Quantum properties of transverse pattern formation in second-harmonic generation

Morten Bache, P. Scotto, R. Zambrini, San Miguel, M. Saffman

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    Abstract

    We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.
    Original languageEnglish
    JournalPhysical Review A
    Volume66
    Issue number1
    Pages (from-to)013809
    Number of pages17
    ISSN2469-9926
    DOIs
    Publication statusPublished - 2002

    Bibliographical note

    Copyright (2002) American Physical Society

    Keywords

    • SYSTEMS
    • FLUCTUATIONS
    • NOISE-REDUCTION
    • OPTICAL PARAMETRIC OSCILLATORS
    • LIGHT
    • 2ND-HARMONIC GENERATION
    • KERR MEDIUM
    • FEEDBACK

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