Search

Four wave mixing in photorefractive media is modelled using a whole beam method for wave propagation and a relaxation technique for temporal grating formation.

Our previous work have experimentally demonstrated that photo-refractive two-beam coupling can be used as an effective device for artifact and defect noise reduction through constant thresholding.

Previously1 we used a weak probe Mollow sideband calculation in a three-level system to calculate thresholdless Raman gain without inversion for comparison with experimental observations. However the complexity of the result makes it difficult to extend this analysis to compute nonlinear wavemixing or phase conjugate reflectivities in the three-level Λ-system. We now show that under conditions of experimental interest, it is possible to model the three-level system by a four-level four laser field closed loop system2 which results in a simple closed form expression for the gain. The advantage to this simple gain expression is that it permits straightforward computation of wavemixing and phase conjugate reflectivity. Detailed analysis of the four level system approach will be presented to clearly identify the regions where it is valid to model a three-level system by a four-level system. In particular, in the limit of low intensity or large detunings, the four level calculation is in good quantitative agreement with three level Mollow sideband gain calculations which in turn agreed qualitatively with experimental results.3-4 We will also show preliminary results of wavemixing calculations for sodium vapor using the simple gain expression produced by this model.

We implement a random-walk scattering model in a nonlinear beam-propagation code to simulate fanning in photorefractive crystals. The characteristics of the scatterers were verified by comparisons of the measured firstorder statistics of the scattered intensity with a theoretical expression of the probability-density function based on a random-walk scattering model. Both the size and the separation of the scatterers can be varied, enabling us to tailor our numerical simulations to experimental measurements of nonamplified and amplified scattering. We show that a one-dimensional model does not accurately simulate amplified scattering for crystals with a nondiagonal electro-optic tensor and that surface scattering alone may not account for the angular dependence of the amplified scattering distributions.

Real time correlation has become of interest in the areas of pattern recognition and optical signaling processing.

Recently, there has been much interest in the Raman gain observed in a Λ system with closely spaced ground states such that both ground states are initially equally populated and are both coupled to the excited state by a single frequency pump. This system is of interest for applications such as frequency shifting and self phase conjugation and as an example of a system that exhibits large optical gain for very small excited state populations. We have studied the mechanism of this gain theoretically and have found qualitative agreement with previously observed experimental results. Briefly, a single frequency pump interacts with both legs of the system. The gain spectrum is interpreted in terms of the energy intervals of the dressed states of the pumped system. The gain mechanism is analogous to the process of sideband amplification in a strongly driven two level system. However, the width of the gain is not limited by the linewidth of the excited state and, for low pump power, is determined by the transit time only. This is consistent with the extremely narrow gains (less than 1 kHz) observed in sodium vapor.

The joint transform correlator (JTC) is well known to be one of the most convenient devices for correlating two images in the sense that there is no need to fabricate a holographic filter. It has been shown previously that by applying additional non-linearities in the joint spectrum plane, such as binarization or saturation, to the joint spectra it is possible to achieve correlation with phase-only information (i.e., correlation with an inverse filter). This process increases the discrimination ability of the correlator. Previously, the nonlinearities for conventional and enhanced JTC required a camera, a computer, and a spatial light modulator for their implementation. We propose an arrangement of degenerate four wave mixing using two barium titanate crystals. This enables us to replace the previously used electronic processing while simultaneously achieving the two non-linearities, binarization and saturation, for a phase-only JTC.

Linear photorefractive mixing is limited to constant intensity. However, the operation theory becomes nonlinear when one of the inputs is amplitude modulated. As in electronics, it is often essential to have amplitude modulation. In this paper, we introduce the solution for the nonlinear photo-refractive mixing theory for weakly absorbing materials with constant intensity response-time product in the low coupling limit. The correction terms to the linear solution appear as a low frequency term (possibly including a dc component) and a high frequency multiplicative absorptive ripple that modulates the sum of the linear and low frequency terms. For many photorefractive mixing devices, any amplitude modulations used produce corrections that are extremely small, typically less than 1%, and these vary inversely proportional to the amplitude modulation frequency.

