Averaged description of wave beams in linear and nonlinear media (the method of moments)

Abstract

For a monochromatic wave beam the moments of the transverse energy-flux density distribution are introduced into consideration. It is shown that in a linear medium a polynomial representation in z holds for moments of any order. In a medium having cubic nonlinearity polynomials in z of corresponding order can be used to represent the moments of zero and first order, and the centrifugal moments of the second order. Examples of the application of the average description of wave beams are considered.