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Physical Review A

Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity

Michael W. Jack, Matthew J. Collett, Daniel F. Walls

Published Mar 1, 1996• 15 citations
Publisher

Abstract

The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1801

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The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a \ensuremathχ(2){\mathrm{\ensuremath{\chi}}}^{(2)}\ensuremathχ(2) medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.
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We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second-harmonic generation process occurring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions independent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.
Quantum fluctuation and quantum entanglement of the pump fields reflected from an optical cavity for type-II second-harmonic generation are theoretically analyzed. The correlation spectra of quadrature components between the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses, and normalized frequency. High correlation of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited as a source for generating entangled states of continuous variables.
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.