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Journal de physique

Noise characteristics of a non-degenerate Optical Parametric Oscillator - Application to quantum noise reduction

Claude Fabre, E. Giacobino, A. Heidmann, Serge Reynaud

Published Jan 1, 1989• 156 citations
Publisher

Abstract

A semi-classical analysis of the noise characteristics of a non degenerate, above threshold, optical parametric oscillator is presented, yielding expressions for the quantum fluctuations of the output field intensities and phases. Particular emphasis is given to the study of the noise on the intensity difference between the two generated fields. The effect of losses, unbalance, detunings and excess pump noise is investigated. A significant quantum noise reduction is found over a broad domain of the parameter space.

DOI
10.1051/jphys:0198900500100120900

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A semi-classical analysis of the noise characteristics of a non degenerate, above threshold, optical parametric oscillator is presented, yielding expressions for the quantum fluctuations of the output field intensities and phases. Particular emphasis is given to the study of the noise on the intensity difference between the two generated fields. The effect of losses, unbalance, detunings and excess pump noise is investigated. A significant quantum noise reduction is found over a broad domain of the parameter space.
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
Quantum states with non-Gaussian statistics generated by optical parametric oscillators (OPO) with fluctuating parameters are studied by means of the kurtosis excess of the external field quadratures. The field generated is viewed as the response of a nonlinear device to the fluctuations of pump laser amplitude and frequency, crystal temperature, and cavity detuning, in addition to quantum noise sources. The kurtosis excess has been evaluated perturbatively up to the third order in the strength of the crystal nonlinear coupling factor and the second order in the classical fluctuating parameters. Applied to the device described in Opt. Expr. 13, 948 (2005), the model has given values of the kurtosis excess in good agreement with the measured ones.
This chapter provides a review of both theoretical and experimental results that are obtained on the Non-Degenerate Optical Parametric Oscillator above threshold operation. In particular it is shown that most of oscillator's characteristics can be understood from the fact that the non-linear crystal emits highly correlated twin photons. The chapter studies the correlation properties between the intensities of the corresponding twin fields. It provides a simple treatment in terms of “corpuscular” photons and gives a proof of the corpuscular model in a fully quantum manner. The chapter provides a classical representation of the fields but in which vacuum fluctuations are properly accounted. This “classical” approach yields the noise spectra of the various measurable quantities in the general case. The chapter presents observation of quantum noise reduction on the difference between the intensities of the two twin beams. It deals with new possible applications of the twin photons to spectroscopy and to the generation of amplitude squeezed laser beams.