Classical Derivation of Nonlinear Susceptibilities for the 32 Crystal Classes in the Harmonic Oscillator Approximation.
HARRY DIAMOND LABS ADELPHI MD
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New applications relating to optical information processing, optical limiting, and frequency-agile laser systems have produced a resurgence of interest in nonlinear optical materials. In this work, we extend the classical anharmonic analysis to describe the nonlinear optical properties of the 32 crystal classes. We derive expressions for and relationships between the nonlinear susceptibility tensor elements in terms of the anharmonic force constants according to the crystal class symmetry. We show that all the susceptibilities thus derived Chi 1, Chi 2, and Chi 3 obey the Kleinman conditions. Finally, we discuss the possible application of these results, coupled with a point-charge model, for estimating the nonlinear force constants, in the prediction of potential new nonlinear materials. Keywords include Nonlinear optics, and Harmonic oscillator model.
- Theoretical Mathematics