
            
           
         
       
     
       FIG. 13A  shows the theoretical phase map of the nanostructures needed to focus the light to the photodiode of the sensor. The hyperbolic phase needed for focusing a normal incident light to a pixel may be given by 
     
       
         
           
             
               
                 
                   
                     φ 
                      
                     
                       ( 
                       ρ 
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           2 
                            
                           π 
                         
                         λ 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               ρ 
                               2 
                             
                             + 
                             
                               f 
                               2 
                             
                           
                         
                         - 
                         f 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     in which ρ is the radial coordinate and f is the distance between the metasurface and the photodiode. 
       FIG. 13B  shows the discrete version of the phase map shown in the  FIG. 13A  based on a unit cell of the nanostructure. For example, the phase map here is divided into 9×9 arrangements to assign each block with a nanostructure with defined phase values. 
       FIG. 14A  shows the nanostructure dimension requirements to achieve the phase map in  FIG. 13B . The values of the nanostructure dimension may be extracted from  FIG. 7A . This design is valid for the case of Dx=Dy, i.e., to design the linear polarization pixel I H , I V , I D  and I D .  FIG. 14B  shows the simulated focused light beam on the photodetector from the designed nanostructure arrangement in  FIG. 14A . 
       FIGS. 15A and 15B  show the nanostructure dimension requirements for both Dx and Dy to achieve the phase map in  FIG. 13B . The values of the nanostructure dimension may be extracted from  FIG. 7A . This design is valid for the case of Dx≠Dy, i.e., to design the QWP and circular polarization pixel IR and IL. 
       FIG. 16  depicts an example arrangement of a wire grid  210  and nanostructures  211  for the multifunctional horizontally (H) polarization filter  201   a  in  FIG. 2A  according to the subject matter disclosed herein. Only one wire of the wire grid  210  is indicated, and only one nanostructure  211  is indicated. The sizes of the nanostructures  211  have been selected using the techniques disclosed herein so that light passing through the filter  201   a  is focused at a pixel at an image plane (i.e., pixel  205  in  FIG. 2A ). The example arrangement depicted in  FIG. 16  may be rotated to the right (or left) to provide an arrangement of a wire grid  210  and nanostructure  211  for the multifunctional vertically polarization filter  201   b  in  FIG. 2A . 
       FIG. 17  depicts an example arrangement of a wire grid  210  and nanostructure  211  for the multifunctional diagonal (D) polarization filter  201   c  of  FIG. 2A  according to the subject matter disclosed herein. Only one wire of the wire grid  210  is indicated, and only one nanostructure  211  is indicated. The sizes of the nanostructures  211  have been selected using the techniques disclosed herein so that light passing through the filter  201   c  is focused at a pixel at an image plane (i.e., pixel  207  in  FIG. 2A ). The example arrangement depicted in  FIG. 17  may be rotated to the right (or left) to provide an arrangement of a wire grid  210  and nanostructure  211  for a multifunctional anti-diagonal (A) polarization filter  201 . 
       FIG. 18  depicts an example arrangement of a wire grid  210  and nanostructure  211  for the multifunctional LHCP polarization filter  201   d  of  FIG. 2A  according to the subject matter disclosed herein. Only one wire of the wire grid  210  is indicated, and only one nanostructure  211  is indicated. The sizes of the nanostructures  211  have been selected using the techniques disclosed herein so that light passing through the filter  201   c  is focused at a pixel at an image plane (i.e., pixel  208  in  FIG. 2A ). The example arrangement depicted in  FIG. 17  may be rotated to the right (or left) to provide an arrangement of a wire grid  210  and nanostructure  211  for a multifunctional RHCP polarization filter  201 . 
       FIG. 19  depicts an example embodiment of a multifunctional polarization filter  1900  for a unit-cell pixel according to the subject matter disclosed herein. The multifunctional polarization filter  1900  may be used to detect six polarization states according to the subject matter disclosed herein. The polarization filter  1900  includes a filter  1901   a  that horizontally (H) polarizes light passing through the filter  1901   a , a filter  1901   b  that vertically (V) polarizes light passing through the filter  1901   b , a filter  1901   c  that diagonally (D) polarizes light passing through the filter  1901   c , and a filter  1801   d  that circularly polarizes light passing through the filter  1901   d.    
