The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators

Unitary matrix approach for a precise voltage dependent characterization of reflective liquid crystal devices by average Stokes polarimetry

Precise characterization of parallel-aligned liquid crystal on silicon microdisplays has an important impact in many advanced photonics applications. We show liquid crystal on silicon (LCoS) modeled as a non-absorbent reciprocal device. Combined with time-average Stokes polarimetry, LCoS enables us to demonstrate robust measurements across the whole applied voltage range for the retardance and its flicker, and also as a novelty for the director orientation. We obtain that the director orientation changes across the voltage range, especially at larger applied voltages. This is a small effect, but it may provide a deeper insight into the internal dynamics in the liquid crystal layer, and in sensitive phase-only applications will produce a coupling between amplitude and phase.

Characterization of the spatially anamorphic phenomenon and temporal fluctuations in high-speed, ultra-high pixels-per-inch liquid crystal on silicon phase modulator

High-birefringence liquid crystal (LC) in ultrathin LCOS panels was adopted to prepare high phase precision (mSTD =λ/50) and phase accuracy (mAPAE% ∼8%) with suppressed pixel-level crosstalk effects. In conjunction with optimized digital driving scheme, the zero order light loss was found directly related to the phase accuracy error. Meanwhile, the world's fastest pure phase modulation LCOS with a response time of ∼0.87 ms at 45 °C was also achieved. The low-temporal flicker (P-P ∼2.0%) with high-speed LC responses was demonstrated by applying new digital driving scheme. Finally, the 4K2 K LCOS-SLM (∼7000 PPI) was evaluated its difficulties and opportunities.

Combining average molecular tilt and flicker for management of depolarized light in parallel-aligned liquid crystal devices for broadband and wide-angle illumination

We demonstrate a complete semiphysical and analytical model describing the angular and wavelength dependencies not only of retardance, but also its flicker, in parallel aligned liquid crystal (PA-LC) devices. It relies on the fitting of the molecules' equivalent tilt angle as a function of applied voltage. The wide range of calculations it offers without requiring extensive characterization makes the model unique. We focus on PA-LCoS application as a polarization state generator across the visible spectrum and for a wide range of incidence angles. This approach offers novel capabilities for managing arbitrary states of both full and partial polarization. To highlight the richness of situations with PA-LCoS devices, we provide results for two different digital addressing sequences producing different levels of flicker.

Pursuing High Quality Phase-Only Liquid Crystal on Silicon (LCoS) Devices

Fine pixel size and high-resolution liquid crystal on silicon (LCoS) backplanes have been developed by various companies and research groups since 1973. The development of LCoS is not only beneficial for full high definition displays but also to spatial light modulation. The high-quality and well-calibrated panels can project computer generated hologram (CGH) designs faithfully for phase-only holography, which can be widely utilized in 2D/3D holographic video projectors and components for optical telecommunications. As a result, we start by summarizing the current status of high-resolution panels, followed by addressing issues related to the driving frequency (i.e., liquid crystal response time and hardware interface). LCoS panel qualities were evaluated based on the following four characteristics: phase linearity control, phase precision, phase stability, and phase accuracy.

Experimental Minimum-Error Quantum-State Discrimination in High Dimensions

Quantum mechanics forbids perfect discrimination among nonorthogonal states through a single shot measurement. To optimize this task, many strategies were devised that later became fundamental tools for quantum information processing. Here, we address the pioneering minimum-error (ME) measurement and give the first experimental demonstration of its application for discriminating nonorthogonal states in high dimensions. Our scheme is designed to distinguish symmetric pure states encoded in the transverse spatial modes of an optical field; the optimal measurement is performed by a projection onto the Fourier transform basis of these modes. For dimensions ranging from D=2 to D=21 and nearly 14 000 states tested, the deviations of the experimental results from the theoretical values range from 0.3% to 3.6% (getting below 2% for the vast majority), thus showing the excellent performance of our scheme. This ME measurement is a building block for high-dimensional implementations of many quantum communication protocols, including probabilistic state discrimination, dense coding with nonmaximal entanglement, and cryptographic schemes.

Inline digital holographic movie based on a double-sideband filter

This Letter proposes a new optical architecture based on a double-sideband filter, simultaneously applied at the Fourier plane, for inline digital holography. The proposed architecture not only allows removal of the conjugate images in the reconstruction process but also reduces the distortions that usually appear when using a single-sideband filter. We first introduce the mathematical model that explains the method and then describe the optical setup used for the implementation. The optical system includes a parallel aligned liquid crystal display placed at the Fourier plane that simultaneously filters positive and negative frequencies, when properly combined with linear polarizers. This feature makes the device useful to register dynamic processes. Finally, we tested the setup by registering a holographic movie of microscopic moving objects placed at different planes.

