Langevin treatment of quantum fluctuations and optical patterns in optical parametric oscillators below threshold

A. Gatti, H. Wiedemann, L. A. Lugiato, I. Marzoli, Gian Luca Oppo, Stephen M. Barnett

Research output: Contribution to journalArticlepeer-review

112 Citations (Scopus)

Abstract

A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO’s). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.

Original languageEnglish
Pages (from-to)877-897
Number of pages21
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume56
Issue number1
DOIs
Publication statusPublished - 1 Jul 1997

Keywords

  • Langevin model
  • quantum fluctuations
  • pattern formation
  • optical parametric oscillators (OPO’s)
  • transverse spatial dimensions
  • gaussian input beams
  • correlation functions

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