Nonlinear Dielectric Polarization in Optical Media

TLDR

Second‑order dielectric polarization in optical media arises from ionic crystal dispersion, with lattice contributions dominating the linear electro‑optic effect and suggesting significant nonlinearity compared to electronic responses. The study aims to determine the mechanism behind second‑harmonic generation in strong laser beams by testing the symmetry of the effect. Four mechanisms are identified: three lattice‑based (anharmonicity, second‑order moment, Raman scattering) that are strongly frequency‑dependent, and one electronic, frequency‑flat, subject to additional symmetry constraints. The electronic mechanism, being dominant at optical frequencies, reduces the number of independent constants to one for materials such as quartz and KDP.

Abstract

The physical mechanisms which can produce second-order dielectric polarization are discussed on the basis of a simple extension of the theory of dispersion in ionic crystals. Four distinct mechanisms are described, three of which are related to the anharmonicity, second-order moment, and Raman scattering of the lattice. These mechanisms are strongly frequency dependent, since they involve ionic motions with resonant frequencies lower than the light frequency. The other mechanism is related to electronic processes of higher frequency than the light, and, therefore, is essentially flat in the range of the frequencies of optical masers. Since this range lies an order of magnitude higher than the ionic resonances, the fourth mechanism may be the dominant one. On the other hand, a consideration of the linear electro-optic effect shows that the lattice is strongly involved in this effect, and, therefore, may be very much less linear than the electrons. It is shown that the question of the mechanism involved in the second harmonic generation of light from strong laser beams may be settled by experiments which test the symmetry of the effect. The electronic mechanism is subject to further symmetry requirements beyond those for piezoelectric coefficients. In many cases, this would greatly reduce the number of independent constants describing the effect. In particular, for quartz and KDP there would be a single constant.