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Physical Review Letters

Squeezing in the self-pulsing domain

Nicolas Pettiaux, Paul Mandel, Claude Fabre

Published Apr 8, 1991• 22 citations
Publisher

Abstract

We study analytically the squeezing spectrum of second-harmonic generation in the self-pulsing regime. We prove that squeezing is still defined in the presence of a limit cycle. When the input field exceeds the self-pulsing threshold, the intensity spectrum remains smaller than the shot-noise limit in a frequency domain around the self-pulsing frequency.

DOI
10.1103/physrevlett.66.1838

Related papers

Squeezing spectrum in second-harmonic generation in the self-pulsing domain

Claude Fabre, Nicolas Pettiaux, Paul Mandel

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.

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Second-harmonic generation (SHG) in doubly resonant optical resonators (resonant for the pump and for the harmonic wave) is a subject rich in outstanding challenges: the demonstration of self-pulsing, in which the intracavity field amplitudes undergo a Hopf bifurcation to a stable limit cycle,1 and chaos; the generation of near-perfect squeezing near but below the self-pulsing threshold; the generation of squeezed radiation in the self-pulsing regime; and the demonstration of quantum nondemolition measurements.

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

A Sánchez-Díaz, P García-Fernández

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.

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The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.

Physical Review A•Nov 1, 1985•365 citations
We study analytically the squeezing spectrum of second-harmonic generation in the self-pulsing regime. We prove that squeezing is still defined in the presence of a limit cycle. When the input field exceeds the self-pulsing threshold, the intensity spectrum remains smaller than the shot-noise limit in a frequency domain around the self-pulsing frequency.
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.
Second-harmonic generation (SHG) in doubly resonant optical resonators (resonant for the pump and for the harmonic wave) is a subject rich in outstanding challenges: the demonstration of self-pulsing, in which the intracavity field amplitudes undergo a Hopf bifurcation to a stable limit cycle,1 and chaos; the generation of near-perfect squeezing near but below the self-pulsing threshold; the generation of squeezed radiation in the self-pulsing regime; and the demonstration of quantum nondemolition measurements.
We analyze the quantum fluctuations of second harmonic generation at the Hopf bifurcation and in the limit-cycle regime near the critical point using many-body techniques. The many-body approach does not make use of linearization approximations and can thus be used to study finite-size effects. Finite-size corrections reduce the amount of squeezing at the Hopf bifurcation and eliminate infinities predicted by the linearization approach at this point and in the self-pulsing regime. The characteristic frequencies of the linearized fluctuation spectra in the self-oscillation regime are shifted and new spectral structures are observed.
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.