Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

Generation of cylindrical vector modes via astigmatic mode conversion

In this work, we propose and demonstrate experimentally a compact technique for generating cylindrical vector beams based on a Michelson interferometer and a π-astigmatic mode converter. The latter is required to invert the topological charge of higher-order Laguerre-Gauss (LG) beams. Our proposed technique generalizes the use of astigmatic mode conversion, commonly associated only with scalar beams, to vector beams with a non-homogeneous polarization distribution. We anticipate that many applications based on Michelson interferometers will benefit from the unique properties of vector beams.

Volume holographic illuminator for Airy light-sheet microscopy

Airy light sheets combined with the deconvolution approach can provide multiple benefits, including large field of view (FOV), thin optical sectioning, and high axial resolution. The efficient design of an Airy light-sheet fluorescence microscope requires a compact illumination system. Here, we show that an Airy light sheet can be conveniently implemented in microscopy using a volume holographic grating (VHG). To verify the FOV and the axial resolution of the proposed VHG-based Airy light-sheet fluorescence microscope, ex-vivo fluorescently labeled Caenorhabditis elegans (C. elegans) embryos were imaged, and the Richardson-Lucy deconvolution method was used to improve the image contrast. Optimized parameters for deconvolution were compared with different methods. The experimental results show that the FOV and the axial resolution were 196 µm and 3 µm, respectively. The proposed method of using a compact VHG to replace the common spatial light modulator provides a direct solution to construct a compact light-sheet fluorescence microscope.

Universal Polarization Transformations: Spatial Programming of Polarization Scattering Matrices Using a Deep Learning-Designed Diffractive Polarization Transformer

Controlled synthesis of optical fields having nonuniform polarization distributions presents a challenging task. Here, a universal polarization transformer is demonstrated that can synthesize a large set of arbitrarily-selected, complex-valued polarization scattering matrices between the polarization states at different positions within its input and output field-of-views (FOVs). This framework comprises 2D arrays of linear polarizers positioned between isotropic diffractive layers, each containing tens of thousands of diffractive features with optimizable transmission coefficients. After its deep learning-based training, this diffractive polarization transformer can successfully implement Ni No = 10 000 different spatially-encoded polarization scattering matrices with negligible error, where Ni and No represent the number of pixels in the input and output FOVs, respectively. This universal polarization transformation framework is experimentally validated in the terahertz spectrum by fabricating wire-grid polarizers and integrating them with 3D-printed diffractive layers to form a physical polarization transformer. Through this set-up, an all-optical polarization permutation operation of spatially-varying polarization fields is demonstrated, and distinct spatially-encoded polarization scattering matrices are simultaneously implemented between the input and output FOVs of a compact diffractive processor. This framework opens up new avenues for developing novel devices for universal polarization control and may find applications in, e.g., remote sensing, medical imaging, security, material inspection, and machine vision.

Real-time Stokes polarimetry using a polarization camera

This Lab Note introduces the "Stokes Camera," a simple experimental arrangement for real-time measurement of spatial amplitude and polarization and thus spatially resolved Stokes parameters. It uses a polarization sensitive camera and a fixed quarter-wave plate, providing a one-shot, digital solution for polarization measurement that is only limited by the frame rate of the camera and the computation speed of the provided code. The note also provides background information on relevant polarization theory and vector vortex beams, which are used as a demonstration of the device.

Image encryption using binary polarization states of light beam

Optical image/data encryption techniques are mostly based on the manipulation of spatial distributions of light's amplitude, phase, and polarization. Information encoding with phase involves complex interferometric set-up and polarization encoding requires Stoke's parameter measurement. Hence, they create difficulties in optical implementation. Considering the practical limitations, in this study, we demonstrate a method of single-shot intensity recording-based color image encryption by encoding the information in binary polarization states. The proposed method does not require Stoke parameter calculation. As a proof-of-concept, we demonstrated the technique with coherent and partially coherent light sources. Use of partially coherent light overcomes the speckle problem and makes the system cost-effective, useful for practical applications.

