Description of intermodulation generation of nonlinear responses beyond the validity of the power series expansion

Abstract

Weakly nonlinear responses are commonly described by a power series expansion. However, intermodulation distortion products that cannot be described by a power series have been observed in a variety of physical systems. As the power series description is only applicable within its radius of convergence, we choose an alternative approach based on Fourier coefficients to describe intermodulation levels beyond the convergence of the power series. The description over a wide power range allows us to make a decision about models and to determine previously inaccessible model parameters. We apply the approach to data obtained from the characterization of the nonlinear dielectric susceptibility of a glass ceramic in the microwave range. The data are accurately modeled by a saturable absorber's response. We obtain the absorber's linear contribution to the polarization (χ1=10−5) as well as its characteristic ratio of nonlinear and linear polarization (χ3/χ1=10−9 m2/V2). Due to the small contribution of the saturable absorber to the overall polarization, the material shows a highly linear response (χ3=10−14 m2/V2).