Chapter 2 - Wave-Equation Description of Nonlinear Optical Interactions

Abstract

This chapter examines how Maxwell's equations describe the generation of new frequency components of the electromagnetic field. Any material sample contains an enormous number TV of atomic dipoles, each oscillating with a phase that is determined by the phases of incident fields. If the relative phasing of these dipoles is correct, the field radiated by each dipole will add constructively in the forward direction, leading to radiation in the form of a well-defined beam. The system will act as a phased array of dipoles when a certain condition, known as the phase-matching condition, is satisfied. Under these conditions, the electric field strength of the radiation emitted in the forward direction will be N times larger than that because of any one atom and consequently, the intensity will be N2 times as large. In principle, it is possible to achieve the phase-matching condition by making use of anomalous dispersion, that is, the decrease in refractive index with increasing frequency that occurs near an absorption feature. However, the most common procedure for achieving phase matching is to make use of the birefringence displayed by many crystals. Birefringence is the dependence of the refractive index on the direction of polarization of the optical radiation.