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Quantum Optics Journal of the European Optical Society Part B

Quantum noise reduction in lasers with intracavity second-harmonic generation and injected signal

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

Published Oct 1, 1990• 5 citations
Publisher

Abstract

The authors consider a laser with intracavity second-harmonic generation and injected signal at either the second-harmonic or the fundamental frequency. With a strong injected signal at the second-harmonic frequency, near-perfect phase squeezing at non-zero classical intensity is found. A weak injected signal at the second harmonic gives 50% intensity squeezing in the output at the second harmonic, at an adjustable frequency. A moderate injected signal at the fundamental gives 50% intensity squeezing at the second harmonic for a relatively small nonlinearity.

DOI
10.1088/0954-8998/2/5/003

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The authors consider a laser with intracavity second-harmonic generation and injected signal at either the second-harmonic or the fundamental frequency. With a strong injected signal at the second-harmonic frequency, near-perfect phase squeezing at non-zero classical intensity is found. A weak injected signal at the second harmonic gives 50% intensity squeezing in the output at the second harmonic, at an adjustable frequency. A moderate injected signal at the fundamental gives 50% intensity squeezing at the second harmonic for a relatively small nonlinearity.
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We consider lasers with intracavity nonlinear elements, e.g., two-photon absorption, second-harmonic generation, as a possible means to reduce the amplitude fluctuations in a laser. While amplitude squeezing up to 37% may be obtained for the internal field, only a modest amount of noise reduction (10% for two-photon absorption, effectively zero for second-harmonic generation) is found in the output field at the laser frequency. In the second-harmonic field an amplitude-noise reduction of 50% below the shot-noise level may be achieved.
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 have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.
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.