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

We present a compact optical polarization-splitting common-path interferometer based on a zero-twist liquid crystal display (LCD). The LCD is encoded with a diffraction grating pattern and illuminated with a polarization state with both horizontal and vertical components. The polarization component perpendicular to the director axis of the liquid crystal molecules is not affected by the LCD and forms the reference beam. However, the polarization component parallel to the director axis is diffracted at an angle determined by the period of the grating. By imposing an analyzer polarizer, these two beams create an interferogram that can either display retardance patterns encoded onto the LCD or analyze external birefringent optical elements. The programmability of the system allows new ways of increasing the utility of the interferograms. Experimental results are provided, including the visualization of optical vortices with different and opposite topological charges.     

Polarization pattern of vector vortex beams generated by q-plates with different topological charges

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.     

Microellipsometer with radial symmetry

We report on a novel microellipsometer that uses a spatially filtered high-numerical-aperture (NA) lens for large-angle ellipsometric illumination and high spatial resolution. A radially symmetric ellipsometric signal is achieved with two half-wave plates to produce a pure polarization rotation and a birefringent cube as a radial analyzer. This radial symmetry offers a better signal-to-noise ratio compared with other microellipsometer techniques. Ellipsometric measurement with a spatial resolution of 0.5 microm is performed with a He-Ne (632.8-nm) laser source and an objective lens with an NA of 0.8. Experimental data on SiO2 samples with different thicknesses are in good agreement with spectroscopic ellipsometer results. We acquired ellipsometric images of photoresist microstructure through scanning the sample. Surface profiles of the photoresist microstructure are derived from the ellipsometric data and compared with the results from a stylus profiler.     

Aberrations introduced by a lens made from a birefringent material

We incorporate an algorithm for ray tracing in birefringent media into a full ray-tracing package based on the Mathematica software application. To validate the package, we compare the calculated and observed wave-front aberration introduced by an optical system that comprises lenses fabricated from birefringent material. Using the package, we calculate the influence of the lens shape factor on the aberrations associated with the e-ray polarization and show that it differs significantly from that of the o-ray polarization.     

Polarization-selective computer-generated holograms: design, fabrication, and applications

We constructed polarization-selective computer-generated holograms that apply an independent phase profile during readout by horizontal and vertical light polarizations. These elements are composed of two surface-relief-etched birefringent substrates joined face to face. We describe the design methodology for arbitrary birefringent substrate and gap materials. We show how these holograms are fabricated with standard microelectronics technology and discuss the effects of etching and alignment errors on performance. We demonstrated a diffraction efficiency of 60% with a polarization contrast ratio of >100:1 using a multilevel phase hologram made from two birefringent lithium niobate substrates. We also showed that a single-layer SiO(2) thin-film antireflection coating on all surfaces can reduce reflections from the high-index substrates without significant effect on hologram performance. We also consider some possible applications of this technology and demonstrate experimentally a dual focal-length lens and a self-interconnecting binary 2 × 2 polarization switch.     

Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices

We study the modulation of programmable birefringent devices when they are illuminated by elliptically polarized light. We apply the theory to liquid-crystal display panels (LCDs). We consider the setups at the input and the output sides of the LCD as polarization-state generators (PSGs) or detectors (PSDs). We demonstrate that once the programmable birefringent device is described by a physical model, the amplitude and phase modulation depend only on the polarization state at the input of the device and on the output state detected behind it. This permits optimization of the modulation response only in terms of the input and the output states and the physical model of the device. The procedure to find the PSG and PSD configurations is detailed by using a geometrical interpretation of the states and the plates on the Poincaré sphere.     

Analysis and Comparison of Birefringent Fibre Ring Resonator Types

Abstract

We present a theoretical model that can be used to determine the output of fibre ring resonators made with birefringent fibre, and with different types of polarization-selective or polarization-insensitive couplers. We derive tolerances for the coupler polarization crosstalk, splice alignment, and input polarization mode purity necessary for optimum operation of each type.     

