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Journal of Modern Optics

Phase Diffusion and Quantum Noise in the Optical Parametric Oscillator: A Semiclassical Approach

J.-Y. Courtois, A. D. Smith, Claude Fabre, Serge Reynaud

Published Jan 1, 1991• 33 citations
Publisher

Abstract

We calculate by the semiclassical method the noise spectra of a non-degenerate optical parametric oscillator operating above threshold when taking into account two independent diffusion processes on the pump phase and on the signal-idler phase difference. We also show that the phase diffusion processes are important when calculating the quantum noise in an optical parametric oscillator for noise frequencies close to the beat frequency between the signal and idler modes.

DOI
10.1080/09500349114550201

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We calculate by the semiclassical method the noise spectra of a non-degenerate optical parametric oscillator operating above threshold when taking into account two independent diffusion processes on the pump phase and on the signal-idler phase difference. We also show that the phase diffusion processes are important when calculating the quantum noise in an optical parametric oscillator for noise frequencies close to the beat frequency between the signal and idler modes.
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 fluctuations in the phase of the pump in a degenerate optical parametric oscillator are modeled by a classical phase-diffusion process, and their influence on squeezing is studied. To this end, appropriate quadrature variables, relative to the instantaneous phase of the pump, are introduced. The squeezing is calculated both inside and outside the cavity. In both cases it is found to be degraded by the phase fluctuations, which may be understood in terms of the time lag in the response of the system to an instantaneous change in the pump phase. This effect might account for a small part of the residual noise present in current experiments. Correlation functions for the field of the oscillator for finite pump linewidth are derived and discussed.
A general approach for describing complex quantum-mechanical systems in terms of ccc-number variables is discussed on the basis of a formalism developed by Lax. We apply this formalism to the particular problem of noise fluctuations in parametric oscillators. From a microscopic Hamiltonian describing light interacting with optically active atoms in a cavity with loss, we arrive at an equation for the motion in terms of ccc-number variables. We then solve this system for the noise properties of the signal mode near threshold and above, when the pump and idler modes may be treated adiabatically, and compare our work with the results of Graham, who treated the signal and idler symmetrically.
The dependence of quantum correlations of twin beams on the pump finesse of an optical parametric oscillator is studied via a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results quantitatively.