Abstract:
A sub-wavelength grating is placed inside a liquid crystal variable optical retarder to reduce polarization dependence of the optical retardation generated by the variable optical retarder. A small thickness of the sub-wavelength grating, as compared to a conventional waveplate, reduces the driving voltage penalty due to the in-cell placement of the sub-wavelength grating.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Provisional Patent Application No. 61/692,896 filed Aug. 24, 2012, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to optical retarders, and in particular to variable optical retarders for imparting a variable phase delay to an optical beam. 
       BACKGROUND OF THE INVENTION 
       [0003]    Liquid crystal variable optical retarders are used to impart a variable optical phase delay, and/or change the state of polarization of an optical beam. In a typical liquid crystal variable optical retarder, a few micrometers thick layer of a liquid crystal fluid is sandwiched between two transparent electrodes. When a voltage is applied to the electrodes, an electric field between the electrodes orients liquid crystal molecules, which are highly anisotropic. Field-induced orientation of the liquid crystal molecules changes an effective index of refraction of the liquid crystal layer, which affects an optical phase of an optical beam propagating through the liquid crystal layer. When the optical beam is linearly polarized at 45 degrees to a predominant direction of orientation of the liquid crystal molecules termed “director”, the induced optical phase difference can change the polarization state of the optical beam, for example, it can rotate the linear optical polarization. When the optical beam is linearly polarized along the predominant direction of orientation of the liquid crystal molecules, a variable optical phase delay is imparted to the optical beam by the variable optical retarder. 
         [0004]    Arrays of variable optical retarders can be constructed by arranging an array of individually controllable pixels under a common liquid crystal layer. When a linearly polarized optical beam illuminates such an array, pre-determined optical phase patterns can be imparted to the beam, allowing variable focusing or steering of the optical beam without any moving parts. Arrays of variable optical retarders have found a variety of applications in beam scanning/steering, optical aberrations correction, and so on. 
         [0005]    One disadvantage of liquid crystal variable retarders is that they typically require a polarized optical beam for proper operation. This disadvantage, however, is not intrinsic and may be overcome by using an appropriate polarization diversity arrangement. By way of example, G. D. Love in an article entitled “Liquid-Crystal Phase modulator for unpolarized light”, Appl. Opt., Vol. 32, No 13, p. 2222-2223, 1 May 1993, disclosed a reflective polarization-insensitive variable optical retarder. Referring to  FIG. 1 , a variable optical retarder  10  of Love has a quarter-wave plate (QWP)  11  disposed between a liquid crystal cell  12  and a mirror  13 . In operation, an incoming vertically linearly polarized (V-LP) optical beam  14  propagates through the liquid crystal cell  12 , the quarter-wave plate  11 , and is reflected by the mirror  13  to propagate back through the quarter-wave plate  11  and the liquid crystal cell  12 . The reflected optical beam is shown at  16 . The liquid crystal cell  12  has a director  15  oriented vertically; therefore, the variable optical phase delay will be imparted on the optical beam  14  on the first pass, without changing its state of polarization. The quarter-wave plate  11  is oriented to change the vertical state of polarization to a left hand-circular polarization (LH-CP), which accordingly changes to a right hand-circular polarization (RH-CP) upon reflection from the mirror  13 . On the second pass, the quarter-wave plate  11  changes the right hand-circular polarization to horizontal linear polarization (H-LP), which will not be changed by the liquid crystal cell  12 , since its director  15  is oriented perpendicular to it, that is, is oriented vertically. One can see that, if the incoming optical beam  14  were horizontally polarized (not shown for simplicity), it would be reflected vertically polarized and phase-delayed by the same amount, only not on the first but the second pass through the liquid crystal cell  12 . Therefore, if the optical beam  14  were unpolarized or randomly polarized, it would be phase-delayed by a same amount regardless of its state of polarization. Thus, the variable optical retarder  10  is polarization-insensitive. 