Subwavelength Diffractive Optical Elements for Generation of Terahertz Coherent Beams with Pre-Given Polarization State

Coherent terahertz beams with radial polarization of the 1st, 2nd, and 3rd orders have been generated with the use of silicon subwavelength diffractive optical elements (DOEs). Silicon elements were fabricated by a technology similar to the technology used before for the fabrication of DOEs forming laser terahertz beams with pre-given mode content. The beam of the terahertz Novosibirsk Free Electron Laser was used as the illuminating beam. The experimental results are in good agreement with the results of the computer simulation.

Complex spatial light modulation capability of a dual layer in-plane switching liquid crystal panel

Complex spatial light modulator (SLM), which can simultaneously control the amplitude and phase of light waves, is a key technology for wide-range of wave-optic technologies including holographic three-dimensional displays. This paper presents a flat panel complex spatial light modulator that consists of dual in-plane switching liquid crystal panels with double-degrees of freedom of voltage inputs. The proposed architecture features single-pixel level complex light modulation enabling complex light modulation in entire free space, which is most contrast to conventional macro-pixel based complex modulation techniques. Its complex light modulation capability is verified with theoretical simulation and experimental characterization, and a three-dimensional holographic image reconstruction without conjugate noise. It is believed that the proposed flat panel complex SLM can be an essential device for a wide range of advanced wave optic technologies.

Spatial-light-modulator-based dual shearing direction shearography

We propose a dual shearing shearography system based on a spatial light modulator (SLM). Compared to spatial phase shift shearography, the advantages of this system include its simple structure, relatively high light efficiency, and good phase map quality. Digital shearography is a fast, practical, non-contact, whole-field, and anti-turbulent optical approach to non-destructive testing (NDT) and strain measurement. Because the shearing direction determines the strain direction being measured, tests using multiple shearing directions are sometimes required to obtain strain in different directions and detect all defects. Various setups, based on the spatial phase shift method, have been proposed to solve the issue. While some of these setups perform well, they may also introduce new problems, such as poor phase map quality and low light efficiency. We present a sequential dual shearing shearographic system with good phase map quality and high light efficiency. Due to the SLM's high-speed response, capable of reaching hundreds of hertz, SLM-based dual shearing direction shearography allows for fast temporal phase shifting and shearing direction switching while providing very good phase map quality. Unlike the spatial phase shift method, which has low light efficiency due to its need for a small aperture to enable a relatively large speckle size to cover multiple pixels, the proposed method is based on a fast temporal phase shift and does not have this limitation. In addition, SLM can provide a programmable and adjustable shearing method in any direction and distance, which is beneficial for strain measurements and NDT requiring strain measurements in different directions using a small and precise shearing distance. We describe in detail the theory derivation and non-destructive testing application results for the SLM-based dual shearing direction shearography system.

Direct-write orientation of charge-transfer liquid crystals enables polarization-based coding and encryption

Optical polarizers encompass a class of anisotropic materials that pass-through discrete orientations of light and are found in wide-ranging technologies, from windows and glasses to cameras, digital displays and photonic devices. The wire-grids, ordered surfaces, and aligned nanomaterials used to make polarized films cannot be easily reconfigured once aligned, limiting their use to stationary cross-polarizers in, for example, liquid crystal displays. Here we describe a supramolecular material set and patterning approach where the polarization angle in stand-alone films can be precisely defined at the single pixel level and reconfigured following initial alignment. This capability enables new routes for non-binary information storage, retrieval, and intrinsic encryption, and it suggests future technologies such as photonic chips that can be reconfigured using non-contact patterning.

Polarisation-insensitive generation of complex vector modes from a digital micromirror device

In recent time there has been an increasing amount of interest in developing novel techniques for the generation of complex vector light beams. Amongst these, digital holography stands out as one of the most flexible and versatile with almost unlimited freedom in the generation of scalar and complex vector light fields featuring arbitrary polarisation distributions and spatial profiles. In this manuscript we put forward a novel technique, which relies on the polarisation-insensitive attribute of Digital Micromirror Devices (DMDs). In a prior work where we outlined a new detection scheme based on Stokes projections we alluded to this technique. Here we outline the creation process in full, providing all the details for its experimental implementation. In addition, we fully characterise the performance of such technique, providing a quantitative analysis of the generated modes. To this end, we experimentally reconstruct the transverse polarisation distribution of arbitrary vector modes and compare the ellipticity and flatness of the polarisation ellipses with theoretical predictions. Further, we also generate vector modes with arbitrary degrees of non-separability and determine their degree of concurrence comparing this to theoretical predictions.

