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Physical Review A

Second-harmonic generation inside a laser cavity with slowly decaying atoms

R. B. Levien, Matthew J. Collett, Daniel F. Walls

Published Mar 1, 1993• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.47.2324

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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.
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.
The input-output theory, originally developed for a linear coupling between cavity mode a and a bath, is extended to a coupling that is quadratic in the cavity mode operator a. We then apply this to second-harmonic generation, in a cavity that is resonant at the fundamental frequency and has an active laser medium working at the fundamental frequency. We find intensity squeezing of 50% below the shot-noise level in the output light at the second-harmonic frequency, whether or not the cavity is resonant at the second-harmonic frequency. To compare the singly resonant cavity to the doubly resonant cavity, we develop in an appendix a general technique for extracting a single mode from a continuum.
Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.
We discuss quantum-fluctuation characteristics of a second-harmonic generation system that uses an optical resonator to confine only the fundamental field. It was predicted that the available amount of squeezing is limited to 1.76 dB for the fundamental output and 9.54 dB for the second-harmonic output, respectively, irrespective of system parameters. However, these predictions are based on low-order perturbation theory and are unavailable if the nonlinear coupling between the fundamental and the second harmonic becomes large. We consider the spatial evolution of the fields and reveal that the maximum amount of squeezing depends on the cavity loss: Even an arbitrary amount of squeezing is possible for both the fundamental output and the second-harmonic output. We also consider the possibility of parametric oscillation of empty cavity modes pumped by the generated second harmonic and derive the following prediction: In a system that uses a type I phase-matched crystal, the oscillation of the side mode hardly occurs because of sum-frequency generation with the fundamental and scarcely imposes any limitations on squeezing. On the other hand, a system with a type II phase-matched crystal suffers from the oscillation of the polarization mode orthogonal to that of the fundamental input, and squeezing of the second-harmonic output is limited to 3 dB.
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.
We analyze amplitude squeezing from a singly resonant frequency-doubling laser oscillating at a single frequency. In this laser system, the cavity loss depends on the intensity of the oscillating fundamental field, so that conventional analyses based on a mean-field approximation become invalid in a highly pumped regime. To avoid this inconvenience, we consider spatial evolution of fields both in a laser medium and in a nonlinear crystal. It is predicted for the first time that a combination of excess nonlinearity and modest laser saturation can increase the output noise. We propose novel indices to evaluate the possible noise enhancement and suggest a design rule for squeezed light generation.