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16th Congress of the International Commission for Optics: Optics as a Key to High Technology

Photon statistics of four-wave mixing of nonclassical light with pump depletion

Jan Peřina

Published Jul 26, 1993• 1 citation
Publisher

Abstract

Photon statistics and nonclassical behaviour of four-wave mixing are examined using the approximation of small fluc- tuations around a stationary point, including the coupling of modes, pump depletion, effects of nonlinear dynamics, nonclassical behaviour of input light, external noise and losses.
DOI
10.1117/12.2308449

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The statistical properties of nonlinear oscillators modeling dissipative forward four-wave mixing are investigated, adopting the Fokker-Planck equation approach. The photon statistics are shown to be insensitive to the nonlinearities and are formulated in terms of the superposition of coherent and chaotic fields. The only approximation in describing the squeezing properties consists in the way of including thermal noise. The effect of the initial coherent amplitudes, that of the interplay of the coupling constants, and that of the reservoir on the squeezing properties are studied. An interesting connection between the revivals of coherent amplitudes and squeezing is pointed out.
Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.