Ring-shaped liquid crystal structures through patterned planar photo-alignment

Patterned liquid crystal (LC) configurations find widespread applications in functional devices such as lenses, gratings, displays and soft-robots. In combination with external stimuli such as an applied electric field, photo-alignment at the surfaces offers an attractive way to stabilize different LC structures in the bulk of a device. Herein, a planar LC cell is developed using a photo-alignment layer at the bottom substrate and a rubbed nylon film at the top substrate. Patterned planar photo-alignment is achieved by modulating the linear polarization with a spatial light modulator (SLM) and projecting the pattern onto the bottom substrate. A ring pattern is written into the photo-alignment layer with a continuous rotation between an inner radius and an outer radius. In the other regions the alignment is parallel to the rubbing direction at the top substrate. Four different LC configurations are observed: structure A in which a ring-shaped region is formed with an out of plane (vertical) orientation perpendicular to the substrate, structure B which has a single disclination loop and a 180° twist at the inner region of the photo-patterned ring (r < r_in), structure C which has no discontinuities but a 360° twist in the inner region of the photo-patterned ring (r < r_in) and structure D with 2 disclination loops. The LC director configuration for all 4 structures is simulated through finite element (FE) Q-tensor simulations and the optical transmission for each structure is simulated using a generalized beam propagation method.

Gouy phase effects on propagation of pure and hybrid vector beams

The robustness of the polarization spatial distribution of vector beams upon propagation is crucial for a number of applications, including optical communications and materials processing. This study has been commonly centered on Gouy phase effects on focused vector beams. In this work, we present a theoretical and experimental analysis of the Gouy phase's effects on the propagation of pure and hybrid vector beams. Experimental results at various axial planes, before and past the focus, are obtained by using a simplified liquid-crystal spatial light modulator-based optical system that allows the easy generation of these beams. Furthermore, a new alternative optical set-up that is devoid of moving elements is demonstrated, which simplifies this study. We experimentally verify the differences between pure and hybrid vector beams upon propagation. While the first ones remain stable, hybrid vector beams show Gouy phase effects that demonstrate an optical activity where the local polarization states rotate by an angle that depends on the propagation distance. Experimental results agree with the theory.

Photonic Discrete-time Quantum Walks and Applications

We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.

Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry

Electronic speckle-pattern interferometry (ESPI) is a powerful tool for precise, full-field, and non-contact contouring of optically rough surfaces. Due to the interferometric principle, the sensitivity of ESPI is directly related to the involved wavelengths and is thereby a global parameter. Surfaces with a broad variation of phase gradients, as, for instance, a target with both smooth and comparatively steep areas, result in just partially resolvable fringe interferograms. In recent studies, spatial light modulators (SLMs) have been implemented to adapt the interferometric reference phase front to the measurement task and broaden or squeeze the fringe spacing locally in critical areas. This method is limited by diffraction effects, observable for all types of phase-only SLMs. We demonstrate a straight-forward model, describing the diffraction-based intensity distortions occurring in interferograms after wavefront adaptation. The aim is to characterize the intensity distortions by means of the proposed model and minimize their impact, especially with regard to phase-only spatial light modulation in ESPI. For validation, the modeled behavior of SLMs is compared to the experimental results, obtained for two different SLM designs. Finally, experiments are presented, which demonstrate a successful adaptation of the interferometric reference phase front in compliance with the boundary conditions determined by the model.

Achromatic linear retarder with tunable retardance

We present a universal design and proof-of-concept of a tunable linear retarder of uniform wavelength response in a broad spectral range. It consists of two half-wave retarders (HWR) between two quarter-wave retarders (QWRs), where the uniform retardance can be tuned continuously by simply rotating one of the HWRs. A proof-of-concept of this design is built by using commercially available Fresnel rhomb retarders that provide retardation with almost wavelength uniformity in the visible and near infrared from 450 to 1550 nm. The design is universal, since other achromatic QWRs and HWRs could also be employed. The system is experimentally demonstrated to control the state of polarization of a supercontinuum laser.

