Information Dynamics of Photorefractive Two-Beam Coupling

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: $d\rho /dz=\left[\right[{\sigma }_0,\rho ],\rho ]/4\mathrm{}$. $[A,B]=AB-BA$ is the commutator of two operators, $\rho$ is a density operator that embodies the state of the optical field, and ${\sigma }_0$ is a coupling operator. A solution exists in closed form for specific cases and is amenable to numerical integration in general. The evolution of $\rho$ is unitary and approaches a block diagonal in a representation that diagonalizes ${\sigma }_0$.