         [0006]    One drawback of the variable optical retarder  10  of  FIG. 1  is that placing the quarter-wave plate  11  between the liquid crystal cell  12  and the mirror  13  increases a distance D between the mirror  13  and the liquid crystal cell  12 . This is detrimental, because the incoming optical beam  14  diverges while propagating through the distance D. The beam divergence increases the beam spot size on the liquid crystal cell  12 . The increased beam spot size is detrimental in a variable retarder array configuration, in which the liquid crystal cell  12  is pixilated, because it reduces the spatial resolution. 
         [0007]    Another disadvantage of the variable optical retarder  10  is that the liquid crystal cell  12  has to be transmissive to accommodate the external quarter-wave plate  11 . Transmissive liquid crystal cells usually have a higher optical loss in a double-pass configuration than reflective liquid crystal cells in a single-pass configuration, because in a transmissive cell, the incoming light has to pass twice through two transparent electrodes. The transparent electrodes have to both conduct electricity and transmit light. These requirements are somewhat contradictory, and as a result, the transparent electrodes usually introduce some extra optical loss into the system. 
         [0008]    James et. al. in an article entitled “Modeling of the diffraction efficiency and polarization sensitivity for a liquid crystal 2D spatial light modulator for reconfigurable beam steering”, J. Opt. Soc. Am. A, Vol 24, No. 8, p. 2464-2473, discloses a reflective polarization-insensitive liquid crystal retarder array, in which one of the electrodes is made highly reflective, and the quarter-wave plate is placed inside the liquid crystal cell. The resulting optical loss is lower in this case, because in the James device, the incoming optical beam passes twice through a single transparent electrode, not through two electrodes. However, inside placement of the quarter-wave plate reduces electrical field across the liquid crystal layer, thus requiring a higher driving voltage to compensate for the electric field decrease. 
       SUMMARY OF THE INVENTION 
       [0009]    It is an objective of the invention to provide a variable optical retarder, in which the polarization sensitivity would be reduced without excessive optical loss or driving voltage penalties. 
         [0010]    In accordance with the invention, a dielectric or semiconductor sub-wavelength grating is placed inside a liquid crystal variable optical retarder between an electrode and a liquid crystal layer. The sub-wavelength grating acts as a quarter-wave plate, while having a very small thickness, so that the driving voltage penalty due to the in-cell placement of the sub-wavelength grating is lessened. The sub-wavelength grating can also be made highly reflective, for example, it can include a multilayer dielectric high reflector, which further reduces optical loss in comparison with a metal reflector. 
         [0011]    In accordance with one aspect of the invention, there is provided a liquid crystal variable optical retarder comprising: 
         [0012]    a first continuous flat electrode; 
         [0013]    a second substantially transparent continuous flat electrode opposed to the first electrode; 
         [0014]    a liquid crystal layer having a director and disposed between the first and second electrodes, for imparting a variable optical phase shift to light impinging on the second electrode when a voltage is applied between the first and second electrodes; and 
         [0015]    a sub-wavelength grating disposed between the liquid crystal layer and the first electrode and having grating lines at an acute angle, preferably 45 degrees, to the director. 
         [0016]    In accordance with the invention, there is further provided a variable optical retarder for imparting a variable phase delay to an optical beam impinging thereon, the variable optical retarder comprising: 
         [0017]    a substrate having a pixel electrode; 
         [0018]    a sub-wavelength grating disposed on and separate from the pixel electrode, for imparting a first optical retardation to the optical beam impinging thereon, the sub-wavelength grating having a plurality of grating lines running parallel to each other; 
         [0019]    a liquid crystal layer on the sub-wavelength grating, for imparting a second optical retardation to the optical beam propagating therethrough; and 
         [0020]    a substantially transparent backplane electrode on the liquid crystal layer; 
         [0021]    wherein the second optical retardation is varied when a voltage is applied between the pixel and backplane electrodes, thereby imparting the variable phase delay to the optical beam propagating through the liquid crystal layer; 
         [0022]    wherein a director of the liquid crystal layer forms an acute angle with the grating lines, whereby sensitivity of the variable optical retarder to a state of polarization of the optical beam is lessened. 
