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Annual Meeting Optical Society of America

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

Claude Fabre, Nicolas Pettiaux, Paul Mandel

Published Jan 1, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1990.thb1

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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.
We present a semiclassical and quantum analysis of a nonlinear optical interaction in a cavity in which an externally driven fundamental mode at frequency \ensuremath{\omega} transforms into the second-harmonic mode 2\ensuremath{\omega} and then into the fourth-harmonic mode 4\ensuremath{\omega} via cascaded frequency-doubling processes $\ensuremath{\omega}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}2\ensuremath{\omega}$ and $2\ensuremath{\omega}+2\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}4\ensuremath{\omega}.$ In the adiabatic limit of the strongly damped fourth-harmonic mode the nonlinear system is equivalent to the process of intracavity second-harmonic generation combined with nonlinear two-photon absorption from the second-harmonic mode. Semiclassical steady states and linear stability analysis show that possible operation regimes are substantially different from those for the pure second-harmonic-generation process. It is shown in particular that the system is characterized by two critical points: Starting from a certain critical value of the driving field intensity, one observes self-pulsing instability; however, at higher intensities, beyond a second critical point, the system turns back to the stable generation regime. Moreover, under appropriate values of the control parameters, one may arrive at a complete quenching of self-pulsing behavior and at stabilization of the steady states in the entire domain of the driving field intensity. These stabilization properties become important when turning to the analysis of the quantum fluctuations and quadrature squeezing effect in the fundamental and second-harmonic modes within the ranges of linearized treatment of fluctuations. Due to the emergence of stability in the behavior of the system at high level of coherent excitation, the system becomes capable of generation of bright light with enhanced squeezing properties.
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.
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.
Classical and quantum fluctuations are analyzed in the system of type-II harmonic generation where two frequency-degenerate subharmonic fields with orthogonal polarizations are required for the generation of a harmonic field. The two subharmonic fields as well as the harmonic fields are on resonance in a cavity. It is found that there is no self-pulsing behavior as predicted for the type-I case where the intensities of both the subharmonic and the harmonic fields undergo fast oscillation. Instead there exists a threshold that is identified as the onset of an optical parametric oscillator (OPO) formed by a subharmonic mode with its polarization orthogonal to the input polarization (not the original modes). When the loss for the harmonic field is small, most of the input power is converted to the output power of the OPO. Under this circumstance, quantum-nondemolition measurements of the input can be performed at certain frequencies. The spectra of squeezing are calculated for the two subharmonic modes and it is found that both modes are squeezed for a certain range of frequency. The output of the OPO is found to exhibit phase squeezing.