Implementation of nearly arbitrary spatially varying polarization transformations: an in-principle lossless approach using spatial light modulators

A fast and automated scheme for general polarization transformations holds great value in adaptive optics, quantum information, and virtually all applications involving light-matter and light-light interactions. We present an experiment that uses a liquid crystal on silicon spatial light modulator to perform polarization transformations on a light field. We experimentally demonstrate the point-by-point conversion of uniformly polarized light fields across the wavefront to realize arbitrary, spatially varying polarization states. Additionally, we demonstrate that a light field with an arbitrary spatially varying polarization can be transformed to a spatially invariant (i.e., uniform) polarization.

Vector polymorphic beam

A scalar polymorphic beam is designed with independent control of its intensity and phase along a strongly focused laser curve of arbitrary shape. This kind of beam has been found crucial in the creation of freestyle laser traps able to confine and drive the motion of micro/nano-particles along reconfigurable 3D trajectories in real time. Here, we present and experimentally prove the concept of vector polymorphic beam adding the benefit of independent design of the light polarization along arbitrary curves. In particular, we consider polarization shaped tangential and orthogonal to the curve that are of high interest in optical manipulation and laser micromachining. The vector polymorphic beam is described by a surprisingly simple closed-form expression and can be easily generated by using a computer generated hologram.

Q-plates with a nonlinear azimuthal distribution of the principal axis: application to encoding binary data

We encode q-plates where the angular orientation of the principal axis is varied spatially with a nonstandard distribution. In the usual q-plate design, the orientation of the optical axis depends linearly on the azimuthal angle. In this work, we examine cases where this azimuthal dependence is nonlinear. We consider two cases: first, where the principal axis distribution is like an inverse-tangent function of the azimuth; and second, where it displays linear and flat segments. This last case is proposed as a new method for encoding binary data into the azimuthal lobes of the vector beam. We encode these patterns using a spatial light modulator system that allows new and exotic q-plate designs without the difficulty of fabricating individual plates. Experimental results are presented.

Three-dimensional characterization of tightly focused fields for various polarization incident beams

Tightly focused vectorial optical beams have found extensive applications in variety of technical fields like single-molecule detection, optical tweezers, and super-resolution optical microscopy. Such applications require an accurate measurement and manipulation of focal optical fields. We have developed a compact instrument (with dimensions of 35 × 35 × 30 cm³) to rapidly measure the intensity distribution in three dimensions of the focused fields of vectorial beams and any other incident beams. This instrument employs a fluorescent nanoparticle as a probe to scan the focal region to obtain a high spatial resolution of intensity distribution. It integrates a liquid-crystal spatial light modulator to allow for tailoring the point spread function of the optical system, making it a useful tool for multi-purpose and flexible research. The robust applicability of the instrument is verified by measuring the 3D intensity distributions of focal fields of various polarization and wavefront modulated incident beams focused by a high NA (=1.25) objective lens. The minimal data acquisition time achievable in the experiment is about 8 s for a scanning region of 3.2 × 3.2 μm² (512 × 512 pixels). The measured results are in good agreement with those predicted by the vectorial diffraction theory.

Vector Beam Polarization State Spectrum Analyzer

We present a proof of concept for a vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG). As a result, a two-dimensional polarization diffraction grating is formed that generates six different q-plate channels with topological charges from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. Consequently, 36 different channels are generated in parallel. This special polarization diffractive element is experimentally demonstrated using a single phase-only spatial light modulator in a reflective optical architecture. Finally, we show that this system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment. We expect that these results would be useful for applications in optical communications.

Off-axis points encoding/decoding with orbital angular momentum spectrum

Encoding/decoding off-axis points with discrete orbital angular momentum (OAM) modes is investigated. On-axis Laguerre-Gaussian (LG) beams are expanded into off-axis OAM spectra, with which off-axis points are encoded. The influence of the mode and the displacement of the LG beam on the spread of the OAM spectrum is analysed. The results show that not only the conventional on-axis point, but also off-axis points, can be encoded and decoded with OAM of light. This is confirmed experimentally. The analytical result here provides a solid foundation to use OAM modes to encode two-dimensional high density information for multiplexing and to analyse the effect of mis-alignment in practical OAM applications.

