Second harmonic generation in random nonlinear dielectrics: Effective medium approximations and dilute limit expressions

摘要

Based on a general expression previously derived for the effective coefficient for second harmonic generation (SHG) in a random composite of nonlinear dielectrics, we develop and compare several possible effective medium approximations (EMAs). The general expression involves the volume average of products of local field factors of the form ,and the three EMAs amount to different decoupling schemes, and they all invoke the EMA for a linear binary composite. The performance of these EMAs is assessed by comparing with numerical results obtained by simulations on random resistor networks. We also derived the corresponding dilute limit expressions for each of the EMAs. The expressions differ in the terms that are proportional to the SHG coefficient of the majority component, and the different decoupling schemes give different terms that are quadratic in the dielectric contrast between the linear dielectric constants of the two constituents at the fundamental and second harmonic frequencies.