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Quantum Optics Journal of the European Optical Society Part B

Phase instability and intensity squeezing in lasers with two-photon saturable absorbers

P G Fernandez, Luigi A. Lugiato, Francisco Javier Bermejo

Published Feb 1, 1991• 6 citations
Publisher

Abstract

It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.

DOI
10.1088/0954-8998/3/1/005

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Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Dec 1, 1996•1 citation
It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.
Lasers with two-photon saturable absorbers exhibit a phase instability similar to that of two-photon optical bistability. Beyond the phase instability threshold the output intensity breaks into spontaneous oscillations. Analytical perturbative solutions have been found and we have linearized the Fokker-Planck equation around these solutions. The drift and diffusion matrices have been perturbatively developed and we obtained a time-dependent Ornstein-Uhlenbeck stochastic process. We have calculated the amplitude correlations and squeezing spectrum near but above the threshold for a Hopf bifurcation in bad cavity conditions.
We perform a systematic comparison between the spectrum of the intensity fluctuations and the spectrum of squeezing optimized with respect to the phase of the local oscillator, for the case of a one-photon single-mode optical bistability. In the bad-cavity limit the quantum noise reduction in the intensity fluctuations becomes comparable to the optimum level of squeezing. We consider also the case of a one-photon, single-mode laser with injected signal and show that under appropriate conditions the system can exhibit a meaningful level of squeezing.
The amplitude and phase noise spectra of the internal and external field of a microcavity are calculated using the quantum mechanical Langevin equations. We assume that two-photon absorber works inside a cavity, which brings photon-number squeezing in the internal field as well as the external field. The individual frequency components of the output field have strong squeezing at cavity resonance due to the interference between the input and the cavity field, which is similar to the quadrature squeezing in a parametric oscillator and the photon number squeezing in a saturated laser oscillator. However, the degree of the squeezing is not perfect becuase the material fluctuation remains.
A two-photon laser is modeled as NNN two-level atoms interacting via a two-photon transition with a single resonant-cavity field mode. The quadratic form of this interaction makes such a system a candidate to exhibit reduced quantum fluctuations (squeezing) in one quadrature of the output field. A Fokker-Planck equation containing all leading quantum noise terms is derived following the method of Haken. A linearized fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing may be present in two-photon optical bistability. Our calculations confirm the results of Lugiato and Strini, who adopted a factorization of moment equations.
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.
Two-photon bistability in a system of three-level atoms driven by a single-frequency field shows nearly ideal squeezing close to a dynamic instability threshold, occurring in the lower branch of the steady-state bistability curve. The squeezing is maximized and becomes very broad band in the bad cavity limit. Such results which were previously predicted on the basis of an effective two-level model, are demonstrated here and analysed by a full three-level treatment of the atoms. In addition, important restrictions and new features are found.