Behavior of total internal reflection in optical crystals

It is shown that a crystal can be cut so that one incident beam undergoing reflected from an inclined face inside the crystal excites four beams, two ordinary and two extraordinary, propagating in different directions. Pis’ma Zh. Tekh. Fiz. 25, 46–51 (January 12, 1999)     

Spatial-Frequency Response of Photorefractive Phase Conjugators with Ce:BaTiO(3)

We propose and demonstrate an interferometric method to measure thespatial-frequency response of photorefractive phase conjugators withCe:BaTiO(3). Two coherent beams are incident on a crystaland form an interference pattern inside the crystal. The two beamsundergo stimulated photorefractive backscattering, which creates theircorresponding phase conjugations. Then the four waves interactwithin the crystal. The spatial-frequency resolution of the phaseconjugators is measured to be as high as 3750 line pairs/mm by use ofthe interferometric method. There are several factors that limitthe measured spatial resolution when using a U.S. Air Force ResolutionChart. The output modulation deviates from the input modulation forhigh spatial frequencies. In the presence of a strong additionalpump beam, the output modulation of the phase conjugators is almost thesame as the input modulation for a wide range of input spatialfrequencies. The phase conjugator exhibits a large dynamic range ofintensity. We analyze theoretically the modulation transferfunction of photorefractive phase conjugators withCe:BaTiO(3) for two mutually coherent beams. Thetheoretical analysis is in agreement with the experimental resultswithin a small incident-angle region.     

Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index n(o) and n(e)2/n(o), where n(o) and n(e) are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre-Gauss and Bessel-Gauss beams propagating through an anisotropic crystal are given.     

New polarization effects accompanying pair production in crystals

It is shown that a crystal proves to be birefringent in a wide angular region due to asymmetry of high-energy electron (positron) scattering by crystal axes. This makes it possible to transform strongly divergent hard γ-quantum beams, produced by proton accelerators, to linearly and circularly polarized beams.     

Formation of all fourteen Bravais lattices of three-dimensional photonic crystal structures by a dual beam multiple-exposure holographic technique

We make use of a dual beam multiple-exposure (DBME) holographic technique for the formation of all 14 Bravais lattices of three-dimensional photonic crystal microstructures. For simplicity of experimental implementation, the DBME method has been modified such that, prior to each exposure, once the proper angle between the wave vectors of the interfering beams is chosen, a single axis rotation of the recording medium gives the desired results. The parameters required for the generation of the lattice structures have been derived by appropriate modification of interference of four noncoplanar beams (IFNB) analysis for corresponding implementation in the DBME technique, and the results have been verified by computer simulations. After giving a comparative study of the results with the IFNB method, recording geometries for the DBME approach are also proposed in order to realize all 14 Bravais lattices experimentally.     

Implementation of ordinary and extraordinary beams interference by application of diffractive optical elements

Abstract

We apply diffractive optical elements in problems of transformation of Bessel beams in a birefringent crystal. Using plane waves expansion we show a significant interference between the ordinary and extraordinary beams due to the energy transfer in the orthogonal transverse components in the nonparaxial mode. A comparative analysis of the merits and lack of diffractive and refractive axicons in problems of formation non-paraxial Bessel beams has shown the preferability of diffractive optics application in crystal optics. The transformation of uniformly polarised Bessel beams in the crystal of Iceland spar in the nonparaxial mode by application of a diffractive axicon is investigated numerically and experimentally.     

Engineering of the space-variant linear polarization of vortex-beams in biaxially induced crystals

We considered the propagation of Bessel beams through the biaxially induced birefringent crystal implemented by the mechanical torsion of the uniaxial crystal around its optical axis. Analyzing the solutions to the wave equation in the form of eigenmodes, we found that the system enables us to convert the beams with a uniform distribution of the linear polarization at the beam cross section into radially, azimuthally, and spirally polarized beams. Moreover, we revealed that the above system permits us to convert the beams with the space-variant linear polarization in accordance with the rule -s?s+1, where s is the topological index of the centered polarization singularity.     

The effect of optical activity on the coherent interaction of screening solitons in a cubic photorefractive crystal

The coherent interaction of solitonlike beams in a cubic photorefractive crystal of sillenite type has been studied by method of numerical modeling. The effect of optical activity on the attraction and repulsion of light beams is considered for various orientations of the external electric field.     

Rotational spin Hall effect in a uniaxial crystal

We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value of some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.     

