Asymmetric transmissive behavior of liquid-crystal diffraction gratings

Dynamic Control of Light Direction Enabled by Stimuli-Responsive Liquid Crystal Gratings

The ability to control light direction with tailored precision via facile means is long-desired in science and industry. With the advances in optics, a periodic structure called diffraction grating gains prominence and renders a more flexible control over light propagation when compared to prisms. Today, diffraction gratings are common components in wavelength division multiplexing devices, monochromators, lasers, spectrometers, media storage, beam steering, and many other applications. Next-generation optical devices, however, demand nonmechanical, full and remote control, besides generating higher than 1D diffraction patterns with as few optical elements as possible. Liquid crystals (LCs) are great candidates for light control since they can form various patterns under different stimuli, including periodic structures capable of behaving as diffraction gratings. The characteristics of such gratings depend on several physical properties of the LCs such as film thickness, periodicity, and molecular orientation, all resulting from the internal constraints of the sample, and all of these are easily controllable. In this review, the authors summarize the research and development on stimuli-controllable diffraction gratings and beam steering using LCs as the active optical materials. Dynamic gratings fabricated by applying external field forces or surface treatments and made of chiral and nonchiral LCs with and without polymer networks are described. LC gratings capable of switching under external stimuli such as light, electric and magnetic fields, heat, and chemical composition are discussed. The focus is on the materials, designs, applications, and future prospects of diffraction gratings using LC materials as active layers.

On liquid crystal diffractive optical elements utilizing inhomogeneous alignment

Formation of a desired liquid crystal (LC) director distribution by the use of inhomogeneous anchoring and pre-tilt angle for electrically controlled diffractive optical elements (DOE) is studied. Such LC DOE can have high periodicity and diffraction efficiency. At the same time they are free of constructive regularities, e.g. a periodic arrangement of the electrodes or thickness deviations, which have undesired impact on diffractive characteristics of LC DOE of other types. We focus on evaluation of potential functional abilities of LC DOE with inhomogeneous alignment. The reasons causing restriction of the LC DOE diffraction efficiency and periodicity are considered. Approaches for improvement of characteristics of the LC DOE are discussed.

Coupled-wave analysis of vector holograms. 3. Effects of intrinsic distribution of optical axis in anisotropic media

We investigated theoretically the interference of two counterpropagating polarized light beams in optically anisotropic media whose optical axis is in the film plane and is gradually rotated around the thickness direction. Results indicated that pure polarization modulation without intensity variation is obtained in the inhomogeneous media when the total angle of the rotation is much smaller than the total retardation. Reflective anisotropic gratings recorded by the polarization modulation were formulated as the perturbation of the dielectric tensor, and diffraction properties were studied using coupled-wave analysis (CWA) and a numerical method. By assuming that the period of the intrinsic distribution is substantially larger than that of the induced one, we demonstrated that CWA estimates the diffraction efficiency and the polarization state of the diffracted light with high accuracy.

Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation

The diffraction properties of thick vector holograms were analyzed with the use of a simple coupled-wave theory. Two eigenpolarizations in the holograms were determined based on the dielectric perturbation, and diffraction efficiencies for the polarizations were calculated by applying the Kogelnik method. The results were compared with those simulated by the finite-difference time-domain method. As a result, it was demonstrated that the diffraction efficiencies calculated by the two methods are in good agreement for any incident polarization when the modulation depth of the anisotropic phase retardation is substantially smaller than the mean retardation. In addition, we confirmed that coupled-wave analysis provides reasonable accuracy for relatively large modulation in the case of Bragg incidence with eigenpolarization.

Experimental study of an ultrasmall pixel, one-dimensional liquid-crystal device

A one-dimensional, ultrasmall pixel liquid-crystal (LC) device is experimentally demonstrated. The device has a one-dimensional array of ten 1 mm long, interdigitated, reflective gold electrodes on a glass substrate and a common transparent electrode on the opposite substrate. The interdigitated electrodes are 2 microm wide, separated by a 1 microm interelectrode gap. Operating as a dynamic, reflective, 3 microm pitch diffractive grating, the device simulates the performance of a reflective, ultrasmall, 3 microm pixel, spatial light modulator (SLM). It was shown that, for a proper choice of LC cell thickness (less than 2 microm), LC material (Merck's BL006 high-birefringence mixture), and driving conditions, the device can attain relatively high diffraction efficiency, thus demonstrating the practical feasibility of a 3 microm pixel, LC SLM.

