Optical Theorem in Nonlinear Media

TL;DR

This paper extends the optical theorem to nonlinear media, analyzing how electromagnetic waves are scattered and extinguished in nonlinear materials, with applications to advanced microscopy techniques.

Contribution

It introduces a generalized optical theorem for nonlinear media and applies it to second harmonic generation and Kerr effects in microscopy.

Findings

Derived a nonlinear optical theorem for electromagnetic scattering.

Analyzed power extinction in nonlinear scatterers.

Discussed implications for near-field optical microscopy.

Abstract

We consider the optical theorem for scattering of electromagnetic waves in nonlinear media. This result is used to obtain the power extinguished from a field by a nonlinear scatterer. The cases of second harmonic generation and the Kerr effect are studied in some detail. Applications to nonlinear apertureless scanning near-field optical microscopy are considered.