Experimental Demonstration of a Highly Efficient Fan-out Polarization Grating

Highly efficient fan-out elements are crucial in coherent beam combining architectures especially in coupled laser resonators where the beam passes through the fan-out element twice per round trip. Although the theoretical efficiency is usually less than 86%, the Dammann gratings are ubiquitously utilized in a variety of types of coherent beam combining systems due to the facile design and fabrication. In the current paper, we experimentally demonstrate a highly efficient fan-out polarization grating. It is the first time to our knowledge that all the three space-variant parameters of a polarization grating are simultaneously optimized to achieve the function of multi-beam splitting. Besides the high fan-out efficiency, the ability to control the polarization states of individual split beams is another advantage of this polarization grating. The novel polarization grating is promising to find applications in laser beam combining systems.

Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator

We generate programmable vector beams with arbitrary q-plates encoded using a spatial light modulator system. Consequently, we can analyze new and exotic q-plate designs without the difficulty of fabricating individual plates. We show experimental results for positive and negative integer and new fractional vector beam values.

Analysis of a segmented q-plate tunable retarder for the generation of first-order vector beams

In this work we study a prototype q-plate segmented tunable liquid crystal retarder device. It shows a large modulation range (5π rad for a wavelength of 633 nm and near 2π for 1550 nm) and a large clear aperture of one inch diameter. We analyze the operation of the q-plate in terms of Jones matrices and provide different matrix decompositions useful for its analysis, including the polarization transformations, the effect of the tunable phase shift, and the effect of quantization levels (the device is segmented in 12 angular sectors). We also show a very simple and robust optical system capable of generating all polarization states on the first-order Poincaré sphere. An optical polarization rotator and a linear retarder are used in a geometry that allows the generation of all states in the zero-order Poincaré sphere simply by tuning two retardance parameters. We then use this system with the q-plate device to directly map an input arbitrary state of polarization to a corresponding first-order vectorial beam. This optical system would be more practical for high speed and programmable generation of vector beams than other systems reported so far. Experimental results are presented.

Laser beam splitting by polarization encoding

A scheme is proposed to design a polarization grating that splits an incident linearly polarized beam to an array of linearly polarized beams of identical intensity distribution and various azimuth angles of linear polarization. The grating is equivalent to a wave plate with space-variant azimuth angle and space-variant phase retardation. The linear polarization states of all split beams make the grating suitable for coherent beam combining architectures based on Dammann gratings.

Four-dimensional key design in amplitude, phase, polarization and distance for optical encryption based on polarization digital holography and QR code

We demonstrate that all parameters of optical lightwave can be simultaneously designed as keys in security system. This multi-dimensional property of key can significantly enlarge the key space and further enhance the security level of the system. The single-shot off-axis digital holography with orthogonal polarized reference waves is employed to perform polarization state recording on object wave. Two pieces of polarization holograms are calculated and fabricated to be arranged in reference arms to generate random amplitude and phase distribution respectively. When reconstruction, original information which is represented with QR code can be retrieved using Fresnel diffraction with decryption keys and read out noise-free. Numerical simulation results for this cryptosystem are presented. An analysis on the key sensitivity and fault tolerance properties are also provided.

Encoding high-order cylindrically polarized light beams

In this work we present a setup for the experimental production of cylindrically polarized beams, as well as other variations of polarized light beams. The optical system uses a single transmissive phase-only spatial light modulator, which is used to apply different spatial phase modulation to two output collinear R and L circularly polarized components. Different cylindrically polarized light beams can be obtained by applying different phase shifts to these two circularly polarized components. The system is very efficient since modulation is directly applied to the light beam (as opposed to other common methods operating in the first order of encoded diffraction gratings). Different variations to the cylindrically polarized light beams are also reported, obtained by adding linear or quadratic relative phase shifts between the two circular polarization components of the light beam. Experimental results are provided in all cases.

