Coherence properties of optical fields in a nonlinear dielectric

Abstract

Coherence properties of optical fields in a nonlinear dielectric are studied taking into account their vector nature. Maxwell’ equations and a complete expansion of polarization in the electric field are used to obtain equations of propagation of coherence functions in a nonlinear dielectric. It is shown that coherence functions of order (N, M) withN≠M may be nonzero in a dielectric for fields of all the origins. A method of solving the equations of propagation of coherence functions by approximation is given. These equations are solved for the case of plane waves in an isotropic dielectric. It is shown that the intensity of second harmonic has a dependence on the fourth-order coherence functions of the fundamental. This is a generalization of the results of Beran and De Velis and of Ducuing and Bloembergen for scalar light field that the intensity of the second harmonic depends on the average square intensity of the fundamental. It is also shown that the coefficient giving nonlinear dependence of polarization on the electric field in the lowest order can be obtained from the measurements of intensity of second harmonic and fourth-order coherence functions of fundamental. The coherence function of order (1, 2) is also calculated explicitly.