Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices.

We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.

Role of entanglement in two-photon imaging.

The use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever the strength of the correlations between the two photons. We consider a two-photon imaging system in which one photon is used to probe a remote (transmissive or scattering) object, while the other serves as a reference. We discuss the role of entanglement versus correlation in such a setting, and demonstrate that entanglement is a prerequisite for achieving distributed quantum imaging.

Fractal features of dark, maintained, and driven neural discharges in the cat visual system.

We employ a number of statistical measures to characterize neural discharge activity in cat retinal ganglion cells (RGCs) and in their target lateral geniculate nucleus (LGN) neurons under various stimulus conditions, and we develop a new measure to examine correlations in fractal activity between spike-train pairs. In the absence of stimulation (i.e., in the dark), RGC and LGN discharges exhibit similar properties. The presentation of a constant, uniform luminance to the eye reduces the fractal fluctuations in the RGC maintained discharge but enhances them in the target LGN discharge, so that neural activities in the pair cease to be mirror images of each other. A drifting-grating stimulus yields RGC and LGN driven spike trains similar in character to those observed in the maintained discharge, with two notable distinctions: action potentials are reorganized along the time axis so that they occur only during certain phases of the stimulus waveform, and fractal activity is suppressed. Under both uniform-luminance and drifting-grating stimulus conditions (but not in the dark), the discharges of pairs of LGN cells are highly correlated over long time scales; in contrast discharges of RGCs are nearly uncorrelated with each other. This indicates that action-potential activity at the LGN is subject to a common fractal modulation to which the RGCs are not subjected.

Entanglement in cascaded-crystal parametric down-conversion.

We use spontaneous parametric down-conversion in a cascade of crystals, driven by a single monochromatic cw pump laser, to study the interference of entangled photon pairs. By changing the distance between the crystals, the observed quantum interference pattern varies continuously from that associated with a longer single crystal to that associated with independent emissions from two distinct crystals. Postselection via spectral filtering suppresses this phenomenon. These findings are expected to advance the field of quantum-state engineering.

Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion.

We present a novel interferometric technique for performing ellipsometric measurements. This technique relies on the use of a nonclassical optical source, namely, polarization-entangled twin photons generated by spontaneous parametric downconversion from a nonlinear crystal, in conjunction with a coincidence-detection scheme. Ellipsometric measurements acquired with this scheme are absolute; i.e., they do not require source and detector calibration.

Spatial shifts of the conjugate beam generated by a nondegenerate photorefractive phase-conjugate mirror.

We demonstrate that the phase conjugation of a beam during nondegenerate four-wave mixing is accompanied by a spatial shift relative to the degenerate conjugate-beam location. Experiments with a photorefractive phase-conjugate mirror reveal that the phase-conjugate beam shifts have a nonmonotonic dependence on the probe's detuning frequency and comprise both lateral displacements of up to 218 mum and angular tilts of up to 34 arc sec. An approximate theory based on spatial dispersion coefficients is in partial agreement with the experimental results.

Modes of resonators with dispersive phase-conjugate mirrors.

We investigate the transverse and longitudinal modes of a resonator consisting of a spherical mirror, a Gaussian aperture, and a dispersive phase-conjugate mirror (PCM). The photorefractive PCM introduces spatial dispersion in the form of lateral and focal shifts along with temporal dispersion. For both degenerate and nondegenerate operation, the decentered Gaussian beam was found to be a mode whose peak intensity is displaced from the resonator axis. In the nondegenerate case, the components of a mode oscillating at a pair of frequencies that are up and down shifted from the pump frequency by the same amount have different spatial distributions, so that the intensity pattern moves periodically across the output mirror. The resonance frequencies of the longitudinal modes are calculated numerically.

Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator.

All-optical signal-to-noise ratio improvements by stochastic resonance have been obtained by use of the intensity bistability of a unidirectional photorefractive ring resonator. A signal-to-noise ratio gain of 10.5 dB has been obtained with a near-unity signal-to-noise ratio input signal at 6 mHz.

Reconstruction of a vibrating object from its time-averaged image intensities by the use of exponential filtering.

We consider the reconstruction of a complex-valued object that vibrates in some out-of-plane modes. The reconstruction is based on the phase-retrieval method with the use of two intensity measurements: the two time-averaged image intensities of the object illuminated coherently, which are modulated in two Fourier-transform planes of the object by the use of two filters with exponentially decaying transmittances that complement each other. We discuss the necessary condition of the vibration for the reconstruction method. Computer-simulated examples of retrieving the phases of one-dimensional objects demonstrate that the reconstruction of a sinusoidal-vibrating and a Gaussian random-vibrating object can be treated by this method.

Reconstruction of a complex-valued object in double-passage coherent imaging through a random-phase screen.

We consider the reconstruction of a complex-valued object that is coherently illuminated and viewed through the same random-phase screen. The reconstruction is based on two intensity measurements: the intensity of the Fourier transform of the image and the intensity of the Fourier transform of the image when modulated with an exponential filter. The illumination beam has a Gaussian intensity profile of arbitrary width, and the phase screen is assumed to be described by a Gaussian random process of large variance and arbitrary correlation length. Computer-simulated examples of the reconstruction of a two-dimensional complex object demonstrate that the reconstruction is robust.

Decentered Gaussian beams.