Simultaneous measurement of phase and local orientation of linearly polarized light: implementation and measurement results

Optical components manipulating both polarization and phase of wave fields find many applications in today's optical systems. With modern lithography methods it is possible to fabricate optical elements with nanostructured surfaces from different materials capable of generating spatially varying, locally linearly polarized-light distributions, tailored to the application in question. Since such elements in general also affect the phase of the light field, the characterization of the function of such elements consists in measuring the phase and the polarization of the generated light, preferably at the same time. Here, we will present first results of an interferometric approach for a simultaneous and spatially resolved measurement of both phase and polarization, as long as the local polarization at any point is linear (e.g., for radially or azimuthally polarized light).

Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain

We propose a multiple-image encryption scheme, based on polarized light encoding and the interference principle of phase-only masks (POMs), in the Fresnel-transform (FrT) domain. In this scheme, each secret image is converted into an intensity image by polarized light encoding, where a random key image and a pixilated polarizer with random angles are employed as keys. The intensity encrypted images produced by different secret images are convolved together and then inverse Fresnel-transformed. Phase and amplitude truncations are used to generate the asymmetric decryption keys. The phase-truncated inverse FrT spectrum is sent into an interference-based encryption (IBE) system to analytically obtain two POMs. To reduce the transmission and storage load on the keys, the chaotic mapping method is employed to generate random distributions of keys for encryption and decryption. One can recover all secret images successfully only if the corresponding decryption keys, the mechanism of FrTs, and correct chaotic conditions are known. The inherent silhouette problem can be thoroughly resolved by polarized light encoding in this proposal, without using any time-consuming iterative methods. The entire encryption and decryption process can be realized digitally, or in combination with optical means. Numerical simulation results are presented to verify the effectiveness and performance of the proposed scheme.

Generation and double-slit interference of higher-order vector beams

A method for generating vector beams with higher-order states of polarization based on a setup with a one phase-only liquid crystal spatial light modulator is proposed. The polarization properties and double-slit interference of the higher-order vector beams were investigated in detail. The cross section intensity distributions were flower-like for higher-order vector beams when passing through a linear polarizer. Misplacements appeared in the double-slit interference fringes, which divided each fringe into several discrete parts, i.e., 2P-1 for P≥2, and 3 for P=1, where P is the polarization order number. When associated with optical petal orientations analysis of the beam spots behind a linear polarizer, the double-slit interference can be used to detect and analyze higher-order vector beams.

Vectorial optical field generator for the creation of arbitrarily complex fields

Generation of vectorial optical fields with complex spatial distribution in the cross section is of great interest in areas where exotic optical fields are desired, including particle manipulation, optical nanofabrication, beam shaping and optical imaging. In this work, a vectorial optical field generator capable of creating arbitrarily complex beam cross section is designed, built and tested. Based on two reflective phase-only liquid crystal spatial light modulators, this generator is capable of controlling all the parameters of the spatial distributions of an optical field, including the phase, amplitude and polarization (ellipticity and orientation) on a pixel-by-pixel basis. Various optical fields containing phase, amplitude and/or polarization modulations are successfully generated and tested using Stokes parameter measurement to demonstrate the capability and versatility of this optical field generator.

Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain

In this paper, an image encryption scheme based on polarized light encoding and a phase-truncation approach in the Fresnel transform domain is proposed. The phase-truncated data obtained by an asymmetric cryptosystem is encrypted and decrypted by using the concept of the Stokes-Mueller formalism. Image encryption based on polarization of light using Stokes-Mueller formalism has the main advantage over Jones vector formalism that it manipulates only intensity information, which is measurable. Thus any intensity information can be encrypted and decrypted using this scheme. The proposed method offers several advantages: (1) a lens-free setup, (2) flexibility in the encryption key design, (3) use of asymmetric keys, and (4) immunity against special attack. We present numerical simulation results for gray-scale and color images in support of the proposed security scheme. The performance measurement parameters relative error and correlation coefficient have been calculated to check the effectiveness of the scheme.

Reconfigurable beams with arbitrary polarization and shape distributions at a given plane

Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.