         [0023]    In accordance with another aspect of the invention, there is provided a liquid-crystal-on-silicon spatial light modulator comprising a trim retarder, wherein the trim retarder includes a sub-wavelength grating. 
         [0024]    In accordance with yet another aspect of the invention, there is further provided a method for imparting a variable phase delay to a beam of light, the method comprising: 
         [0025]    (a) propagating the beam through a liquid crystal layer and then through a sub-wavelength grating having grating lines oriented at an angle to a director of the liquid crystal layer; 
         [0026]    (b) reflecting the beam propagated in step (a) to propagate the beam back through the liquid crystal layer; and 
         [0027]    (c) while performing steps (a) and (b), applying an electric field to the liquid crystal layer via a pair of flat electrodes external to, and parallel to the liquid crystal layer and the sub-wavelength grating, to vary an optical retardation of the liquid crystal layer, thereby varying the phase delay of the beam of light; wherein the flatness of the electrodes facilitates spatial uniformity of the applied electric field, thereby facilitating spatial uniformity of the varied optical retardation of the liquid crystal layer. 
         [0028]    In a preferred embodiment, the sub-wavelength grating does not contain any metal, which reduces optical loss and electric field fringing or shielding effects. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]    Exemplary embodiments will now be described in conjunction with the drawings, in which: 
           [0030]      FIG. 1  is a schematic view of a prior-art polarization-insensitive liquid crystal variable optical retarder; 
           [0031]      FIGS. 2A and 2B  are side and plan cross-sectional views, respectively, of a variable optical retarder of the invention; 
           [0032]      FIG. 3A  is a side cross-sectional view of an embodiment of the variable optical retarder of  FIGS. 2A and 2B ; 
           [0033]      FIGS. 3B and 3C  are magnified side cross-sectional views of a pixel area of two embodiments of the variable optical retarder of  FIG. 3A ; 
           [0034]      FIG. 4  is a side cross-sectional view of a liquid-crystal-on-silicon (LCoS) implementation of the variable optical retarder of  FIG. 3A ; 
           [0035]      FIG. 5  is a spatial light modulator having therein a trim retarder in form of a sub-wavelength  grating; 
           [0036]      FIG. 6  is a flow chart of a method for imparting a variable phase delay to a beam of light according to the invention; 
           [0037]      FIG. 7  is a theoretical plot of effective refractive indices, birefringence, and a height of a sub-wavelength grating used in the variable optical retarders of  FIGS. 2A ,  2 B, and  FIGS. 3A  to  3 C, as a function of a fill factor of the sub-wavelength features, computed in an approximation of a grating pitch being much smaller than wavelength; 
           [0038]      FIG. 8  is the fill factor dependence of an optical retardance, polarization-dependent loss, and insertion loss of an example tantala (Ta 2 O 5 )—air lamellar grating on aluminum substrate, computed using an electromagnetic theory at a finite grating pitch of 0.8 micrometers; and 
           [0039]      FIG. 9  is a plot of voltage drop across the liquid crystal layer vs. voltage applied to a variable optical retarder having an in-cell sub-wavelength grating, in comparison with a corresponding voltage drop in a variable optical retarder having an in-cell conventional quarter-wave waveplate in place of the in-cell sub-wavelength grating. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0040]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. In  FIGS. 2A ,  2 B and  3 A,  3 B, and  3 C, similar numerals refer to similar elements. 
         [0041]    Referring to  FIGS. 2A and 2B , a variable optical retarder  20  of the invention includes a first continuous flat electrode  21  and a second substantially transparent continuous flat electrode  22  opposed to the first electrode  21 , a liquid crystal layer  26 , and a sub-wavelength grating  24  disposed between the liquid crystal layer  26  and the first electrode  21 . As seen in  FIG. 2B , the sub-wavelength grating  24  has a plurality of grating lines  25  running parallel to each other. A director  27  of the liquid crystal layer  26  is at an angle a of 45 degrees with respect to the grating lines  25 . The sub-wavelength grating  24  has a quarter-wavelength retardation in a single pass, amounting to half-wave retardation in a double pass. 