Previous work has presented an optical approach to frequency- division multiplexing that allows entire images to be demultiplexed in a single operation. In this paper, we introduce the photorefractive theory for baseband transmission and demultiplexing of video images. In addition, we introduce the photorefractive linear theory for calculating the number of images that can be demultiplexed. Our calculation shows that given our assumptions, it is theoretically possible to demultiplex a large number of images for materials with small electro-optic coefficients. When a photorefractive medium that has a large electro-optic coefficient is used, then there is significant noise that arises because of non-linear interactions within the crystal. Increasing the number of stored images reduces the recall efficiency but does not change this noise.

We show that adaptive optical autocorrelation can be used to measure the typical grain size of a rough surface. According to second-order statistics,1 the autocorrelation of the optical image of a surface provides a measurement of its grain size. This grain size may be found from the ratio of the peak (de) intensity to the broad background intensity in the autocorrelation. A photorefractive autocorrelator may be made by modifying a four-wave mixing correlator.2 A beam bearing an image of the rough surface is presented as one input to a correlator using bismuth germanate (BGO) in the Fourier plane. After passage through the BGO, this beam is phase conjugated by a barium titanate crystal. The resulting complex conjugate of the image beam is presented automatically self-aligned as the second input. The third input is a plane wave in the Fourier plane. The output of the device is the autocorrelation of the constant amplitude, phase modulated surface image. This autocorrelation consists of a sharp (de component) surrounded by a broad low-intensity background of the cross correlation of the rough surface.3 The ratio of the de component to the cross correlation component is used to determine the surface roughness properties. Care was taken to capture all of the diffracted light from the surface to avoid finite aperture effects.4 The autocorrelator measurements agree with microscopic surface measurements.

While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.

Many optical image processing operations such as edge enhancement may be performed by suitable linear spatial filters. A broader class of operations is made available by extending this technique to nonlinear filters. An example of this is the use of a logarithmic nonlinearity for conversion of multiplicative to additive noise [1]. In this work, we demonstrate that phase preserving thresholding in the Fourier plane which linearly transmits signals above a certain intensity, reduces additive signal dependent noise, such as noise from coherent artifacts, image defects and uniformity noise.

Experimental results are presented for an optical phase rectifier using nonlinear optical processing. We show that this device can be used to convert complex amplitude multiplicative optical noise on a positive scalar image to additive optical noise. Our implementation of phase rectification uses diffusive photorefractive two-beam coupling in a thin crystal of barium titanate. A weak plane wave reference beam is amplified point by point to saturation using the noisy image as a strong pump. At saturation all the power at a given point in the noisy pump is transferred to the corresponding overlap point in the weak plane wave. The amplitude of the reference becomes that of the pump but, because the beam coupling occurs in the diffusion regime, the phase of the reference remains uniform after amplification. The converted image can be subjected to additional noise reduction using methods for dealing with additive (signal dependent) noise,1 or multiplicative positive scalar noise.2 Such treatment is possible because the Fourier transform of the converted image shows the diffraction pattern of the signal embedded in a broad and weak speckle pattern. Alternative implementations of real-time optical rectification using optically addressed spatial light modulators require that the output amplitude of the spatial light modulator be specifically adjusted to be the square root of the input intensity. Cascading an initial optical phase rectifier with a Fourier-plane phase-preserving thresholding device1 dramatically reduces multiplicative noise with good optical efficiency and provides a coherent signal output.

A new technique for dealing with multiplicative complex speckle noise on coherently imaged amplitude objects is presented. This technique uses phase cancellation via quadratic nonlinearity to convert the multiplicative noise into additive noise on the Fourier spectrum. This is accomplished using a noisy image as the pump and a clean planar reference beam as the probe in a degenerate four-wave mixing phase conjugator. The counterpropagating pump is provided by the phase conjugate of the noisy image from a total internal reflection self-pumped phase conjugator whose input is the noisy image transmitted through the first crystal. The phase conjugate output is read off from the clean probe; the remaining noise on the Fourier spectrum of the output image is additive and can be removed by nonlinear filtering in the Fourier plane [1].