Simulative method for the optical processor reconfiguration on a dynamically reconfigurable optical platform

With the reconfiguration technique, users can configure the optical processor of a new optical computing platform, the ternary optical computer (TOC), into 42 specific basic operation units, and reconfigure it when the computation is completed. A simulative method of software for this technique is proposed in this paper. Also, an elaborate experiment based on this software is discussed. This simulation of reconfiguration demonstrates that the theory of reconfiguring optical processor in TOC is valid and also lays the foundation for the hardware implementation of the reconfiguration technique.

Complete polarization control of light from a liquid crystal spatial light modulator

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

Generating inhomogeneously polarized higher-order laser beams by use of diffractive optical elements

We propose an improved version of the earlier developed optical arrangement for generating inhomogeneously polarized laser light modes with the aid of a diffractive optical element (DOE) with carrier frequency. By eliminating lenses from the optical arrangement, we achieve the miniaturization, reduced light losses, a smaller number of parameters being matched, and a simpler system adjustment procedure. Note that all the capabilities of the previous version, namely, the universality and simple readjustment to different polarization types, are fully retained. The numerical modeling of the polarization mode combiner has made it possible to analyze its performance and capabilities. In the experiments, the quality of the resulting beams is shown to be improved. For generating higher-order cylindrical beams, a lower-order mode at the output of the polarization mode combiner is additionally transformed with a DOE that operates in the zero diffraction order, introducing radial phase changes.

Polarization characteristics of the metallic structure with elliptically helical metamaterials

In the last few years, there has been growing interest in the research of the polarizing optics consisting of sub-wavelength metamaterials due to the advantages of broad wavelength ranges, high temperature durability, and compact structures. So far, the metallic structure with the sub-wavelength metamaterials has been proved to achieve the linearly and the circularly polarized light. Therefore, there should be one question raised easily: Is it possible for the metallic structure with sub-wavelength metamaterials to generate the elliptically polarized light? To answer this question, we proposed a metallic structure with elliptically helical nanowires, and analyzed the polarization states of the transmitted light using FDTD method. It is confirmed that this metallic structure does have a giant elliptical dichroism. Furthermore, we also compared the distinct optical performances of elliptical single-, double-, three-, and four-helixes, and made a qualitative explanation for them.

Jones matrix treatment for optical Fourier processors with structured polarization

We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response. We apply the method to show and analyze an experiment in which a regular scalar diffraction grating is converted into equivalent polarization diffraction gratings by means of an appropriate polarization filtering. The technique is further demonstrated to generate arbitrary structured polarizations. Excellent experimental results are presented.

Control method for the optical components of a dynamically reconfigurable optical platform

We propose a control method for the optical components of a dynamically reconfigurable optical platform, the ternary optical computer (TOC). The optical components are made of liquid-crystal cell arrays (LCCAs) and polarizers, so the control method is for generating the pilot signals of the LCCAs to meet user demands. In this work, we first briefly introduce the TOC theory, the modules in the TOC monitor system, and the addressing of these LCCAs. Then we focus on the method for generating the control information (CI) of optical components, i.e., the encoder and the operator in the TOC according to the operands and the information about the basic operating units needed by an operation. In addition, we define data structures, some of which store the information to generate the CI and others that mainly store the generated CI. Finally we provide an example to verify the proposed method and conduct an experiment to generate the LCCA CI. The results demonstrate the correctness and feasibility of the method.

Grating-based optical scheme for the universal generation of inhomogeneously polarized laser beams

We propose and analyze a new optical system to transform linearly polarized laser modes into axially symmetric (radial or azimuthal) modes that show more promise in various applications, as well as generating various inhomogeneously polarized configurations. The system is based on the coherent composition of modal beams with phase diffraction gratings that allow the intermode phase shift to be varied without the need for auxiliary components. What makes the system simple and universal is the use of diffractive optical elements to generate required mode patterns with specific space orientation along with the simultaneous generation of different beams with different transverse mode content, all of which can subsequently be combined.

Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating

Both radially polarized and azimuthally polarized beams can be decomposed into linear combinations of circularly polarized vortex beams having opposite vortex charges. We show experimental evidence for this decomposition using a specially designed vortex sensing diffraction grating that generates multiple vortex patterns having different senses of circularly polarization in the different diffracted orders. When this grating is illuminated with a radially or azimuthally polarized beam, the grating separates the components into different diffracted orders. Experimental results are shown.

