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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spontaneous spatial structures and spatial squeezing in optical parametric oscillators

Massimo Brambilla, D. Camesasca, A. Gatti, Luigi A. Lugiato, Gian‐Luca Oppo

Published Dec 1, 1993• 1 citation
Publisher

Abstract

We demonstrate that the optical parametric oscillator is an ideal system for studying spatial pattern formation and quantum effects in spatial structures. In the first part of the article we analyze a semiclassical model which includes diffraction in the paraxial approximation, and we show the formation of rolls, zig-zag patterns, dislocations, filamentation, and optical chaos. In the second part of the paper we describe the spatial structure of the squeezed vacuum state emitted by the optical parametric oscillator below the threshold for signal generation.

DOI
10.1117/12.164771

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We demonstrate that the optical parametric oscillator is an ideal system for studying spatial pattern formation and quantum effects in spatial structures. In the first part of the article we analyze a semiclassical model which includes diffraction in the paraxial approximation, and we show the formation of rolls, zig-zag patterns, dislocations, filamentation, and optical chaos. In the second part of the paper we describe the spatial structure of the squeezed vacuum state emitted by the optical parametric oscillator below the threshold for signal generation.
In the first part of the paper we define the spatial spectrum of squeezing following an operational procedure, and we show in general how the spatial structure of squeezed states can be described in terms of correlation functions of quadrature components of the electric field. In the second part we formulate an appropriate quantum model for a degenerate optical parametric oscillator (OPO) with plane mirrors, and we analyze it extensively below the threshold for signal generation. The correlation length diverges when the OPO approaches threshold; this picture provides an ideal completion of the analogy with critical phenomena in second-order phase transition at equilibrium. The spatial configuration of the correlation function exhibits the phenomenon of ``quantum image:'' the signal field, which is purely generated by quantum noise, shows an ordered spatial structure which is observable via the spatial correlation function.
We analyze the quantum properties of the signal near field emitted by a degenerate parametric oscillator below threshold, including diffraction and its effects on the threshold for signal generation. The field is probed by a local oscillator field of arbitrary spatial configuration. The results are expressed in terms of an appropriate spectrum which describes how the level of squeezing varies with the angle from the direction of propagation. The results hold for cavities both with plane and with spherical mirrors.
A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO's). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.
Summary form only given.We study spatiotemporal fluctuations of the signal field in the output from a degenerate optical parametric oscillator using the Langevin model of A. Gatti et al. (1997). The spatial structure of the output signal is calculated for pump values just below the threshold for the formation of patterns with a critical wave vector. We consider the effects of a squeezed input signal, both homogeneous and spatially varying, on the output correlations, which can be measured in both the near- and far-field.