David Engström

Optical manipulation of colloids and defect structures in anisotropic liquid crystal fluids

Optical trapping in anisotropic fluids such as liquid crystals shows inherently different behavior compared to that in isotropic media. Anisotropic optical and visco-elastic properties of these materials result in direction-sensitive and polarization-dependent interaction of the focused laser beam with colloidal inclusions, defects and structures of long-range molecular order, providing new means of non-contact optical control. Optical trapping properties are further enriched by laser-induced realignment of the optical axis that can be observed in these liquid crystalline materials at relatively low trapping laser powers. Optical manipulation of particles and defects in these anisotropic fluids is of immense importance for their fundamental study and from the standpoint of technological applications such as light-directed colloidal self-assembly and generation of tunable photonic architectures in liquid crystals. We review the basic physical mechanisms related to optical trapping in anisotropic liquid crystalline fluids and demonstrate how it can be employed in quantitative studies of colloidal interactions and both topological and mechanical properties of defects.

Diffraction-based determination of the phase modulation for general spatial light modulators

We describe a characterization method based on diffraction for obtaining the phase response of spatial light modulators (SLMs), which in general exhibit both amplitude and phase modulation. Compared with the conventional interferometer-based approach, the method is characterized by a simple setup that enables in situ measurements, allows for substantial mechanical vibration, and permits the use of a light source with a fairly low temporal coherence. The phase determination is possible even for a SLM with a full amplitude modulation depth, i.e., even if there are nulls in the amplitude transmission characteristic of the SLM. The method successfully determines phase modulation values in the full 2pi rad range with high accuracy. The experimental work includes comparisons with interferometer measurements as well as a SLM characterization with a light-emitting diode (LED).

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.

Calibration of spatial light modulators suffering from spatially varying phase response

We present a method for converting the desired phase values of a hologram to the correct pixel addressing values of a spatial light modulator (SLM), taking into account detailed spatial variations in the phase response of the SLM. In addition to thickness variations in the liquid crystal layer of the SLM, we also show that these variations in phase response can be caused by a non-uniform electric drive scheme in the SLM or by local heating caused by the incident laser beam. We demonstrate that the use of a global look-up table (LUT), even in combination with a spatially varying scale factor, generally does not yield sufficiently accurate conversion for applications requiring highly controllable output fields, such as holographic optical trapping (HOT). We therefore propose a method where the pixel addressing values are given by a three-dimensional polynomial, with two of the variables being the (x, y)-positions of the pixels, and the third their desired phase values. The coefficients of the polynomial are determined by measuring the phase response in 8 × 8 sub-sections of the SLM surface; the degree of the polynomial is optimized so that the polynomial expression nearly replicates the measurement in the measurement points, while still showing a good interpolation behavior in between. The polynomial evaluation increases the total computation time for hologram generation by only a few percent. Compared to conventional phase conversion methods, for an SLM with varying phase response, we found that the proposed method increases the control of the trap intensities in HOT, and efficiently prevents the appearance of strong unwanted 0th order diffraction that commonly occurs in SLM systems.

Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator

The limited number of pixels and their quantized phase modulation values limit the positioning accuracy when a phase-only one dimensional spatial light modulator (SLM) is used for beam steering. Applying the straightforward recipe for finding the optimal setting of the SLM pixels, based on individually optimizing the field contribution from each pixel to the field in the steering position, the inaccuracy can be a significant fraction of the diffraction limited spot size. This is especially true in the vicinity of certain steering angles where precise positioning is particularly difficult. However, by including in the optimization of the SLM setting an extra degree of freedom, we show that the steering accuracy can be drastically improved by a factor proportional to the number of pixels in the SLM. The extra degree of freedom is a global phase offset of all the SLM pixels which takes on a different value for each steering angle. Beam steering experiments were performed with the SLM being set both according to the conventional and the new recipe, and the results were in very good agreement with the theoretical predictions.

Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering

A novel retrocommunication link utilizing reflective multiple quantum well (MQW) optical modulators and nonmechanical beam steering and tracking is demonstrated. Large aperture reflective MQW modulators using AlGaAs/GaAs are optimized and manufactured. The modulators exhibit a contrast ratio larger than 4:1 and a modulation bandwidth of 10 MHz. Nonmechanical beam steering and tracking are studied using nematic liquid crystal (NLC) spatial light modulators (SLMs). The communication link is comprised of a retromodulating array with four MQW modulators and a transceiver using a NLC SLM for beam steering and tracking. Transfer of audio, real-time image data and pseudorandom bit sequences over 100-m range while tracking the moving retromodulator is shown. The link is capable of transferring data at approximately 8 Mbps.

Reducing the effect of pixel crosstalk in phase only spatial light modulators

A method for compensating for pixel crosstalk in liquid crystal based spatial light modulators is presented. By modifying a commonly used hologram generating algorithm to account for pixel crosstalk, the intensity errors in obtained diffraction spot intensities are significantly reduced. We also introduce a novel method for characterizing the pixel crosstalk in phase-only spatial light modulators, providing input for the hologram generating algorithm. The methods are experimentally evaluated and an improvement of the spot uniformity by more than 100% is demonstrated for an SLM with large pixel crosstalk.

Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change

We present a method for reducing intensity fluctuations that typically occur when a spatial light modulator is updated between consecutive computer generated holograms. The method is applicable to most iterative hologram generating algorithms and minimizes the average phase difference between consecutive holograms. Applications with high stability requirements, such as optical force measurement with holographic optical tweezers, should benefit from this improvement.

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.

Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm

Algorithms based on the fast Fourier transform (FFT) for the design of spot-generating computer generated holograms (CGHs) typically only make use of a few sample positions in the propagated field. We have developed a new design method that much better utilizes the information-carrying capacity of the sampled propagated field. In this way design tasks which are difficult to accomplish with conventional FFT-based design methods, such as spot positioning at non-sample positions and/or spot positioning in 3D, are solved as easily as any standard design task using a conventional method. The new design method is based on a projection optimization, similar to that in the commonly used Gerchberg-Saxton algorithm, and the vastly improved design freedom comes at virtually no extra computational cost compared to the conventional design. Several different design tasks were demonstrated experimentally with a liquid crystal spatial light modulator, showing highly accurate creation of the desired field distributions.