Efficient method for evaluation of second-harmonic generation by surface integral equation

Abstract

A frequency-domain method based surface integral equation of the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai formulation is presented as a full wave analysis to evaluate surface second-harmonic generation from noble metal nanoparticles of virtually arbitrary shape. According to the similar solution of fields and boundary conditions at fundamental and second-harmonic frequency, we get the derivation of surface integral equation formulations with only half unknowns compared with the conventional surface integral equation method. Simultaneously, the condition number of impedance matrix has been sharply declined. Numerical examples of gold nanospheres of different radius are presented to demonstrate the accuracy and efficiency of the proposed method. To further research the distribution of surface nonlinear polarization and properties of the second-harmonic radiation, we apply our method to a noncentrosymmetric L-shaped gold nanoparticle studied experimentally. This method provides an efficient and promising approach for evaluation of nonlinear optical radiation generated from metal nanoparticles array and optimization design of nonlinear nanoantennas.