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Optics Letters

Bright squeezing by singly resonant second-harmonic generation: effect of fundamental depletion and feedback

Joji Maeda, Kazuro Kikuchi

Published Jun 1, 1996• 11 citations
Publisher

Abstract

We analyze the squeezing characteristics of a singly resonant second-harmonic-generation system, in which only the fundamental light is confined in a plain cavity resonator, with consideration for fundamental depletion in a nonlinear crystal. The system was analyzed under the mean-field approximation, which neglects the variation of the field in the crystal, and as much as 9.5 dB of squeezing was predicted in the second-harmonic output. On the basis of the self-consistent method, we analyze the system, which is driven by such an intense fundamental input that the mean-field approximation is not valid, and predict that an arbitrary amount of squeezing will be available in this regime.

DOI
10.1364/ol.21.000821

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Journal of the Optical Society of America B•Jul 1, 1996•18 citations
We analyze the squeezing characteristics of a singly resonant second-harmonic-generation system, in which only the fundamental light is confined in a plain cavity resonator, with consideration for fundamental depletion in a nonlinear crystal. The system was analyzed under the mean-field approximation, which neglects the variation of the field in the crystal, and as much as 9.5 dB of squeezing was predicted in the second-harmonic output. On the basis of the self-consistent method, we analyze the system, which is driven by such an intense fundamental input that the mean-field approximation is not valid, and predict that an arbitrary amount of squeezing will be available in this regime.
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.
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.
We determine the theoretical singly resonant second-harmonic generation squeezing performance of several cavity designs and nonlinear materials. We show that, for the doubling of the 1064-nm output of Nd:YAG lasers, monolithic cavities made from periodically poled LiNbO3 (PPLN) will produce the largest amount of squeezing. We also present experimental results for a free-space cavity with a PPLN sample that yielded slightly less than 0.6 dB of measured squeezing. The cavity performance as a function of input power agrees with our theoretical predictions and shows the superior performance of periodically poled materials for the production of bright squeezed light.
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.
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.