A generalization of the Gaussian beam is obtained by introducing a complex-valued shift in the transverse dimension. The resulting beam has a Gaussian intensity distribution with width varying as an ordinary Gaussian beam, but whose peak traces an inclined linear trajectory. The wave fronts are displaced laterally in a sheared fashion. This generalized beam preserves its form after passing through arbitrary paraxial optical components, even if they are decentered. The peak-intensity line is modified by such systems as if it were a ray.

Adaptation with a stabilized retinal image: effect of luminance and contrast.

The addition of a uniform increment of luminance (L) to a faded retinally-stabilized target results in the subjective reappearance of the image with contrast opposite to that of the target. This phenomenon, called apparent phase reversal (APR), reveals a nonlinear gain mechanism in the adaptation process. The magnitude of the threshold increment to elicit APR (Lapr) is a measure of the state of stabilized adaptation. In the experiments reported here, Lapr was studied as a function of background luminance (Lo) and contrast (m) of the adapting stimulus. It was found that Lapr increases with increasing Lo, but does not depend on m. The data are analyzed within the context of a previously proposed model of stabilized image fading consisting of a multiplicative inverse gain followed by a subtractive process. It was found that the addition of a contrast processing stage was required to account for the relationship between Lapr and m.

Reconstruction of a complex-valued object in coherent imaging through a random-phase screen.

We consider the reconstruction of a complex-valued object that is coherently illuminated and then viewed through a random-phase screen. The reconstruction involves a phase retrieval based on two intensity measurements. The first is a measurement of the long-exposure averaged intensity of a Fourier transform of the image; it yields full information on the magnitude of the object Fourier transform but noi nformation on its phase. The second measurement is made with the image field modulated by an exponential function. This modulation has the effect of shifting the Fourier-transform function along the imaginary axis of the complex plane of its argument, thus making its intensity dependent on the unknown object phase. This method is capable of reconstructing the object except for an inherent ambiguity corresponding to a simple displacement. The effects of the noise arising from averaging over finite, instead of infinite, exposure times and the quantum noise were assessed. A computer-simulated example of reconstru ting a two-dimensional object demonstrated that the reconstruction is robust. The reconstruction error increases with an increase of the variance of the random-phase function and with a decrease of its correlation length.

Fading time of retinally-stabilized images as a function of background luminance and target width.

Fading time of a retinally-stabilized difference-of-Gaussian (DOG) stimulus depends on the background luminance, contrast and spatial frequency content of the stimulus. A model of the visual system including a nonlinear multiplicative, non-local and fast process followed by a linear subtractive, local and slower process accounts for these effects. Analysis of the fading time data allows us to estimate the spatiotemporal characteristics of the proposed adaptation processes. The model is consistent with recent models of normal light adaptation from the probe-flash paradigm.

Reducing Berreman's 4 x 4 formulation of liquid-crystal-display optics to 2 x 2 Jones vector equations.

We use a perturbation expansion to obtain a generalized 2 x 2 Jones vector description that is equivalent to Berreman's description. We show that for typical liquid-crystal displays (LCD's) the bulk reflections are weak so that the first-order 2 x 2 Jones solution is generally sufficient and affords fast and reasonably accurate computations of the overall optical properties of LCD devices.

Dynamics of adaptation for vision with a stabilized image.

The addition of a uniform increment of light to a high-contrast image that has been stabilized on the retina reveals marked perceptual nonlinearities. When the increment is small, the pattern appears in its original phase (OP), large increments produce an apparent phase reversal (APR), and intermediate increments may yield an apparently blank field or an oscillation of the apparent phase. In the present series of studies the threshold values used to produce a stable OP and APR were determined as a function of adaptation time before the application of the increment. The stabilized target had a luminance profile consisting of the difference of two Gaussians. A model of detection incorporating a multiplicative gain controlled by a filtered version of the stimulus was used to account for the occurrence of the OP and the APR and the transitory phenomena following the uniform increment. It is argued that the midpoint of the transition zone between the OP and APR, corresponding to blanking, enables us to estimate the shape of the step response function of the gain filter independently of the subsequent detection processes.

Complex amplitude reflectance of the liquid crystal light valve.

The complex amplitude reflectance of the liquid crystal light valve (LCLV) is determined as a function of the writing intensity and applied voltage using an approximate model. The input and output polarizers are assumed to have arbitrary directions. The theoretical results based on this model match our experimental measurements. This theory allows us to optimize the operation of the LCLV as an intensity or phase-only spatial light modulator. When the polarizers are orthogonal and the input polarizer is at -34 degrees with the front liquid crystal director, the intensity reflectance reaches 100% (compared to 81% for the conventional configuration). Phase-only modulation is realizable by use of appropriate applied voltage bias and configuration of polarizers.

Optical implementation of the Hopfield algorithm using correlations.

We propose a method for the implementation of the Hopfield algorithm using inner products of unipolar data. This approach is particularly useful for image recognition.

Impulse-response function of photorefractive phase conjugation.

Explicit expressions for the impulse-response function of a photorefractive phase conjugator are derived. The expressions are in the form of an infinite series of Bessel functions. The results are derived by using the undepleted pump approximation and are therefore valid at least for small time intervals, even when the conjugator is unstable.

Lateral and focal shifts of phase-conjugated beams in photorefractive materials.

It is predicted that when a dc electric field is present or when a probe beam contains temporal frequencies different from that of the pump waves a beam reflected from a photorefractive phase-conjugate mirror will experience lateral and focal shifts. These shifts are a consequence of angular dependence of the phase of the reflectivity and are similar to the Goos-Hänchen effect. The phenomenon becomes more pronounced near resonance.