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Quantum Optics Journal of the European Optical Society Part B

Amplitude squeezing from second-harmonic generation in a laser cavity

P Garcia-Fernandez, Luigi A. Lugiato, Francisco Javier Bermejo, P. Galatola

Published Feb 1, 1990• 21 citations
Publisher

Abstract

The authors consider the problem of second harmonic generation in an optical cavity which contains both the laser and the nonlinear crystal. They calculate the spectrum of the amplitude fluctuations in the output field, for the mode which is generated by the laser. They focus on the case that the damping constant of this mode is much larger than all the other relaxation rates of the system, and show that in this limit the spectrum is correctly described by the universal normal form for two-photon processes. Finally, they show in general that in the framework of linearised theories the spectrum of the intensity fluctuations in the output field reduces exactly to the spectrum of squeezing of the amplitude quadrature component.

DOI
10.1088/0954-8998/2/1/005

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The authors consider the problem of second harmonic generation in an optical cavity which contains both the laser and the nonlinear crystal. They calculate the spectrum of the amplitude fluctuations in the output field, for the mode which is generated by the laser. They focus on the case that the damping constant of this mode is much larger than all the other relaxation rates of the system, and show that in this limit the spectrum is correctly described by the universal normal form for two-photon processes. Finally, they show in general that in the framework of linearised theories the spectrum of the intensity fluctuations in the output field reduces exactly to the spectrum of squeezing of the amplitude quadrature component.
A quantum theory of self-convers of the lasing frequency in active nonlinear crystals placed in a cavity is developed. The generation of nonclassical (quadrature squeezed) light upon self-doubling of the laser radiation frequency is studied in detail, with no limitations on the relations between the relaxation times of the inverse population and the polarization of the medium and the lifetime of a photon in the cavity. The fluctuation spectra of the quadrature components of the fields of the laser radiation and its second harmonic are studied in dependence on the pumping parameters and the parameters of the cavity. Numerical calculations are performed for a Nd:Mg:LiNbO 3 crystal with a regular domain structure.
We consider the process of second-harmonic generation (SHG) in a cavity that is resonant for both the fundamental- and second-harmonic modes. It has been previously shown that such a system displays a phase instability leading to self-pulsing and that one gets important intensity squeezing on both the fundamental- and second-harmonic mode for pump intensities close to but below, this instability threshold. Such a squeezing has been recently observed. We have analytically calculated the intensity-noise spectrum of the frequency-doubled field above such an instability threshold, using a semiclassical input-output technique for the treatment of quantum fluctuations.1 Such a method, introduced to deal with fluctuations around a stable solution, has been generalized to the self-pulsing domain. As expected, the instability brings excess noise to the output beams, especially around the zero-frequency, the self-oscillation frequency, and its harmonics. Remarkably, some regions exist in which where the noise increase is small; squeezing still occurs in this frequency range far in the instability domain.
We consider second-harmonic generation within a laser cavity. Garc\'{\i}a-Fern\'andez et al. [Quantum Opt. 2, 49 (1990)] found that large-amplitude squeezing may be obtained in the fundamental output if the cavity loss rates are high compared to the atomic decay rates. We extend their calculations, taking fully into account the phase diffusion of the laser field, and considering different dynamical regimes. We obtain large-amplitude squeezing in the second-harmonic output if the cavity loss rate at the second harmonic is high compared to the atomic decay rates. However, the cavity loss rate at the fundamental may still be slow compared to the atomic loss rate.
Excellent squeezing in intracavity second-harmonic generation has been predicted to occur on cavity resonance in the output intensity fluctuations. Cavity detunings cause laser phase noise to couple in and reduce the squeezing observable. Here we consider the effects of laser phase fluctuations on the output-squeezing spectrum. Laser phase noise is modeled as an Ornstein-Uhlenbeck (colored-noise) Gaussian stochastic process and its effects are compared with the white-noise limit. This indicates that the white-noise model may qualitatively overestimate the deleterious effects of laser fluctuations on sideband squeezing. We compare our results with the recently reported experiment of Pereira et al. [Phys. Rev. A 38, 4931 (1988)] and present an analysis of the empty cavity for comparison.