Two-dimensional polarization rotator using a twisted-nematic liquid-crystal display

We present a novel configuration for a twisted-nematic liquid-crystal display (TN-LCD) that makes it operate as a controllable polarization rotator. We extend a previously reported polarization rotator configuration using a zero-twist LCD inserted between two quarter-wave plates. We first operate the TN-LCD in the polarization eigenvector configuration and show how this system can act as an equivalent voltage-controlled wave plate. Next we incorporate this wave plate into the optical rotator configuration. We show that the plane of polarization of the transmitted light can be rotated as a function of the phase introduced by the display. Finally, we create a 2D polarization mask where different areas of the TN-LCD form different polarization states. Experimental results are included.     

Phasor analysis of eigenvectors generated in liquid-crystal displays

We analyze optical systems for creating phase-only operation of a liquid-crystal display (LCD). We introduce a new formalism in which any input or output polarization state can be described in terms of a linear combination of the eigenvectors of the LCD. We use a phasor analysis to examine the linear combination of the eigenvectors and show how improved performance can be obtained with a new configuration. We experimentally compare the intensity and phase operation for two configurations with the same spatial light modulator and show the improved performance with the new configuration.     

Common-path optical heterodyne profilometer: a configuration

A novel configuration that combines a linearly polarized He-Ne laser and a birefringent lens to produce a common-path polarized optical heterodyne profilometer with respect to the heterodyned P and S waves has been set up. In this profilometer a linear polarized frequency-stabilized He-Ne laser was used with an acousto-optical modulator to replace the Zeeman laser as the light source that had two polarization eigenstates in different temporal frequencies. The proposed interferometer shows a more symmetric and ideal common-path structure than the conventional optical heterodyne profilometers with the Zeeman laser. The phase error aroused by the elliptical polarization and the nonorthogonality of the two eigenpolarization modes of the Zeeman laser can be reduced. The system's resolution in the vertical direction reaches 2 A, and in a 27-mum scanning range the repeatability of the surface profile measurements is shown to be 5 A.     

Polarization smoothing in a convergent beam

A birefringent wedge in a collimated 351-nm beam provides polarization smoothing at the Omega laser facility and provided it for the Nova laser. At the National Ignition Facility, the best place to put such an optic is after the final focus lens. In a converging beam, a flat birefringent plate can closely mimic the polarization-smoothing action of a wedge. In this new design the flat plate is nearly a Z-cut crystal; for the wedges, the optical axis of the crystal lies far from the plate normal.     

Polarization encoding and multiplexing of two-dimensional signals: application to image encryption

We discuss an optical system that encodes an input signal to a polarization state, using a spatial light modulator (SLM). Using two SLMs the optical system multiplexes two 2D signals in the polarization domain, and we demonstrate the multiplexing of two binary images. The encryption and decryption of two binary images using an XOR operation is also presented.     

High-resolution underwater acoustic imaging with lens-based systems

In recent years, several sonars designed for high-resolution, short-range underwater imaging have been developed. These imaging systems use an acoustic lens to focus the incoming waves on an array of transducers. In this article we describe three prototype systems that use a line-focus or a point-focus lens and operate at a frequency of 300 kHz or 3 MHz. The line-focus lens produces two-dimensional (2D) intensity images, while the point-focus lens produces 3D intensity images. We present sample images taken from moving and stationary platforms, and discuss the techniques used for processing the acoustic backscatter data to reconstruct and visualize the scene. The images, particularly those taken with a point-focus lens, show a remarkable degree of detail. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 377–385, 1997     

Time domain synthesis of electro-optical birefringent system for optical waveform generation

In this paper is described a novel technique for producing an electro-optical intensity synthesizer which can generate different periodic time domain waveforms through only sine or cosine wave applied-voltages. The synthesizer presented here consists of a series of stages between two polarizers, with each stage consisting of an electro-optic element and a compensator. Every electro-optical element has the same applied-voltage function but different azimuth angles and ratios between the longitudinal and transverse lengths. The main principle is the synthesis of an electro-optic effect and a polarization interference effect in the time domain. This technique is based on an expanded Fourier positive-direction searching algorithm, which can not only simplify the calculation process but also produces many choices of structural parameters for different waveforms generation. A three-stage synthesis of an electro-optical birefringent system for continuous square waveform is undertaken to prove the principle.     

