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Journal of the Optical Society of America B

Active versus passive squeezing by second-harmonic generation

Andrew G. White, Timothy C. Ralph, Hans‐A. Bachor

Published Jul 1, 1996• 18 citations

Abstract

The characteristics of squeezed light generated by both passive (occurring in a cavity external to a laser) and active (occurring within a laser cavity) second-harmonic generation (SHG) are investigated and contrasted. Squeezing of both the fundamental and the second harmonic is discussed, and the issue of doubly versus singly resonant behavior is addressed. We examine passive squeezing by explicitly modeling the intrinsically noisy output of the pump laser and coupling it to a passive, multiport, lossy SHG cavity. Low-frequency degradation of the squeezing caused by the laser pump noise is predicted and provides a probable explanation for previous discrepancies between theory and experiment. Active squeezing is quantitatively modeled by a three-level laser model that retains all laser dynamics. Previously disparate predictions are reconciled. For one parameter set two regimes of squeezing are predicted: 50% squeezing at frequencies lower than the laser relaxation oscillation, and near-perfect squeezing at frequencies above. A particular problem of active squeezing is highlighted: The fast dephasing of the laser coherence introduces considerable excess noise likely to mask squeezing in experimental situations. We conclude that, although passive SHG is a practical source of squeezing, active SHG is unlikely to be so in the foreseeable future.

DOI: 10.1364/josab.13.001337

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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.

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.

Theoretical analysis of squeezed light generation by phasematched SHG, applicable generally to various SHG configurations and appropriate for mutual comparison, is presented. The analysis is based on analytical solutions of the linearized differential equations in space coordinate and the input-output equations for the amplitude fluctuations, and calculations of squeezing spectra using the covariance matrixes. Formulations describing the squeezing characteristics in terms of the device parameters are derived. Typical numerical results are also given to illustrate the features of traveling-wave SHG, singly-resonant SHG, and doubly-resonant SHG configurations including cases where propagation losses are involved. The results, which are consistent with those in previous work, provide many insights for design and application of SHG devices for squeezed-light generation.

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.

An extremely conspicuous passive power noise stabilization is the first, to the best of our knowledge, discovered in a cavity-enhanced second-harmonic generation (SHG) process. Differing from the SHG as a buffer reservoir, the stronger strength of the nonlinear interaction pushes the power noise suppression level to a higher value and exhibits a broadband noise reduction performance due to the mechanism of dynamic pump suppression in the SHG process. The noise is suppressed to near shot noise limit (SNL) among the kHz to MHz frequency range, accompanied by a maximum noise reduction of 35 dB. A comprehensive demonstration indicates that the nonlinear interaction has no function on the phase noise of fundamental and harmonic waves. A theoretical model is also established that is consistent well with the experimental results. The methodology is beneficial to multiple optical metrology experiments.