         [0042]    In operation, an optical beam  28  impinges onto the liquid crystal layer  26  through the second electrode  22 . A voltage V is applied between the first  21  and second  22  electrodes, thereby varying an optical retardation of the liquid crystal layer  26 . As a result, a variable phase delay is imparted to the optical beam  28 . The sub-wavelength grating  24  acts as a quarter-wave plate oriented at α=45 degrees to the director  27 , switching horizontal and vertical polarizations, as explained above with respect to  FIG. 1 , which results in lessening a sensitivity of the variable optical retarder  20  to a state of polarization of the optical beam  28 . In some embodiments, the angle a is not equal to 45 degrees, but remains an acute angle. The retardation value of the sub-wavelength grating  24  can deviate from a quarter-wave in a single pass, if some polarization dependence is required. 
         [0043]    The flatness and evenness of a top surface  23  of the first electrode  21  is beneficial in that the flat and even surface  23  of the first electrode  21 , for example flat to within 0.2 micron, or preferably within 0.1 micron, generates a more even electric field than, for example, a corrugated surface would, which the first electrode  21  would have if the sub-wavelength grating  24  were micromachined directly in the first electrode  21 . A more even electric field is applied to the liquid crystal layer  26 , generating a more uniform optical retardation profile of the liquid crystal layer  26 , and thus lessening unwanted and uncontrollable diffraction effects in the liquid crystal layer  26  perturbed by fringing electric fields. 
         [0044]    The top surface  23  of the first electrode  21  can be made highly reflective, in which case the sub-wavelength grating  24  is made transmissive. However, the sub-wavelength grating  24  itself can be made highly reflective, for example it can include a multilayer dielectric high reflector, not shown, so that a high reflectivity of the surface  23  of the first electrode  21  is not required. Since metal reflectors necessarily incur some optical loss, a high dielectric reflector of the sub-wavelength grating  24  can have a higher reflectivity then the surface  23  of the first electrode  21 , resulting in a lower overall optical loss of the variable optical retarder  20 . To further lower the optical loss and prevent electrical field shielding, the sub-wavelength grating  24  is preferably made of a dielectric or a semiconductor, absent any metal therein; for instance, the sub-wavelength grating  24  can include periodic structure of tantala (Ta 2 O 5 ) or silicon (Si) in a silicon dioxide (SiO 2 ) host. 
         [0045]    Referring now to  FIGS. 3A and 3B , a variable optical retarder  30  of the invention includes a substrate  34 C having a plurality of pixel electrodes  31  formed therein, a sub-wavelength grating  34  disposed on and separate from the pixel electrode  31 , a liquid crystal layer  36  on the sub-wavelength grating  34 , and a substantially transparent backplane electrode  32  on the liquid crystal layer  36 . A glass cover plate  39  supports the backplane electrode  32 , made of indium tin oxide (ITO) or other suitable material. The cover plate  39  has an anti-reflection (AR) coating  39 A. Alignment layers  37  adhered to the sub-wavelength grating  34  and the backplane electrode  32  are used to align liquid crystal molecules in the liquid crystal layer  36 . The sub-wavelength grating  34  has a plurality of grating lines in form of ridges  34 A. The liquid crystal layer  36  extends into gaps  34 B between the ridges  34 A. In the embodiment shown, the substrate  34 C is a silicon dioxide substrate. 
         [0046]    In operation, an optical beam  38  propagates in succession through the AR coating  39 A, the cover plate  39 , the transparent backplane electrode  32 , the liquid crystal layer  36 , impinges onto the sub-wavelength grating  34 , and is reflected by top surfaces  33  of the pixel electrodes  31  to propagate back through the stack in reverse order. The liquid crystal layer  36  and the sub-wavelength grating  34  impart first and second optical retardations, respectively, to the optical beam  38 . The second optical retardation is varied when a voltage is applied between the pixel  31  and backplane  32  electrodes, thereby imparting a variable phase delay to the optical beam  38  propagating through the liquid crystal layer  36 . A director, not shown, of the liquid crystal layer  36  forms a 45 degrees angle with the grating lines  34 A, whereby sensitivity of the variable optical retarder  30  to a state of polarization of the optical beam  38  is lessened. 
