Nonlinear susceptibilities as a function of several complex angular-frequency variables

In this paper, nonlinear susceptibilities of materials are treated as a function of several complex angular-frequency variables, and sum rules for meromorphic nonlinear susceptibilities as well as those for the derivatives of the nonlinear susceptibilities are considered. A method is presented for approximating the real and imaginary parts of the nonlinear susceptibility when only the intensity is known. This presentation is based on the use of conformal mapping and power-series expansion of the nonlinear susceptibility.