     Each of the filters  1901   a - 1901   d  includes a wire grid  210  having an MIM structure and one or more phase-modulating nanostructures  211 , although the wire grid and the phase-modulating nanostructures are only indicated for the filter  1901   a . The size and shapes of the nanostructures  211  are selected as described herein to focus light passing through each filter onto a location on an image plane that corresponds to a pixel of a unit-cell pixel (not shown). For example, the horizontal and vertical dimensions of the phase-modulating nanostructures  211  may be varied based on the graph  700  in  FIG. 7A  to achieve a desired focusing. For example, the phase-modulating nanostructures  211  are depicted as being generally square for the polarizing filters  1901   a - 1901   d , but having different horizontal and vertical dimensions depending upon the position of the nanostructure on the polarizing filter. The phase-modulating nanostructures of the circularly polarizing filter  1901   d  may be generally square or rectangular depending upon the position of the nanostructure on the polarizing filter. 
     The arrangement of the polarization filters  1901   a - 1901   d , in which the horizontally polarization filter  1901   a  is in the upper-left corner of the polarization filter  1900 , the vertically polarization filter  1901   b  in the lower-right corner, the diagonally polarization filter  1901   c  in the lower-left corner, and the circularly polarization filter  1901   d  is in the upper-right corner, is an example arrangement and other arrangements are possible. In an alternative example embodiment, two additional polarization filters, such as an anti-diagonally polarization filter and a circularly polarization filter that would polarize light in the opposite circular direction from the circularly polarization filter  1901   d , may be included in the polarization filter  1900 . Such an alternative embodiment would also use two additional pixels in a unit-cell pixel. 
     Different spectral filters may be positioned in alignment with, for example, one or more polarizers  201 , so that the Stokes parameters may be determined for light of different spectral ranges.  FIGS. 20A-20E  depict a cross-sectional view of an example sequence of forming different spectral filters on an array of photodiodes according to the subject matter disclosed herein. The polarizers  201  are not shown in  FIGS. 20A-20E ; however, the polarizers  201  may be placed on either side of the spectral filters in the light path. In  FIG. 20A , a bottom distributed Bragg reflector (DBR)  2002  is formed on a substrate  2001  that includes an array of photodiodes (not shown). In one embodiment, the bottom DBR  2002  may be formed from alternating layers of SiO 2  and TiO 2 . In  FIGS. 20B-20D , photolithography and patterned masks  2003  may be used to form layers and/or cavities  604  having different heights, or thicknesses, that reflect correspondingly different wavelengths of light to form spectral filters  2005   a - n , as depicted in  FIG. 20E . Each respective spectral filter may be arranged to be aligned with a polarizer  201  and a photodetector. It should be understood that the depiction of the spectral filters  2005   a - n  in  FIG. 20E  is in only one direction or dimension. A cross-sectional view in another orthogonal direction may depict one or more additional spectral filters each covering a different spectral range. 
       FIG. 21  depicts a top view of an example embodiment of an array  2100  of polarizing filters and different spectral filters that may be used with an image sensor to provide on-chip simultaneous full Stokes polarization parameters and multi/hyper spectral imaging according to the subject matter disclosed herein. The array of polarizing filters may include the example embodiment of a polarizer  201 . Different spectral filters may be arranged in optical alignment with different polarizers  201 . For example, a first filter  2101  may be optically aligned with a polarizer  201 , and so on. 
       FIG. 22  depicts an imaging system  2200  that may include polarizing filters and spectral filters that provide on-chip simultaneous full Stokes polarization parameters (both linear and circular polarization) and multi/hyper spectral imaging according to the subject matter disclosed herein. The imaging system  2200  may include a camera  2201  having an image sensor (not shown). The image sensor may include polarizing and spectral filters  2202 , as disclosed herein. An image captured by the image sensor may be processed as a grayscale image  2203  and demosaiced. Additionally, the captured image may be processed to generate images corresponding to multispectral linear and circularly polarized light that passes through the polarizing and spectral filters  2202 . For example, depending upon the particular polarizing and spectral filters  2202  that are used, the captured image may generate multispectral horizontally polarized images  2204 , multispectral vertically polarized images  2205 , diagonally (45 degrees) polarized images  2206 , anti-diagonally polarized images  2207 , right-hand circularly polarized images  2208 , and left-hand circularly polarized images  2209 . Parameters determined from the linearly and circularly polarized images  2204 - 2209  may be used to generate full Stokes parameters for the light of the image. 
