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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Intensity versus amplitude squeezing spectrum in the self-pulsing domain of lasers with two-photon saturable absorbers

A Sánchez-Díaz, P García-Fernández

Published Jun 1, 1996• 0 citations
Publisher

Abstract

In a previous work we have analytically studied the amplitude squeezing spectrum in the self-pulsing domain of lasers with two-photon saturable absorbers [1]. We used a second-order perturbative expansion for the drift and diffusion matrices associated with a time-dependent Ornstein - Uhlenbeck stochastic process. Due to self-pulsing, the correlation functions are time dependent and have been time averaged in order to apply the Wiener - Khintchine theorem . We will show that the amplitude and intensity spectra in the self-pulsing regime are no longer proportional as in the case of the stationary state and the differences between both spectra will be discussed in comparison with the stationary case.

DOI
10.1088/1355-5111/8/3/010

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In a previous work we have analytically studied the amplitude squeezing spectrum in the self-pulsing domain of lasers with two-photon saturable absorbers [1]. We used a second-order perturbative expansion for the drift and diffusion matrices associated with a time-dependent Ornstein - Uhlenbeck stochastic process. Due to self-pulsing, the correlation functions are time dependent and have been time averaged in order to apply the Wiener - Khintchine theorem . We will show that the amplitude and intensity spectra in the self-pulsing regime are no longer proportional as in the case of the stationary state and the differences between both spectra will be discussed in comparison with the stationary case.
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.
A system of N identical superimposed two-level atoms (the Dicke model) interacting with one another and driven by a fluctuating laser field of finite phase and amplitude bandwidths is considered. An exact master equation for the phase-averaged reduced atomic density operator is derived using the theory of multiplicative stochastic processes. It is shown that in the absence of amplitude fluctuations, this equation admits an exact steady-state solution. The exact solution is further used to obtain and analyse the behaviour of the phase-averaged atomic observables and atomic correlation functions in the steady state. The principal results of our analysis is that the phase fluctuations tend to smooth the discontinuities in the observables and the correlation functions found in the non-fluctuating case. Further, including the amplitude fluctuations as well we derive in the high-field limit a Markovian master equation for the density operator averaged over the ensembles of both phase and amplitude fluctuations. The quantum regression theorem is used to derive and discuss exact analytical expressions for the fluorescent spectrum and the second-order intensity correlation function for a system of two interacting atoms.
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.
Numerical modeling of self-action of a beam, whose amplitude is periodically modulated in time, in a two-level saturable absorbing medium is reported. For describe a beam self-action we solve numerically the full set of Maxwell-Bloch equations. We study the influence of the non-stationary self-action of the beam on the transmission of modulation signal through the medium. It is shown that in the time dependence of the polarization and population difference the nonlinear distortions of the modulation signal can be much stronger than in the output field intensity.
The time dependence of the two-photon absorption process is experimentally investigated in the low intensity regime as a function of laser linewidth, Doppler width, polarisation and delay between pulses, using 5 ns pulses at two different frequencies. Excellent agreement is found between experiment and the theoretical predictions of Allen and Stroud. The experiment arguments and expands earlier work on the dependence of linewidth in the two-photon process. The lineshape of the Hansch-type laser producing the pulses is shown to be best described by a Gaussian rather than a Lorentzian or as the result of an Ornstein-Uhlenbeck process.