Nonlinear Optical Properties of Solids: Energy Considerations

It is shown that the interaction between macroscopic, nondissipative media, and time-varying electromagnetic fields can be described by a time-averaged potential function. From this function it is possible to derive phenomenologically the tensors that describe any of the usual electro- and magneto-optic effects for electric and magnetic fields of any frequency. In addition, these same potential functions describe the various optical nonlinearities like harmonic generation in potassium dihydrogen phosphate, and harmonic generation by electric quadrupole and magnetic dipole nonlinearities.The symmetry relations first derived by Armstrong, Bloembergen, Ducuing, and Pershan for electric dipole nonlinearities follow directly from the methods presented here. In addition, one can derive analogous relations for electric quadrupole and magnetic dipole nonlinearities. These relations also demonstrate the reciprocal nature of the linear electro-optic effect and rectification of light. The Faraday effect and the production of a dc magnetization due to incident circularly polarized light are also reciprocal effects.