     Further, the captured image may be processed to generate non-polarized multispectral images  2210 , and/or red (R), green (G) and blue (B) images  2211 . If the multispectral filters include filters for infrared (IR), multispectral IR images  2212  may be generated by the imaging system  2200 . Images may be generated that indicate the degree of linear polarization (DoLP)  2213  and the degree of circular polarization (DoCP)  2214  may also be generated. 
       FIG. 23  depicts an electronic device  2300  that includes an image sensor having one or more multifunctional polarization filters according to the subject matter disclosed herein. Electronic device  2300  may be used in, but not limited to, a computing device, a personal digital assistant (PDA), a laptop computer, a mobile computer, a web tablet, a wireless phone, a cell phone, a smart phone, a digital music player, or a wireline or wireless electronic device. The electronic device  2300  may also be part of, but not limited to, an ADAS, a mobile-device imaging system, an industrial imaging system, robotics, etc. The electronic device  2300  may include a controller  2310 , an input/output device  2320  such as, but not limited to, a keypad, a keyboard, a display, a touch-screen display, a camera, and/or an image sensor, a memory  2330 , an interface  2340 , a GPU  2350 , and an imaging processing unit  2360  that are coupled to each other through a bus  2370 . The controller  2380  may include, for example, at least one microprocessor, at least one digital signal processor, at least one microcontroller, or the like. The memory  2330  may be configured to store a command code to be used by the controller  2310  or a user data. 
     Electronic device  2300  and the various system components of electronic device  2300  may include the image processing unit  2360 , which includes an image sensor having multifunctional polarization filters according to the subject matter disclosed herein. The interface  2340  may be configured to include a wireless interface that is configured to transmit data to or receive data from a wireless communication network using a RF signal. The wireless interface  2340  may include, for example, an antenna, a wireless transceiver and so on. The electronic system  2300  also may be used in a communication interface protocol of a communication system, such as, but not limited to, Code Division Multiple Access (CDMA), Global System for Mobile Communications (GSM), North American Digital Communications (NADC), Extended Time Division Multiple Access (E-TDMA), Wideband CDMA (WCDMA), CDMA2000, Wi-Fi, Municipal Wi-Fi (Muni Wi-Fi), Bluetooth, Digital Enhanced Cordless Telecommunications (DECT), Wireless Universal Serial Bus (Wireless USB), Fast low-latency access with seamless handoff Orthogonal Frequency Division Multiplexing (Flash-OFDM), IEEE 802.20, General Packet Radio Service (GPRS), iBurst, Wireless Broadband (WiBro), WiMAX, WiMAX-Advanced, Universal Mobile Telecommunication Service—Time Division Duplex (UMTS-TDD), High Speed Packet Access (HSPA), Evolution Data Optimized (EVDO), Long Term Evolution—Advanced (LTE-Advanced), Multichannel Multipoint Distribution Service (MMDS), and so forth. 
     Embodiments of the subject matter and the operations described in this specification may be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification may be implemented as one or more computer programs, i.e., one or more modules of computer-program instructions, encoded on computer-storage medium for execution by, or to control the operation of, data-processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially-generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. A computer-storage medium can be, or be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial-access memory array or device, or a combination thereof. Moreover, while a computer-storage medium is not a propagated signal, a computer-storage medium may be a source or destination of computer-program instructions encoded in an artificially-generated propagated signal. The computer-storage medium can also be, or be included in, one or more separate physical components or media (e.g., multiple CDs, disks, or other storage devices). Additionally, the operations described in this specification may be implemented as operations performed by a data-processing apparatus on data stored on one or more computer-readable storage devices or received from other sources. 
     While this specification may contain many specific implementation details, the implementation details should not be construed as limitations on the scope of any claimed subject matter, but rather be construed as descriptions of features specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment may also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination may in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. 
     Thus, particular embodiments of the subject matter have been described herein. Other embodiments are within the scope of the following claims. In some cases, the actions set forth in the claims may be performed in a different order and still achieve desirable results. Additionally, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous. 
     As will be recognized by those skilled in the art, the innovative concepts described herein may be modified and varied over a wide range of applications. Accordingly, the scope of claimed subject matter should not be limited to any of the specific exemplary teachings discussed above, but is instead defined by the following claims.