         [0047]    Preferably, the top surfaces  33  of the pixel electrodes  31  are flat to avoid fringing electrical fields and associated liquid crystal refractive index spatial modulation as explained above. To increase reflectivity, the sub-wavelength grating  34  can be made reflective. Also in one embodiment, the liquid crystal layer  36  director forms an acute angle with the grating lines (ridges  34 A) not necessarily equal to 45 degrees. Shapes of the grating lines other than rectangular ridges  34 A can be used, including triangular, trapezoidal, and the like. The sub-wavelength  grating  34  preferably has an optical retardation of a quarter-wavelength in a single pass, that is, a quarter-wavelength retardation when the optical beam  38  propagates down in  FIG. 3A , plus a quarter-wavelength retardation when the optical beam  38  is reflected to propagate up in  FIG. 3A . As explained above w.r.t. the variable optical retarder  20  of  FIG. 2 , the sub-wavelength grating  34  of the variable optical retarder  30  of  FIG. 3A  preferably includes a dielectric or a semiconductor, and most preferably is a pure dielectric absent any metal therein for low optical loss and low disturbance to the electric field generated by the pixel  31  and backplane  32  electrodes. By way of a non-limiting example, the grating lines or ridges  34 A of the sub-wavelength grating  34  can be made of tantala (Ta 2 O 5 ). 
         [0048]    In an embodiment of the variable optical retarder  30  shown in  FIG. 3C , the tantala ridges  34 A are formed in the silicon dioxide substrate  34 C, which planarizes the sub-wavelength grating  34 , so that the lower alignment layer  37  is flat, and, accordingly, the liquid crystal layer  36  is flat on both sides. This provides a more stable sub-wavelength grating  34 , because it does not include a sub-wavelength grating structure partially formed by liquid crystal material, as is seen in  FIG. 3B . 
         [0049]    It is to be understood that, although  FIGS. 3A to 3C  show a plurality of pixel electrodes  31  under the common liquid crystal layer  36 , the sub-wavelength grating  34 , and the backplane electrode  31 , the variable optical retarder  30  can include only one pixel electrode  31 , effectively making the variable optical retarder  30  a non-pixilated optical retarder, which can be used in applications where the entire optical beam  38  needs to be given a same variable optical phase shift. 
         [0050]    The pixilated variable optical retarders  30  of  FIGS. 3A to 3C  can be advantageously implemented in liquid-crystal-on-silicon (LCoS) technology. Referring now to  FIG. 4 , a LCoS variable optical retarder  40  is shown. In the LCoS variable optical retarder  40 , the silicon dioxide substrate  34 C is an overlayer on a silicon substrate  42  having thereon a driver circuitry  41  under the plurality of pixel electrodes  31 , for independently applying a voltage to each of the pixel electrodes  31 . The silicon driver electronics  41  can be compact, fast, and can accommodate a very large number of the pixel electrodes  31 . 
         [0051]    Speed and compactness of LCoS technology has resulted in its successful use in spatial light modulators for high-definition optical projector equipment. According to one aspect of the present invention, sub-wavelength gratings can be used in a LCoS-based spatial light modulator as a trim retarder. Trim retarders provide a relatively small birefringence which, in combination with the voltage-controlled birefringence of the liquid crystal layer of a LCoS spatial light modulator, provides a wider viewing angle and improves image contrast. Turning to  FIG. 5 , a spatial light modulator  50  includes a silicon substrate  52 , driver electronics  51 , a pixilated variable optical retarder  55 , a sub-wavelength grating trim retarder  54 , and an AR coating  53 . 