Speckle fields generated with binary diffusers and synthetic pupils implemented on a spatial light modulator

Digitally controllable Gaussian speckle fields were experimentally generated by implementing binary diffusers and synthetic pupils on a liquid crystal spatial light modulator. The synthetic pupil comprises a Ronchi phase mask and a proper filtering of its diffraction orders. The binary diffuser is displayed inside an aperture defined onto the Ronchi phase mask. We demonstrated that this implementation replaces the need of using a ground glass and a physical pupil. In this way, the average speckle size, the statistical independence among the generated speckle patterns, and the average intensity distribution can be dynamically controlled.

Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices

Parallel-aligned (PA) liquid-crystal on silicon (LCoS) microdisplays are especially appealing in a wide range of spatial light modulation applications since they enable phase-only operation. Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of their linear retardance and the magnitude of their associated phase fluctuations or flicker, exhibited by many LCoS devices. In this work we apply the calibrated values obtained with this technique to show their capability to predict the performance of spatially varying phase multilevel elements displayed onto the PA-LCoS device. Specifically we address a series of multilevel phase blazed gratings. We analyze both their average diffraction efficiency ("static" analysis) and its associated time fluctuation ("dynamic" analysis). Two different electrical configuration files with different degrees of flicker are applied in order to evaluate the actual influence of flicker on the expected performance of the diffractive optical elements addressed. We obtain a good agreement between simulation and experiment, thus demonstrating the predictive capability of the calibration provided by the average Stokes polarimetric technique. Additionally, it is obtained that for electrical configurations with less than 30° amplitude for the flicker retardance, they may not influence the performance of the blazed gratings. In general, we demonstrate that the influence of flicker greatly diminishes when the number of quantization levels in the optical element increases.

Holographic three-dimensional display and hologram calculation based on liquid crystal on silicon device [invited]

Based on scalar diffraction theory and the geometric structure of liquid crystal on silicon (LCoS), we study the impulse responses and image depth of focus in a holographic three-dimensional (3D) display system. Theoretical expressions of the impulse response and the depth of focus of reconstructed 3D images are obtained, and experimental verifications of the imaging properties are performed. The results indicated that the images formed by holographic display based on the LCoS device were periodic image fields surrounding optical axes. The widths of the image fields were directly proportional to the wavelength and diffraction distance, and inversely proportional to the pixel size of the LCoS device. Based on the features of holographic 3D imaging and focal depth, we enhance currently popular hologram calculation methods of 3D objects to improve the computing speed of hologram calculation.

Phase-shift interference-based wavefront characterization for orbital angular momentum modes

Wavefront characterization for orbital angular momentum (OAM) modes is demonstrated using quadrature phase-shift interference. The phase fronts and intensity profiles of OAM(-2), OAM(-4), OAM(-6), and OAM(-8) are measured. Wavefront correlations between the experimental results and the pure Laguerre-Gaussian modes are calculated to evaluate the measurement. The measured results are in reasonable agreement with the anticipated results based on simulations.

Generation and scanning of Airy beams array by combining multiphase patterns

The method of superimposing multiple phase patterns to generate and deflect multi Airy beams is proposed in this paper. A Dammann grating and an optimized splitting grating are superimposed, respectively, with an Airy cubic phase pattern to generate an array of 4×4 equal-space Airy beams. By adding a deflection grating to the superimposed phase patterns, the transverse self-accelerated Airy beams array can be deflected arbitrarily in two-dimensional plane. The impacts of superimposed phase patterns on the transverse acceleration and size of main lobe of Airy beams in array are discussed in this paper. Meanwhile, the accuracy of the steering method and the impact of the phase modulation depth on the size of the Airy beams are introduced.

Polarimetric method for liquid crystal displays characterization in presence of phase fluctuations

A polarimetry based method able to characterize optical properties of linear Liquid Crystal Displays (LCDs), even in presence of time-fluctuations of the phase, is proposed in this work. In particular, mean linear retardance, Liquid Crystal (LC) fast axis orientation and phase fluctuation amplitude of LCDs can be obtained with the proposed alternative technique. This technique enables to achieve these important features of LCDs with a set-up significantly less complicated to build up and with faster measurements than previously proposed techniques, which are based on diffraction or interferometry experiments. The validity of the technique is tested by measuring two different LCDs: one monopixel PA-LC panel working in transmission and a reflective PA-LCoS display. The technique provides similar results than those obtained by using previously proposed methods, confirming the validity of our alternative technique.

Positional stability of holographic optical traps

The potential of digital holography for complex manipulation of micron-sized particles with optical tweezers has been clearly demonstrated. By contrast, its use in quantitative experiments has been rather limited, partly due to fluctuations introduced by the spatial light modulator (SLM) that displays the kinoforms. This is an important issue when high temporal or spatial stability is a concern. We have investigated the performance of both an analog-addressed and a digitally-addressed SLM, measuring the phase fluctuations of the modulated beam and evaluating the resulting positional stability of a holographic trap. We show that, despite imparting a more unstable modulation to the wavefront, our digitally-addressed SLM generates optical traps in the sample plane stable enough for most applications. We further show that traps produced by the analog-addressed SLM exhibit a superior pointing stability, better than 1 nm, which is comparable to that of non-holographic tweezers. These results suggest a means to implement precision force measurement experiments with holographic optical tweezers (HOTs).

Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.