Simple method of detecting ferroelectric domains with non-phase-matched second-harmonic generation

We demonstrate a new method of detecting the presence of ferroelectric domains based on non-phase-matched second-harmonic generation. If a domain boundary is tilted relative to the input and output faces of the crystal, the far-field second-harmonic light consists of multiple beams, in contrast to the single beam generated in a single-domain crystal. The angular separation of the beams provides a measure of the tilt of the domain wall if the refractive-index difference n(2omega) - n(omega) is known.     

Minimum theoretical requirements for three-dimensional scanning-laser Doppler anemometry

An investigation of the minimum number of intersecting beams that is required for laser Doppler anemometry (LDA) incorporating only a single detector is presented. We aim to provide decisive arguments for using four beams as the minimum requirement for complete three-dimensional velocity reconstruction even though three beams supply three velocity components. We derive expressions for the detected signals of the most general LDA system. From a matrix analysis of these expressions, we conclude that there is no physically realizable arrangement of three beams that results in complete three-dimensional velocity reconstruction and that four beams is the minimum number of beams required. We also determine the optimal arrangement of the four incident beams for unambiguous LDA and for best signal separation and immunity to minor optical alignment errors. To ascertain the velocity components, we scan the specimen in a precise manner relative to the point of focus of the beams, whereas some other researchers alter the frequency of the incident beams. The results obtained with these two methods are equivalent. However, scanning is mechanically simpler than frequency shifting and also allows for the formation of velocity images-images of the flow velocity over a region in two- or three-dimensional space. In particular, we examine systems that are limited by the common practice of using only a single high-numerical-aperture objective for both focusing and detection. We show that using high-numerical-aperture objectives results in the best signal differentiation and immunity to minor alignment errors.     

Monte-Carlo simulation of a neutron Brillouin scattering spectrometer

A Monte-Carlo simulation was done to optimise the setup of a new type of time-of-flight spectrometer, a thermal neutron Brillouin scattering (NBS) spectrometer. After collimation of the incident white neutron beam five incident energies between 20 and 138 meV can be obtained from four different monochromator crystal faces. The monochromatic beam is split into nine pencil-like separate beams to improve the Q-resolution of the NBS-spectrometer. Including the time resolution of the Fermi chopper (after a background chopper) an energy resolution for elastic scattering between 2% and 7% and a momentum transfer resolution of 1.3–2.0% are obtained.     

Holographic imaging and interferometry with non-Bragg diffraction orders on volume and surface-relief gratings in lithium niobate and photo-thermoplastic materials

The recording of holographic volume and surface-relief gratings in a photorefractive crystal using a photo-thermoplastic (PTP) holographic camera with an image-bearing signal beam leads to the appearance of two Bragg and two or more non-Bragg diffracted beams that show the transformed images in each beam (rotation and angular amplification of images). Using this real-time mode of interferometry, the hologram is retrieved with a deformed object beam, resulting in the appearance of fringes with a proper phase shift in each of four diffracted beams. This one-shot (one-exposure) phase-shifting interferometry results in clarification of the object wave-front information (for example, from surface deformation) and solution of the sign ambiguity problem. This procedure demonstrates that high-resolution holographic imaging of the PTP holographic camera static deformations in the order of ～0.1?mm can be revealed on the diffusion reflection surface. In addition, it was demonstrated that using the PTP materials could achieve holographic recording and imaging through phase aberration, with the image appearing in the non-Bragg diffraction order.     

Theoretical and experimental studies of hologram multiplexing that uses a random wave front generated by photorefractive beam fanning

A hologram multiplexing technique-that uses random wave fronts generated by photorefractive beam fanning is investigated. A storage photorefractive crystal generates various random wave fronts to be used as reference beams without the external diffusers such as ground glass and multimode optical fiber that are generally employed. We experimentally demonstrate hologram multiplexing with six images and show that the stored holograms can be selectively retrieved. We also simulate photorefractive beam fanning inside a BaTiO3 crystal, in particular regarding the correlation properties of the fanning beams for the first time to our knowledge, and reveal the conditions of incidence of an object beam and a reference beam required for suppressing image degradation, implementing low-cross-talk retrieval, and producing a large number of stored holograms.     

