Nonlinear Optical Coefficients

Abstract

We consider, from a number of different viewpoints, the tensor coefficients which describe second harmonic generation, optical rectification, and the Pockels or linear electro-optic effect in acentric crystals. Stationary perturbation theory is used to calculate the low-frequency limit of the intrinsic electronic nonlinearity neglecting all effects due to local fields or lattice polarization. Solid methane is used as an example and the result used to estimate the coefficient in hexamethylene tetramine. The calculated result is within a factor of 2 of the experimental figure. The method is susceptible to further refinement and, since it requires only a knowledge of ground state wave functions, and is essentially very simple, it appears to offer a useful approach to the calculation of the coefficients. The classical anharmonic oscillator model is briefly covered and the model is related to a quantal treatment. We find that the anharmonic potential used in the model is directly related to the actual crystalline potential. It can also be related to the charge distribution in the electronic ground state. Local field corrections and the effects of lattice polarization are presented. These alter the nonlinear properties in a simple and obvious way, but one which has been misunderstood in some of the literature. Our results form a theoretical background to Miller's empirical rule relating the nonlinear coefficients to the linear susceptibilities. An extensive table of Miller-reduced tensor coefficients collated from the published literature is presented. Finally, we draw together some of the threads of the previous sections. An appendix deals with the vexing question of definitions.

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