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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Stimulated Raman scattering with initially nonclassical light

Jan Peřina

Published Apr 1, 1991• 0 citations
Publisher

Abstract

Nonclassical light is now available in a number oflaboratories, being generated by Frank—Hertz experiment, optical parametric processes, four-wave mixing including optical fibres, by optical system with feedback, etc. Therefore it is senseful to reconsider various nonlinear optical interactions involving initially nonclassical light ,originally solved with coherent (laser) light. Adopting tools of quasidistributions related to antinormal ordering, the photocount distributions, its factorial moments and characteristics of squeezing of vacuum fluctuations can be investigated assuming initially nonclassical (squeezed) light in the framework of the Heisenberg—Langevin of Schrödinger approaches. Photon statistics of stimulated Raman scattering of squeezed light can be derived assuming phonon system in chaotic, coherent or squeezed states and including additive noise. The influence of nonlinear dynamics can be established on initially inclassical light and it can be shown that the initially nonclassical effects are encresed by the nonlinear dynamics provided that the Stokes mode is less amplified than the anti-Stokes mode is damped, whereas in the opposite case the nonclassical features are smoothed out. Also frequency detuning can be optimized to have maximum nonclassical effects, which are missing with increasing phonon number, even if the phonon system is squeezed. Small initial squeezing can by increased by the nonlinear dynamics, whereas strong squeezing can only be diminished.

DOI
10.1117/12.47501

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Nonclassical light is now available in a number oflaboratories, being generated by Frank—Hertz experiment, optical parametric processes, four-wave mixing including optical fibres, by optical system with feedback, etc. Therefore it is senseful to reconsider various nonlinear optical interactions involving initially nonclassical light ,originally solved with coherent (laser) light. Adopting tools of quasidistributions related to antinormal ordering, the photocount distributions, its factorial moments and characteristics of squeezing of vacuum fluctuations can be investigated assuming initially nonclassical (squeezed) light in the framework of the Heisenberg—Langevin of Schrödinger approaches. Photon statistics of stimulated Raman scattering of squeezed light can be derived assuming phonon system in chaotic, coherent or squeezed states and including additive noise. The influence of nonlinear dynamics can be established on initially inclassical light and it can be shown that the initially nonclassical effects are encresed by the nonlinear dynamics provided that the Stokes mode is less amplified than the anti-Stokes mode is damped, whereas in the opposite case the nonclassical features are smoothed out. Also frequency detuning can be optimized to have maximum nonclassical effects, which are missing with increasing phonon number, even if the phonon system is squeezed. Small initial squeezing can by increased by the nonlinear dynamics, whereas strong squeezing can only be diminished.
Photon statistics of stimulated Raman scattering of squeezed light are considered including additive noise. The phonon system is assumed to be in chaotic or squeezed chaotic states. The influence of nonlinear dynamics is established on the initial non-classical features of light adopting quasi-distribution related to anti-normal ordering, photocount distribution, its factorial moments and principal squeezing parameter. It is shown that the initial non-classical effects are increased by the nonlinear dynamics provided that the Stokes mode is less amplified than the anti-Stokes mode is damped, whereas in the opposite case the non-classical effects are swiftly smoothed out. The frequency detuning can be optimized to have maximum non-classical effects, which can periodically return. However, above a certain bound the non-classical effects are missing with frequency detuning, and also with increasing phonon number, even if the phonon system is squeezed. Small initial squeezing can be increased by the nonlinear dynamics, whereas strong squeezing can only be diminished.
Quantum statistical properties are derived for stimulated Raman scattering by squeezed phonons including squeezing of vacuum fluctuations in radiation modes and sub-Poisson photon behaviour.Initial radiation can be in squeezed thermalized and/or sub-Poisson states, phonon system can also be squeezed.In particular, effects of initial phase conditions, losses, initial nonclassical behaviour and phonon squeezing are demonstrated in terms of reduced factorial moments up to the fifth order in combined photon-photon and photon-phonon modes.Also photon number distribution, quadrature variances and principał squeeze parameters are shown.
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.
Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.
Coherent light coupled to a third-order nonlinear medium is responsible for spontaneous and for stimulated Raman processes. The analytical solutions up to second order in coupling constants of various field modes for spontaneous Raman and for stimulated Raman processes are utilized to obtain the amplitude-squared and amplitude-cubed squeezing of the input coherent light. The amplitude-squared and amplitude-cubed squeezing are completely ruled out for all modes for spontaneous Raman processes. For stimulated Raman processes, we observe that the squeezing for amplitude-squared and amplitude-cubed are possible for pump and for vibrational phonon modes. It is found that the percentage of higher ordered amplitude squeezing decreases with the increase of the orders. The squeezing in Stokes and in anti-Stokes modes are ruled out even for stimulated Raman processes.
An initially prepared coherent state coupled to a second-order nonlinear medium is responsible for stimulated and spontaneous hyper Raman processes. By using an intuitive approach based on perturbation theory, the Hamiltonian corresponding to the hyper Raman processes is analytically solved to obtain the temporal development of the field operators. It is true that these analytical solutions are valid for small coupling constants. However, the interesting part is that these solutions are valid for reasonably large time. Hence, the present analytical solutions are quite general and are fresh compared to those solutions under short-time approximations. By exploiting the analytical solutions of field operators for various modes, we investigate the squeezing, photon antibunching and nonclassical photon statistics for pure modes of the input coherent light responsible for hyper Raman processes. At least in one instance (stimulated hyper Raman processes for vibration phonon mode), we report the simultaneous appearance of classical (photon bunching) and nonclassical (squeezing) effects of the radiation field responsible for hyper Raman processes.