This paper describes the fundamentals of phase-only liquid crystal on silicon (LCOS) technology, which have not been previously discussed in detail. This technology is widely utilized in high efficiency applications for real-time holography and diffractive optics. The paper begins with a brief introduction on the developmental trajectory of phase-only LCOS technology, followed by the correct selection of liquid crystal (LC) materials and corresponding electro-optic effects in such devices. Attention is focused on the essential requirements of the physical aspects of the LC layer as well as the indispensable parameters for the response time of the device. Furthermore, the basic functionalities embedded in the complementary metal oxide semiconductor (CMOS) silicon backplane for phase-only LCOS devices are illustrated, including two typical addressing schemes. Finally, the application of phase-only LCOS devices in real-time holography will be introduced in association with the use of cutting-edge computer-generated holograms. The capabilities and applications of phase-only liquid crystal on silicon (LCOS) technology are reviewed by scientists in China and the United Kingdom. Zichen Zhang and co-workers from Tsinghua University in Beijing and the University of Cambridge describe how an electronically controlled liquid-crystal pixel array on a silicon backplane can be useful for manipulating the phase of coherent light. Such LCOS phase modulators have many potential applications, including real-time holography, head-up displays, wavelength-selective switches and reconfigurable optical add-drop multiplexers. Commercial devices currently offer array sizes of up to about 1-inch diagonal with pixel pitches in the range 6–20 μm. However, the technology is still immature; the liquid-crystal materials and silicon control backplane need to be optimized in order to realize the potential of such devices.

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Fundamentals of phase-only liquid crystal on silicon (LCOS) devices

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.

https://iopscience.iop.org/article/10.1088/0034-4885/76/2/026401/pdf

Optical trapping and binding

The production of strings (disclination lines and loops) has been observed by means of the Kibble mechanism of domain (bubble) formation in the isotropic-nematic phase transition of the uniaxial nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl. The number of strings formed per bubble is about 0.6. This value is in reasonable agreement with a numerical simulation of the experiment in which the Kibble mechanism is used for the order parameter space of a uniaxial nematic liquid crystal.

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

Colloidal particles dispersed in liquid crystals induce nematic fields and topological defects that are dictated by the topology of the colloidal particles. However, little is known about such interplay of topologies. It is now shown that knot-shaped microparticles in liquid crystals induce defect lines that get entangled with the colloidal knots, and that such mutually tangled configurations satisfy topological constraints and follow predictions from knot theory.

Mutually tangled colloidal knots and induced defect loops in nematic fields

Viewing angle characteristics of displays and performance of electro-optic devices are often compromised by the quality of dichroic thin-film polarizers, while dichroic optical filters usually lack tunability and cannot work beyond the visible part of optical spectrum. We demonstrate that molecular-colloidal organic–inorganic composites formed by liquid crystals and relatively dilute dispersions of orientationally ordered anisotropic gold nanoparticles, such as rods and platelets, can be used in engineering of switchable plasmonic polarizers and color filters. The use of metal nanoparticles instead of dichroic dyes allows for obtaining desired polarizing or scattering and absorption properties not only within the visible but also in the infrared parts of an optical spectrum. We explore spontaneous surface-anchoring-mediated alignment of surface-functionalized anisotropic gold nanoparticles and its control by low-voltage electric fields, elastic colloidal interactions and self-assembly, as well as the uses...

Metal nanoparticle dispersion, alignment, and assembly in nematic liquid crystals for applications in switchable plasmonic color filters and E-polarizers.

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.

https://publications.lib.chalmers.se/records/fulltext/179784/local_179784.pdf

Calibration of spatial light modulators suffering from spatially varying phase response

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.

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

We use nanowires with faceted sidewalls for mapping of the patterns of three-dimensional orientational order and defect structures. In chiral nematics, the nanowires follow the local average orientation of rod-shaped molecules. When spatially translated by use of holographic optical tweezers in three dimensions, they mediate direct nondestructive visualization of the helicoidal ground-state structures, edge and screw dislocations, and kinks, as well as enable non-contact manipulation of these defects. We probe interactions of faceted nanowires with different defects and demonstrate their spontaneous self-alignment along the cores of singular defect lines.

/pdf/three-dimensional-imaging-of-liquid-crystal-structures-and-21892i8zpd.pdf

Three-dimensional imaging of liquid crystal structures and defects by means of holographic manipulation of colloidal nanowires with faceted sidewalls

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.

https://www.meadowlark.com/store/applicationNotes/pub/opticaltrapping/MinimizingIntensityFluctuationsHOT.pdf

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

We have implemented several algorithms for hologram generation, aimed for holographic optical tweezers
applications, using the parallel computing architecture CUDA. We compare required computation time for different
implementations of the Gerchberg-Saxton algorithm and provide guidelines for choosing the best suited version with
respect to the application. We also show that additional calculations, compensating for limitations in the used spatial
light modulator and optical system, can be included in the hologram generating software with little or no loss in computational speed.

Martin Persson

Papers

Calibration of spatial light modulators suffering from spatially varying phase response

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

Three-dimensional imaging of liquid crystal structures and defects by means of holographic manipulation of colloidal nanowires with faceted sidewalls

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

Real-time generation of fully optimized holograms for optical trapping applications