Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators

Fast and low loss flexoelectro-optic liquid crystal phase modulator with a chiral nematic reflector

In this paper, we demonstrate a flexoelectro-optic liquid crystal phase-only device that uses a chiral nematic reflector to achieve full 2π phase modulation. This configuration is found to be very tolerant to imperfections in the chiral nematic reflector provided that the flexoelectro-optic LC layer fulfils the half-wave condition. Encouragingly, the modulation in the phase, which operates at kHz frame rates, is also accompanied by low amplitude modulation. The configuration demonstrated herein is particularly promising for the development of next-generation liquid crystal on silicon spatial light modulators.

Design of an off-axis see-through display based on a dynamic phase correction approach

The design and the analysis of an off-axis (50°) diffractive imaging optical system is presented in this paper. A 10°x15° field of view is considered. The optical system is composed of two diffractive optical elements. A static diffractive optical element having a frozen phase transfer function is used to perform a virtual point in the considered field of view. A dynamic diffractive optical element having an adapted calculated phase transfer function is used to compensate for aberrations of the static element. Using a sequential creation of virtual image points and considering human eye characteristics, it is shown that a nine points virtual image can be obtained with current technology. Moreover, it is presented that aberrations can be compensated whatever the position of the virtual point in the 10°x15° field of view. Finally, using rigorous coupled wave analysis, it is shown that an average diffraction efficiency of 79% can be reached across the considered field of view with a standard deviation of nearly 5%.

Fast beam steering with a ferroelectric-liquid-crystal optical phased array

We demonstrate fast, efficient beam steering using a single 1x32 analog ferroelectric liquid crystal (FLC) spatial light modulator. A high-tilt FLC material with 82 degrees optic-axis switching provides, in a reflective-mode device with a passive quarter-wave retarder between a half-wave FLC layer and a mirror, 91% of full 0-2pi phase modulation. Electronic drive based on applied charge gives 200 micros response-time analog modulation.

Near-lossless continuous phase modulation using the analog switching mode (V-shaped switching) in ferroelectric liquid crystals

The analog switching mode in ferroelectric liquid crystals, sometimes referred to as 'V-shaped switching,' has, thanks to its submillisecond switching capability, attracted much interest for future fast electro-optic displays where it is to be used for amplitude modulation. We have studied this mode for analog phase-only modulation. As V-shaped switching is based on a conical motion of the index ellipsoid this presents a challenging problem since both the orientation of the slow and fast axes, as well as the amount of birefringence varies in the switching process. We show theoretically, partly by means of Poincaré sphere analysis, that it is in fact possible to obtain near-lossless analog phase modulation between zero and pi radians in an ideal V-shaped switching cell through careful tuning of the polarization state of the input light. Furthermore, we were able to demonstrate this experimentally in a fabricated cell. Although this cell deviated slightly from the ideal conditions, e.g., the tilt cone half-angle was 38 degrees instead of the desired 45 degrees , we still obtained a continuous phase modulation between zero and 0.78pi rad with less than 2% modulation of the amplitude; the measured values agree very well with our numerical simulations of the real device.

Surface-stabilized ferroelectric liquid-crystal diffraction gratings with micrometer-scale pitches

The first-order diffraction efficiency eta1 of surface-stabilized ferroelectric liquid-crystal (SSFLC) phase gratings is calculated for device thicknesses in the range d = 1 to 5 microm and for pitches p of 5 to 20 microm assuming incident light at 633 nm. The peak value of eta1 as a function of d has negligible dependence on the incoming polarization when p = 20 microm. For smaller pitch values the peak value of eta1 decreases and becomes increasingly dependent on the orientation of the incoming polarization owing to the influence of the domain walls that occur between the SSFLC pixels.

Beam steering experiment with two cascaded ferroelectric liquid-crystal spatial light modulators

The design, construction, and evaluation of a laser beam steerer that uses two binary ferroelectric liquid-crystal (FLC) spatial light modulators (SLMs) operated in conjunction are presented. The system is characterized by having few components and is in principle lossless. Experimentally, a throughput of approximately 20% was achieved. The simple system design was achieved because of the high tilt angle FLC material used in the SLMs, which were specifically designed and manufactured for this study. By coherently imaging the first SLM onto the second SLM, pixel by pixel, we obtained an effective four-level phase structure with a phase step of 90 degrees. An appropriate alignment procedure is presented. The beam steering performance of the system is reported and analyzed.

