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Information Dynamics of Photorefractive Two-Beam Coupling

Dana Z. Anderson, Roger W. Brockett, Nathan Nuttall

An operator approach to two-beam coupling in photorefractive media for which each beam is composed of information that varies in both space and time reduces the problem to a single differential equation: $d\ensuremath{\rho}/dz\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}[[{\ensuremath{\sigma}}_{0},\ensuremath{\rho}],\ensuremath{\rho}]/4$. $[A,B]\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}AB\ensuremath{-}BA$ is the commutator of two operators, $\ensuremath{\rho}$ is a density operator that embodies the state of the optical field, and ${\ensuremath{\sigma}}_{0}$ is a coupling operator. A solution exists in closed form for specific cases and is amenable to numerical integration in general. The evolution of $\ensuremath{\rho}$ is unitary and approaches a block diagonal in a representation that diagonalizes ${\ensuremath{\sigma}}_{0}$.An operator approach to two-beam coupling in photorefractive media for which each beam is composed of information that varies in both space and time reduces the problem to a single differential equation: $d\ensuremath{\rho}/dz\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}[[{\ensuremath{\sigma}}_{0},\ensuremath{\rho}],\ensuremath{\rho}]/4$. $[A,B]\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}AB\ensuremath{-}BA$ is the commutator of two operators, $\ensuremath{\rho}$ is a density operator that embodies the state of the optical field, and ${\ensuremath{\sigma}}_{0}$ is a coupling operator. A solution exists in closed form for specific cases and is amenable to numerical integration in general. The evolution of $\ensuremath{\rho}$ is unitary and approaches a block diagonal in a representation that diagonalizes ${\ensuremath{\sigma}}_{0}$.

Physical Review LettersFeb 15, 199917 citations

Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials

Baruch Fischer, Jeffrey Owen White, Mark Cronin‐Golomb +1 more

We present an exact solution of a nonlinear vector analysis of two-beam coupling and forward four-wave mixing in photorefractive media.In this Letter we present an exact solution with linear absorption for a system of nonlinear differential equations that model two separate photorefractive processes.The first is the coupling of two beams with general

Optics LettersApr 1, 198625 citations

Tunable Twin Beam Generation by Beam Coupling in Photorefractive Media

Mark E. Saffman

Springer eBooksJan 1, 19961 citation

Four-wave mixing in photorefractive crystals with depleted pumps: an analytical treatment

J. Goltz, Theo T. Tschudi

We present an analytical approximative solution of four-wave mixing in photorefractive crystals with depleted pumps for the case of a negative coupling coefficient and then discuss the solution.

Optics LettersApr 15, 19893 citations

Theoretical analysis of the effects of frequency detuning dependence of photorefractive two- beam coupling coefficient on gain and phase-shifts of the signal beam for a coupled unidirectional photorefractive ring resonators

M.K. Maurya, R.A. Yadav

OptikApr 1, 20121 citation

Exact solution of degenerate four-wave mixing in photorefractive media

Aleksander Błȩdowski, Wieslaw Z. Krolikowski

A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.

Optics LettersFeb 1, 198817 citations

Operator-Lattice Treatment of Two-Beam Coupling in Photorefractive Media

Abstract

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Operator-Lattice Treatment of Two-Beam Coupling in Photorefractive Media

Abstract

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