Modeling of the diffraction efficiency and polarization sensitivity for a liquid crystal 2D spatial light modulator for reconfigurable beam steering

A nematic liquid crystal spatial light modulator used as a phase-modulating device and operating in the reflective mode is analyzed using three-dimensional modeling. Two configurations, which differ in their electrode placement relative to a fixed quarter-wave plate, are considered across a range of steering directions, with the grating conformal and in some cases oblique to the pixel grid. For each steering direction the sensitivity of the diffraction orders to the polarization state of the incident wavefront is studied. Optimal alignment of the liquid crystal is suggested to reduce this sensitivity.

Finite-difference time-domain simulation of a liquid-crystal optical phased array

Accurate modeling of a high-resolution, liquid-crystal-based, optical phased array (OPA) is demonstrated. The modeling method is extendable to cases where the array element size is close to the wavelength of light. This is accomplished through calculating an equilibrium liquid-crystal (LC) director field that takes into account the fringing electric fields in LC OPAs with small array elements and by calculating the light transmission with a finite-difference time-domain method that has been extended for use in birefringent materials. The diffraction efficiency for a test device is calculated and compared with the simulation.

Polarization properties of a nematic liquid-crystal spatial light modulator for phase modulation

The polarization properties of a nematic zero-twist liquid-crystal (NLC) spatial light modulator (SLM) were studied. A large ratio between the liquid-crystal (LC) layer thickness and the pixel pitch combined with spatial variations in the applied electric field causes fringing fields between pixels. Depending on the LC alignment, the electric field components within the LC layer can result in a twist deformation. The produced inhomogeneous optical anisotropy affects the polarization of light propagating through the device. We experimentally examined polarization effects in different diffraction orders for both binary and blazed phase gratings. Simulations of the LC deformation together with finite-difference time-domain simulations for the optical propagation were used to calculate the corresponding far-field intensities. It was demonstrated how rigorous simulations of the NLC SLM properties can be used to understand the polarization features of different diffraction orders.

Liquid-crystal blazed grating with azimuthally distributed liquid-crystal directors

We propose a novel formation method of arbitrary phase profiles of circular light by controlling azimuthal angles of liquid-crystal directors; its principle is described theoretically. A new liquid-crystal blazed grating is demonstrated by use of the proposed method. It is revealed that the first-order diffraction efficiency reaches the maximum value (theoretically 100%, experimentally approximately 90%) at an optimum applied voltage when the phase difference between the extraordinary and ordinary rays agrees with one-half the wavelength. Furthermore, the polarization states of the diffracted light beams are analyzed by Stokes parameter measurements, and unique polarization-splitting properties are revealed.

Modeling optical properties of liquid-crystal devices by numerical solution of time-harmonic Maxwell equations

We consider numerical modeling of the optical properties of devices typical of beam-steering devices based on liquid-crystal materials: two-dimensional, anisotropic and inhomogeneous dielectric properties, periodic in one dimension. A mathematical formulation of the system of second-order partial differential equations for the components of the time-harmonic electric field is discretized by using a finite-element method based on curl-conforming edge elements. The discrete equations are also interpreted as equivalent finite-difference equations. It is shown how the resulting large sparse complex system of linear algebraic equations can be solved by an iterative method with convergence accelerated by a preconditioner based on fast Fourier transforms. Benchmarking results and the application to a realistic problem are reported. The practical limitations of the approach and its advantages and disadvantages compared with other approaches are discussed.

On the fringing-field effect in liquid-crystal beam-steering devices

A detailed simulation of the fringing-field effect in liquid-crystal (LC)-based blazed-grating structures has been carried out. These studies are aimed at clarifying the relationship between the width of the fringing-field-broadened phase profile of the blazed grating and the LC cell thickness. This fringing-field broadening of the blazed grating's phase profile is shown to affect mostly the 2pi phase-step zone (fly-back zone) of the blazed grating. The results of the simulations carried out on the blazed-grating structure indicate two main effects of the fringing field: (1) reduction in the attainable diffraction efficiency and (2) limitation of the maximum deflection angle of the device. Both effects are shown to be directly linked to the broadening of the fly-back zone, which is shown to be proportional to the LC cell thickness.