Polarization-selective diffractive optical elements with a twisted-nematic liquid-crystal display

We propose a method for realizing a polarization-selective diffractive optical element by using of a single twisted-nematic liquid-crystal display (TN-LCD). We have demonstrated that two orthogonal polarization-encoding channels can be formed using a single TN-LCD operated in some special conditions. Based on the two orthogonal encoding channels, two orthogonal polarized components of a field with any complex amplitude can be holographically encoded and reconstructed and, hence, different output images with different polarization states could be obtained, or a vector beam with spatially inhomogeneous polarization distributions, as well as the desired complex amplitude distributions, could be combined.

Azimuthally and radially polarized light with a nematic SLM

We demonstrate a technique for generating azimuthally and radially polarized beams using a nematic liquid crystal spatial light modulator and a pi phase step. The technique is similar in concept to prior techniques that interfere TEM(01) and TEM(10) laser modes, but the presented technique removes the requirement of interferometric stability. We calculate an overlap integral of >0.96 with >70% efficiency from an input Gaussian mode. The technique can easily switch between beams with azimuthal and radial polarization.

Full phase and amplitude control in computer-generated holography

We report what we believe to be the first realization of a computer-generated complex-valued hologram recorded in a single film of photoactive polymer. Complex-valued holograms give rise to a diffracted optical field with control over its amplitude and phase. The holograms are generated by a one-step direct laser writing process in which a spatial light modulator (SLM) is imaged onto a polymer film. Temporal modulation of the SLM during exposure controls both the strength of the induced birefringence and the orientation of the fast axis. We demonstrate that complex holograms can be used to impart arbitrary amplitude and phase profiles onto a beam and thereby open new possibilities in the control of optical beams.

Liquid-crystal polarization rotator and a tunable polarizer

A liquid-crystal (LC) voltage-controlled linear polarizer is demonstrated using two LC retarders stacked with two quarter-wave plates and an intermediate linear absorptive polarizer. The device was examined experimentally using unpolarized light and was found to be in accordance with the theoretical prediction. Under certain conditions the device acts as a polarization rotator with possibility for simultaneous amplitude modulation. Hence it has a potential application in high-dynamic-range polarimetric imaging.

Circular-polarization-splitting common-path interferometer based on a zero-twist liquid-crystal display

We present a compact optical circular-polarization-splitting common-path interferometer based on a zero-twist liquid-crystal display (LCD). A blazed diffraction grating is encoded onto the LCD. The optical system produces a reference beam that has one sense of circularly polarized light, while the diffracted beam has the opposite sense of circularly polarized light. Using a linear polarizer, these two beams form an interferogram that can be used to analyze optically active media. Experimental results are provided showing the detection of left-handed-rotary and right-handed-rotary media.

Axially symmetric liquid crystal devices based on double-side photo-alignment

This investigation demonstrates the feasibility of the radial and azimuthal axially symmetric LC structure using double-side photoalignment in a dye-doped liquid crystal (DDLC) cell. A linear and linearly polarized beam is applied to a rotated DDLC cell to produce an axially symmetric LC alignment. Notably, double-sided photoalignment is performed at a temperature that is maintained just above the clear point. Conformation of the axially symmetric LC devices can be controlled by varying the polarization direction of the pumping light, and the simulation results correlate well with OR closely correspond to the experimental results.

Formation of anisotropic diffraction gratings in a polymer-dispersed liquid crystal by polarization modulation using a spatial light modulator

Anisotropic diffraction gratings based on a holographic polymer-dispersed liquid crystal (HPDLC) are realized by interferometric exposure using a spatial light modulator (SLM). The SLM is used in the HPDLC grating formation for anisotropic holographic recordings of two-dimensional polarization states for an incident light beam. The diffraction efficiency for P-polarization and the distinctive ratio of diffraction efficiency in P-polarization to that in S-polarization increases with the signal level applied to the SLM. The resulting volume gratings exhibit diffraction efficiency of more than 60% and a distinctive ratio of diffraction over 100. The microscopic origin of the anisotropic property is investigated by an optical polarizing microscope. The novel characteristics of the anisotropic diffraction properties of HPDLC are applied to an image reconstruction technique.