Self-stabilized recording of fixed gratings at high temperature in LiNbO3:Fe

A high quality fixed holographic grating was recorded in a photorefractive LiNbO(3):Fe crystal at about 100 degrees C in a homemade temperature-controlled vacuum chamber. The recording was carried out using self-stabilization techniques with lambda=532 nm beams guided onto the crystal by polarization maintaining fibers. The diffraction efficiency of the fixed grating was eta=0.44 when measured in the recording setup using the same lambda=532 nm recording beams. A compatible eta was measured with lambda=633 nm in an auxiliary setup, and a 1 mrad angular Bragg selectivity at FWMH was estimated, thus demonstrating the uniformity and good quality of the fixed grating.     

2-D motion estimation using two parallel receive beams

We describe a method for estimating 2-D target motion using ultrasound. The method is based on previous ensemble tracking techniques, which required at least four parallel receive beams and 2-D pattern matching. In contrast, the method described requires only two parallel receive beams and 1-D pattern matching. Two 1-D searches are performed, one in each lateral direction. The direction yielding the best match indicates the lateral direction of motion. Interpolation provides sub-pixel magnitude resolution. We compared the two beam method with the four beam method using a translating speckle target at three different parallel beam steering angles and transducer angles of 0, 45, and 90 degrees. The largest differences were found at 90 degrees, where the two beam method was generally more accurate and precise than the four beam method and also less prone to directional errors at small translations. We also examined the performance of both methods in a laminar flow phantom. Results indicated that the two beam method was more accurate in measuring the flow angle when the flow velocity was small. Computer simulations supported the experimental findings. The poorer performance of the four beam method was attributed to differences in correlation among the parallel beams. Specifically, center beams 2 and 3 correlated better with each other than with the outer beams. Because the four beam method used a comparison of a kernel region in beam pair 2-3 with two different beam pairs 1-2 and 3-4, the 2-to-1 and 3-to-4 components of this comparison increased the incidence of directional errors, especially at small translations. The two beam method used a comparison between only two beams and so was not subject to this source of error. Finally, the two beam method did not require amplitude normalization, as was necessary for the four beam method, when the two beams were chosen symmetric to the transmit axis. We conclude that two beam ensemble tracking can accurately estimate motion using only two parallel receive beams.     

Wide angular aperture holograms in photorefractive crystals by the use of orthogonally polarized write and read beams

We demonstrate a method of simultaneous holographic recording and readout in photorefractive crystals that provides high write-read beam isolation and wide angular bandwidth. The method uses orthogonally polarized read and write beams and parallel tangent diffraction geometry near the equal curvature condition to provide spatially separable, orthogonally polarized diffracted output beams with high isolation and wide Bragg-matched angular bandwidth. The available angular bandwidth of this read-write technique is analyzed, simulated, and experimentally investigated. The measured angular bandwidth internal to the crystal is approximately 18° × 6° for our 45°-cut BaTiO(3) crystal, yet the entire hologram still demonstrates high Bragg selectivity. In contrast, traditional nonparallel-tangent geometries yield angular apertures of the order of 1° × 4°.     

Fringe Formation in an In-Plane Displacement Measurement Configuration with Twofold Increase in Sensitivity: Theory and experiment

A fringe-formation theory for a dual-beam illumination configuration that leads to a twofold increase in sensitivity for the measurement of in-plane displacement is described. Here we have taken into account all four beams simultaneously that are generated at the image plane owing to two-beam illumination and their cross-interference terms for fringe formation. We show that the sensitivity obtainable is the usual interferometric sensitivity when we take into account all four beams simultaneously and doubles only when the retroreflected beams are observed. A detailed theory and an experimental demonstration of the method are presented.     

Plate beamsplitter to produce multiple equal-intensity beams

The design of a plate beamsplitter to produce multiple beams of equal intensity is presented. Multiple beams of equal intensity can be obtained from a plate by varying the reflectances of the front and back surfaces. The application for which we designed the plate beamsplitter was a fourbeam multiplexed galvanometric scanner for a confocal scanning microscope. Multiplexing with four beams increases the effective optical scanning rate (and therefore the confocal imaging rate) to four times the electromechanical scanning rate of the galvanometrically driven mirrors.     

Revealing 180° domains in ferroelectric crystals by photorefractive beam coupling

We describe a simple, optical technique for mapping 180° domains hidden inside photorefractive crystals. We intersect two coherent light beams in the crystal. Photorefractive coupling between the two beams causes one beam to emerge with a map of all the crystal's 180° domains imprinted upon it. We tested many BaTiO(3) crystals and found that they all contained 180° domains, with the relative volume of these domains varying from 25% to 0.1%.