Calculation of the efficiency of polarization-insensitive surface-stabilized ferroelectric liquid-crystal diffraction gratings

A rigorous analysis is presented of the diffraction efficiency of a polarization-insensitive surface-stabilized ferroelectric liquid-crystal (SSFLC) phase grating, taking full account of the internal structure of the ferroelectric liquid-crystal layer. When no field is applied, the twisted director profile in the relaxed state gives an optimum diffraction efficiency for a device thickness between the half-wave-plate and the full-wave-plate conditions. The influence of the magnitude of the spontaneous polarization and applied ac fields are investigated, and it is shown that the diffraction efficiency of a binary SSFLC phase grating can be strongly enhanced with the technique of ac stabilization.

Multiple-phase retrieval for optical security systems by use of random-phase encoding

The technique of the multiple phase encoding for optical security and verification systems is presented in this paper. This technique is based on a 4-f optical correlator that is a common architecture for optical image encryption and verification systems. However, two or more phase masks are iteratively retrieved by use of the proposed multiple phases retrieval algorithm (MPRA) to obtain the target image. The convergent speed of the iteration process in the MPRA is significantly increased and the recovered image is much more similar to the target image than those in previous approaches. In addition, the quantization effects due to the finite resolution of the phase levels in practical implementation are discussed. The relationships between the number of phase masks and the quantized phase levels are also investigated. According to the simulation results, two and three phase masks are enough to design an efficient security verification system with 64 and 32 phase levels, respectively.

Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators

We propose the optical implementation of diffractive optical elements onto electrically addressed liquid-crystal spatial light modulators. We compare the classic implementations onto amplitude-only or phase-only domains with the implementations onto coupled phase and amplitude (spiral) domains. We demonstrate that the coupling between amplitude and phase provides a trade-off between diffraction efficiency and the signal-to-noise ratio in the reconstruction. Furthermore, when investigating the influence of the maximum dephasing on phase domains and spiral domains through the use of optimal trade-off design, we show that phase-only domains with limited maximum dephasing can provide satisfactory performance. Finally, optical implementations are provided.

Four-level phase grating generated by combination of two binary gratings through coherent imaging

With the aim of steering as much incident light power in the +1 diffraction order as possible and suppressing the power in the -1 order, we generated an effective four-level grating by coherently imaging a 180 degrees binary-phase grating onto a 90 degrees phase grating. The periods of the gratings were well matched. The measured overall power fractions in the +1 and -1 orders were 54% and 2%, respectively.

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.

Reconfigurable two-dimensional diffractive phase element with the fractional talbot effect

We investigate the technical feasibility of the optical implementation of a four-phase-level diffractive element with two {0, pi}-phase spatial light modulators in a fractional Talbot configuration. The space-bandwidth product of the spatial light modulators is seen as the main theoretical limitation of the proposed approach. We investigate the robustness of technological and geometrical parameters on the diffraction efficiency of the whole system. Ferroelectric liquid-crystal silicon backplane spatial light modulators are chosen because of their high reconfiguration rates and good electro-optics interface. Similarly, we assess the influence of liquid-crystal technical parameters on system performance.

Complex amplitude modulation by use of liquid-crystal spatial light modulators

We propose to study the conditions for implementation of complex amplitude modulation on standard liquid-crystal spatial light modulators when illuminated by polarized light. The spatial light modulators are used in a conventional configuration, i.e., the voltage is applied parallel to the wave-front propagation direction. The most commonly used liquid-crystal materials are compared and their usefulness in some general applications discussed. Their specificities with respect to different modulation types and application requirements are briefly described. Typical characteristics such as response time, modulation range, and wavelength insensitivity are also discussed. Finally, as an illustration, a first attempt at nomenclature is proposed for the case of a linearly polarized light.