Using two specific models and a model-independent formalism, we show that in addition to the usual quadratic "side, " "out, " and "longitudinal" terms, a previously neglected "out-longitudinal" cross term arises naturally in the exponent of the two-particle correlator. Since its effects can be easily observed, such a term should be included in any experimental fits to correlation data. We also suggest a method of organizing correlation data using rapidity rather than longitudinal momentum differences, since in the former every relevant quantity is longitudinally boost invariant.PACS numbers: 25.75.+rThe experimentally measured Hanbury-Brown -Twiss (HBT) correlation between two identical particles emitted in a high energy collision defines a six-dimensional function of the momenta p~a nd p2 [1]. A popular way of presenting these is in terms "size parameters" derived from a Gaussian fit to the data of the form [2 -5]

The transverse momentum dependence of Hanbury-Brown/Twiss (HBT) interferometry radii for 2-body correlation functions provides experimental access to the collective dynamics in heavy-ion collisions. We present an analytical approximation scheme for these HBT radii which combines the recently derived model-independent expressions with an approximate determination of the saddle point of the emission function. The method is illustrated for a longitudinally boost-invariant hydrodynamical model of a heavy ion collision with freeze-out on a sharp hypersurface. The analytical approximation converges rapidly to the width of the numerically computed correlation function and reproduces correctly its exact transverse momentum dependence. However, higher order corrections within our approximation scheme are essential, and the previously published lowest order results with simple m ⊥ scaling behaviour are quantitatively and qualitatively unreliable.

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The two-pion correlation function can be defined as a ratio of either the measured momentum distributions or the normalized momentum space probabilities. We show that the first alternative avoids certain ambiguities since then the normalization of the two-pion correlator contains important information on the multiplicity distribution of the event ensemble which is lost in the second alternative. We illustrate this explicitly for specific classes of event ensembles.PACS numbers: 25.75.Gz, 25.70.Pq.

Multiboson symmetrization effects on two-particle Bose-Einstein interferometry are studied for ensembles with arbitrary multiplicity distributions. This generalizes the previously studied case of a Poissonian input multiplicity distribution. In the general case we find interesting residual correlations which require a modified framework for extracting information on the source geometry from two-particle correlation measurements. In sources with high phase-space densities, multiboson effects modify the Hanbury Brown-Twiss (HBT) radius parameters and simultaneously generate strong residual correlations. We clarify their effect on the correlation strength (intercept parameter) and thus explain a variety of previously reported puzzling multiboson symmetrization phenomena. Using a class of analytically solvable Gaussian source models, with and without space-momentum correlations, we present a comprehensive overview of multiboson symmetrization effects on particle interferometry. For event ensembles of (approximately) fixed multiplicity, the residual correlations lead to a minimum in the correlation function at nonzero relative momentum, which can be practically exploited to search, in a model-independent way, for multiboson symmetrization effects in high-energy heavy-ion experiments. C

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

The possibilities offered by type II intracavity second-harmonic generation for all-optical parallel processing of images are investigated. By injecting an image in a linearly polarized pump beam and a homogeneous field with orthogonal polarization, we obtain, according to the value of the latter, either frequency and polarization transfer or contrast enhancement and contour recognition. Noise-filtering effects are also predicted.

We investigate the spatial behavior of nonclassical light produced by type I second-harmonic generation in the traveling-wave configuration. An input-output transformation for the system of fundamental and secondharmonic field is derived in the framework of a linearization approach and used to investigate the properties of an optical system, which consists of a crystal with a quadratic nonlinearity pumped at frequency and enclosed in a two-lens telescopic system. If a faint input image at frequency 2 is injected into this device, for a sufficiently large interaction length, the output displays a pair of symmetric amplified versions of the input image at both fundamental and second-harmonic frequency. The analysis of the quantum fluctuations in the output images shows that under certain conditions, this optical device operates noiselessly with respect to the output at frequency , whereas the output images at frequency 2 are affected by a slight degradation of the signal-to-noise ratio.