         [0052]    Turning to  FIG. 6  with further reference to  FIGS. 2A and 2B , a method  60  for imparting a variable phase delay to a beam of light includes a step  61  of providing the sub-wavelength grating  24 ; a step  62  of propagating an optical beam  28  through the liquid crystal layer  26 , and then through the sub-wavelength grating  24 ; a step  63  of reflecting the optical beam  28  to propagate back through the liquid crystal layer  26 ; and a step  64  of applying an electric field to the liquid crystal layer via the pairs of electrodes  21 ,  22 , to vary an optical retardation of the liquid crystal layer  26 , thereby varying the phase delay of the beam of light  28 . The flatness of the electrodes  21 ,  22  facilitates spatial uniformity of the applied electric field, thereby facilitating spatial uniformity of the varied optical retardation of the liquid crystal layer  26 . Preferably, the sub-wavelength grating  24  has a quarter-wavelength optical retardation in a single pass, and the sub-wavelength grating lines are disposed at the angle of 45 ±5 degrees to the director  27  of the liquid crystal layer  26 . The method  60  is equally applicable to the variable optical retarders  30  of  FIGS. 3A to 3C . 
         [0053]    The optical retardation of the sub-wavelength gratings  24  and  34 , and/or the sub-wavelength grating trim retarder  54  can be calculated analytically in an approximation of the grating pitch being much smaller than the wavelength. Referring to  FIG. 7 , analytically computed effective refractive indices for T E  and T M  polarizations n TE    71  and n TM    72 , respectively, birefringence Δn  73 , and a height  74  of a sub-wavelength grating including rectangular ridges having a refractive index of 2.2; gaps between the ridges having a refractive index of 1.0, are plotted as s function of a fill factor defined as ridge width divided by the grating pitch. The calculation was performed at a telecommunications C-band wavelength of 1.55 micrometers. The maximum value for Δn=0.4 is observed at the fill factor of 0.6 at the depth of 0.97 micrometers, which corresponds to the optical retardation of 0.4*0.97=0.39 micrometers, or approximately one quarter of the C-band 1.55 micrometers wavelength. This calculation proves that one quarter of wavelength retardation is readily achievable at reasonable height  74  of a sub-wavelength grating. 
         [0054]    Turning to  FIG. 8 , a retardance  83 , a polarization-dependent loss (PDL)  84 , and an insertion loss (IL)  85  are plotted as a function of the above defined fill factor for a sub-wavelength grating having 0.97 micrometers high Ta 2 O 5  ridges at the pitch of 0.8 micrometers, disposed on aluminum substrate, with air having a refractive index of 1.0 extending into the grooves between the ridges. The retardance  83  is a difference between T M -polarized and T E -polarized zero-order diffracted light phases. One can see that the half-wave retardance occurs at the fill factor of approximately 0.46. The PDL is approximately 0.08 dB, and the average IL is approximately 0.2 dB. 
         [0055]    The grating structure of  FIG. 3B  can be modified to accommodate the air-filled grooves. A thin flat membrane, not shown, can be disposed on top of the grating structure  34 , to create and seal the air channels  34 C between the grating ridges  34 A, thereby preventing the liquid crystal fluid of the layer  36  from filling the air channels  34 C, and providing a planarizing surface for the subsequently disposed alignment layer  37 . For example, a SiO 2  membrane can be used for this purpose, 
         [0056]    Referring now to  FIG. 9  with further reference to  FIG. 3B , a voltage drop across the liquid crystal layer  36  is plotted as a function of the pixel voltage applied between the pixel electrodes  31  and the transparent backplane electrode  32 . A straight line  91  (diamonds) corresponds to a case when a conventional quarter-wave waveplate, not shown, is inserted in place of the sub-wavelength grating  34 . A straight line  92  (rectangles) corresponds to the case shown in  FIG. 3B , that is, when the sub-wavelength grating  34  is used. One can see that using the sub-wavelength grating  34  approximately doubles the voltage drop across the liquid crystal layer  36  at a same pixel voltage, allowing one to achieve considerably higher levels of variable optical retardation. 
         [0057]    The foregoing description of one or more embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.