Photorefractive two-beam coupling with partially coherent light is investigated both theoretically and experimentally. By applying partial-coherence theory, a spatially varying distribution function for the grating visibility is found analytically. For certain beam configurations, this function may be approximated as one-dimensional and the coupled wave equations may be established and solved numerically. When compared to the case of perfect coherence, partial coherence has two major effects on the beam coupling. One is that the effective grating length may be smaller than the crystal length as a result of the spatial-coherence limit. The second is that the visibility distribution over the grating is smaller than the constant visibility of the coherent case.

We describe here a self-aligning interferometric device for the measurement of the thickness, refractive index and absorption coefficient of optical thin films.

The large electro-optical coefficient of barium titanate yields strong two-beam coupling. Here we describe a nonlinear photorefractive technique to reduce noise in a signal that is embedded in additive speckle noise. This approach implements an adaptive Wiener filter, which improves the contrast ratio by a factor of eight for a binary input signal with peaks equal to the noise peak. This technique relies on thresholding the Fourier transform of the noisy signal. The Fourier transform of the signal is a diffraction pattern of high intensity relative to the noise, and two-beam coupling is used to reduce the weaker-intensity noise Fourier transform. Our experimental results shows that it is possible to enhance features that are smaller than the grain size of the noise. The mechanism of enhancement depends on the initial signal-to-noise ratio and the specific geometry of the signal. We have also used the same technique for reducing multiplicative artifact noise and defects in images.

There has been growing interest in the temporal properties of wave mixing processes in photorefractive crystals. Several years ago, temporal instabilities such as frequency detuning [1] and pulsations [2] were observed in self-pumped phase conjugation. Also, there has been considerable interest in the possibility of bistability associated with the multiple solutions of the four-wave mixing coupled wave equations [3]. Especially important was the result of Gauthier et al. [4] where it was shown that instabilities occur for strong nonlinear coupling. As a result, demands for large coupling constants for large energy transfer and high phase conjugate reflectivity may lead to very unstable output. The mechanism responsible for these instabilities was competition among various coupling mechanisms with different time constants [4]. Very recently, a ring oscillator with photorefractive gain and loss was demonstrated experimentally and theoretically for application to associative memories. This system was shown experimentally to exhibit bistability when an external signal beam was injected [5].

Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.

Previous photorefractive holographic filters are limited by the response time of the material. The time correlation filter recognizes a sequence of individual temporal features which are limited only by the speed of the phase modulators in the reference and input signals. This filter operates using photorefractive time-integrated degenerate four- wave mixing with a reference beam and signal beam incident on one side of the bismuth silicon oxide crystal and an incoherent counter-propagating beam to read out the time correlation hologram. When no modulation is applied to the signal, the phase variations in the reference beam erase the hologram. Experimentally measured signals include square wave phase and amplitude modulation for the detection of similar signals, constant longitudinal velocity signals, and periodic transverse signals. The time correlation filter performs a special form of correlation of temporal signals which is not linearly proportional to the modulation. For example, the velocity detection output is strongest at the reference encoded velocity but also gives smaller peak responses at odd integral multiples of the velocity. The device operation agrees with theory developed from time varying photorefractive theory for general signals.

Studies on contrast sensitivity function (CSF) in Alzheimer’s disease (AD) have produced conflicting results, with some investigators suggesting that CSF is impaired generally1 and others reporting that CSF is normal in AD.2 An explanation for the discrepancy in results may involve the range of dementia severity represented by the subject groups in the two studies: Many moderately to severely demented subjects with AD are unable to perform particular CSF tests due to memory, attentional, or other deficits unrelated to visual skills. We have administered to a group of ten patients with AD, of a wide range of dementia severity, a CSF test with low task demands. Sinusoidal gratings of six spatial frequencies (1.5, 3, 6, 12, and 18 cycles/deg) and eight levels of contrast were displayed on photographic plates; subjects indicated the orientation of the gratings (vertical, left oblique, or right oblique). Patients who had been unable to perform tests of CSF involving monitor display of static vertical gratings performed ably with the photographic plates. The results indicate that CSF is depressed at each frequency tested for patients with AD relative to healthy age-matched subjects. This deficit appears to be unrelated to the severity of dementia.

