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.
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.
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.
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.
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.
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.