Isothermal and Isolated Susceptibilities for a Nonlinear Refractive Index

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Abstract
Using a canonical-transformation method, a formal expression for the isothermal polarization induced by an arbitrarily time-varying field is obtained which includes the population change due to the energy shift which is proportional to the field intensity. The result is applied to the static linear susceptibility and nonlinear refractive index induced by an intense laser beam. It is shown for the latter that the lowest- (third-) order isolated susceptibility of an isotropic medium is a lower bound for the isothermal susceptibility if both the polarizations and frequencies of the laser beam and the probe light are the same.