Calculation of the Self-Focusing of Electromagnetic Radiation in Semiconductors

Abstract

A theory for the self-focusing of laser light in InSb is presented. The nonlinear dielectric constant is calculated in the effective-mass approximation and a closed expression is obtained. Similarly closed expressions are obtained for the higher-harmonic-generation coefficients. The equations of self-focusing are shown to follow from a variational principle thereby providing us with a generalization of Fermat's principle. Detailed calculations give, for typical laser conditions, a self-focusing length of ∼ 2 mm.