Paraxial imaging and walk-off effects with birefringent media in refracting surfaces, lenses, and slabs

The paraxial theory of spherical refracting surfaces, spherical lenses, and slabs with one birefringent medium is investigated analytically: using walk-off effects in the paraxial domain, a number of relations between objects and images are deduced, along with cardinal elements, in the case where the optic axis is parallel to the optical axis. This method naturally shows that in some cases first-order astigmatism appears. An argument based on the wavefront (and phase) transformation shows that any spherical birefringent thin lens is stigmatic in the paraxial domain, because the first-order astigmatisms due to the two surfaces of such a lens compensate each other. This is a priori not the case with thick birefringent lenses -- but two such cases are detailed.     

Estimating three-dimensional vehicle motion in an outdoor scene using stereo image sequences

We propose a motion estimation system that uses stereo image pairs as the input data. To perform experimental work, we also obtain a sequence of outdoor stereo images taken by two metric cameras. The system consists of four main stages, which are (1) determination of point correspondences on the stereo images, (2) correction of distortions in image coordinates, (3) derivation of 3D point coordinates from 2D correspondences, and (4) estimation of motion parameters based on 3D point correspondences. For the first stage of the system, we use a four-way matching algorithm to obtain matched point on two stereo image pairs at two consecutive time instants (t_i and t_{i + 1}). Since the input data are stereo images taken by cameras, it has two types of distortions, which are (i) film distortion and (ii) lens distortion. These two distortions must be corrected before any process can be applied on the matched points. To accomplish this goal, we use (i) bilinear transform for film distortion correction and (ii) lens formulas for lens distortion correction. After correcting the distortions, the results are 2D coordinates of each matched point that can be used to derive 3D coordinates. However, due to data noise, the calculated 3D coordinates to not usually represent a consistent rigid structure that is suitable for motion estimation; therefore, we suggest a procedure to select good 3D point sets as the input for motion estimation. The procedure exploits two constraints, rigidity between different time instants and uniform point distribution across the object on the image. For the last stage, we use an algorithm to estimate the motion parameters. We also wish to know what is the effect of quantization error on the estimated results; therefore an error analysis based on quantization error is performed on the estimated motion parameters. In order to test our system, eight sets of stereo image pairs are extracted from an outdoor stereo image sequence and used as the input data. The experimental results indicate that the proposed system does provide reasonable estimated motion parameters.     

Polarization state fixer composed of passive optical devices

We investigate a polarization state fixer that produces light with an arbitrary desired polarization state and constant power from an arbitrary elliptically polarized input light whose principal polarization axis fluctuates randomly. An example of such a device composed of a quarter-wave plate and a polarizer is proposed, and its characteristics at wavelengths of 633 nm and 1550 nm are demonstrated. We conclude that we cannot obtain a passive device that produces fixed-axis, linearly polarized light with a constant power level from an elliptically polarized light with a varying elliptical parameter.     

Reconfigurable imaging systems using elliptical nanowires

Materials that have subwavelength structure can add degrees of freedom to optical system design that are not possible with bulk materials. We demonstrate two lenses that are composed out of lithographically patterned arrays of elliptical cross-section silicon nanowires, which can dynamically reconfigure their imaging properties in response to the polarization of the illumination. In each element, two different focusing functions are polarization encoded into a single lens. The first nanowire lens has a different focal length for each linear polarization state, thereby realizing the front end of a nonmechanical zoom imaging system. The second nanowire lens has a different optical axis for each linear polarization state, demonstrating stereoscopic image capture from a single physical aperture.     

Design of polarization-selective diffractive phase elements in a laser cavity

We report a new design for a polarization-selective laser cavity with birefringent diffractive phase elements. This laser cavity can create two modes with different polarizations and profiles launched separately from two end mirrors. The numerical simulation results show that the constructed laser cavity can successfully generate two orthogonal polarization modes with a uniform circular shaped pattern output from one end mirror and a uniform square-shaped pattern output from another end mirror.