Scattering matrix for non-linear transformation electromagnetic waves

A new mathematical approach based on a generalized concept of the scattering matrix of radar objects is developed to describe the reflection properties of a nonlinear object interacting with polarization waves. This approach involves finding a matrix transformation between the elements of matrix columns which would be invariant to different expansions of the complex vector describing an incident wave. The required invariance is provided by a transformation relating square-law forms of incident wave components with reflected wave components.<>