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Annual Meeting Optical Society of America

Higher-order photon statistics of optical parametric oscillators

Reeta Vyas, A. L. DeBrito

Published Jan 1, 1991• 0 citations
Publisher

Abstract

We discuss two- and three-fold photon statistics for the squeezed light generated by subthreshold degenerate (DPO) and nondegenerate (NDPO) parametric oscillators. In higher-order statistics details of coherence properties are more strongly reflected than in the single-fold statistics. Many experiments use two-fold statistics to extract spectral information about the incident beam. We use phase-space representation to express the operator field variables in terms of independent Gaussian random processes.1 Using the Gaussian property of these field variables and making a Karhunen-Loeve expansion in terms of orthogonal functions, analytical expressions for the two- and three-fold generating functions for the DPO and the NDPO are obtained. From this generating function various statistical quantities such as factorial moments and joint photon counting probability distributions are calculated.

DOI
10.1364/oam.1991.fl4

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Homodyne statistics when the light from a degenerate parametric oscillator (DPO) is mixed with coherent light from a local oscillator are discussed. By using dynamical models of these beams we discuss the photon sequences underlying the superposed beam in terms of photoelectric pulse sequences recorded by a detector. The field produced by the parametric oscillator is expressed in terms of two independent real Gaussian random variables. Using this property of the field variables, we derive the generating function for the photoelectron statistics analytically. From this generating function, expressions for the photoelectron-counting distribution, factorial moments, and the waiting-time distribution are derived. These quantities are directly measurable in photon-counting experiments. The results reported here are applicable to arbitrary strengths of the signal and the local-oscillator fields. We also show that, depending on the relative strength and relative phase between coherent light from the local oscillator and squeezed light from the DPO, the superposed light beam may exhibit many interesting nonclassical features. These and other effects are described and curves are presented to illustrate the behavior.
Statistics of photons emitted by a nondegenerate parametric oscillator (NDPO) operating below threshold are discussed. Analytical expressions for the generating function are obtained when two nondegenerate modes of the NDPO are mixed on a photocathode or when the intensities of the two modes are added. From the generating function, photon-counting distributions and waiting-time distributions as measured by a detector placed outside the cavity are derived. Similarities and differences between the distributions for the NDPO, the degenerate parametric oscillator, degenerate four-wave mixing, nondegenerate four-wave mixing, and thermal light are also discussed.
Photon statistics of light produced by a nondegenerate optical parametric oscillator operating below threshold are calculated. Positive-P representation is used to map quantum dynamics onto a set of classical Langevin equations for the complex field amplitudes associated with the annihilation and creation operators for the field produced by the oscillator. Using a Karhunen Loeve expansion of the resulting stochastic processes the moment generating function for photon counting statistics is obtained.
Nonclassical light beams generated by the degenerate optical parametric oscillator operating below threshold are analyzed in terms of photoelectron-counting sequences. The positive-P representation is used to calculate the generating function for photoelectron statistics in a closed form. This generating function is used to derive expressions for the photoelectron-counting and waiting-time distributions. The dependence of these distributions on mean photon number inside the cavity and efficiency of detection is studied. The relationship between photoelectron-counting sequence and the photon emission sequence is used to present a simple physical picture of light beams produced by the degenerate parametric oscillator.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.