Rectangular prisms of photorefractive crystals such as barium titanate and strontium barium niobate have been used in the past as high-reflectivity high-fidelity self-pumped phase conjugators. The effect is more easily seen in barium titanate than strontium niobate. Although the mechanism of the phase conjugation has been the subject of considerable debate, it has been generally accepted that total internal reflection usually plays an important role. We have fabricated a ring self-pumped phase conjugator using total internal reflection in a triangular prism of strontium barium niobate. The crystal is cut so that reflection gratings cannot play an appreciable role. The phase-conjugate reflectivity and fidelity of the rectangular and triangular devices are compared.

Optical implementation of iterative phase retrieval algorithms (such as the Gerchberg-Saxton algorithm) for reconstruction of phase information from amplitude or intensity measurements is of interest for application to such fields as atmospheric and astronomical imaging, crystallography, and electron microscopy.1,2 In a proposed system employing successive signal iterations through a coherent optical processor in a cavity, unwanted amplitude information builds up on the phase-information bearing beam. Saturating an amplified signal can compensate for this. When two beams are coupled in a photorefractive crystal such as BaTiO3, amplifications of the signal beam can occur at the expense of pump beam depletion. At saturation of the amplitude gain, signal amplitude variations are clipped, preserving phase information. Current work includes characterizing amplitude stripper performance, examining the gain curve calculated from the input and output signals, and looking for maximum saturation sufficient for amplitude stripping relative to the coupling coefficient. Future work includes inserting the amplitude stripper into an optical phase retrieval system and evaluating its effectiveness.

We introduce a semi-self-pumped phase conjugate mirror (PCM) in which one pump is externally injected into a ring resonator while the other is self-induced as in a unidirectional ring resonator. One application is in one-way imaging through optical distortions using a phase conjugate window.1 The original realization of the phase conjugate window was similar to an externally pumped PCM and had the disadvantage of requiring a clean pump beam coherent with the distorted probe. This meant that the clean beam had to bypass the distortion, thus limiting the practical utility of the device. By replacing the externally pumped PCM portion of the device with a semi-self-pumped PCM, the clean beam can be self-induced as an oscillation beam. The second application is as a thresholding phase conjugate mirror which would be useful, for example, in some optical associative memories.2 In the semi-self-pumped phase conjugator, the presence of the externally injected pumping beam suppresses buildup of the self-induced pumping beam until the signal reaches a certain threshold intensity.

Although a variety of optical computing architectures have been analyzed and many individual devices reported, to date few working optical computers have been demonstrated performing a complete, self-contained, recognizable computational function. A conceptually simple but significant computing architecture which appears accessible to complete all-optical implementation is the cellular automaton (CA). Murdocca discussed the CA in comparison with symbolic substitution (1). Taboury et al showed how general cellular processors could be realized using sets of holograms (2).

We report photorefractive passive phase conjugation1 of GaAIAs laser radiation at 815-865 nm and Ar+ laser radiation at 1090 nm. A ring passive phase conjugate mirror was used with BaTiO3 as the real-time holographic gain medium. At least 1.5 mW (50 mW/cm2) was required for the PPCM to begin operation. At 3.6 mW (126 mW/cm2) the reflectivity reached 16%, corresponding to 25% after correction for Fresnel reflections. The rise time, defined here as time taken to 90 % of steady state, was approximately 5/1 s W/cm2 at 514.5 and 815 nm, where /is the incident intensity. When the GaAIAs laser was replaced by an Ar+ laser emitting 35 mW (1.4 W/cm2) at 1090 nm the rise time measured 500// s W/cm2. In spite of the length of this time, the steady-state reflectivity reached 18% uncorrected for Fresnel reflections. We describe effects of the phase conjugate feedback into GaAIAs lasers and attempts at active mode locking. The fact that the PPCM operates at 1090 nm indicates that it can be used to correct distortions in Nd:YAG laser systems where aberrations in the solid-state gain medium might possibly be severe.