Closed Form Resonance Solution in Metallic Nanoparticles with Cubic Nonlinearity

Higher order intensity of light introduces third order nonlinear susceptibility in metallic nanostructures. Circuit theory is often used to represent complex phenomena and adequately models the frequency dependent linear resonance in metallic nanostructures with great accuracy. In this article, we use the linear circuit approach and propose a compact impedance model to represent resonance in metallic nanoparticle with cubic nonlinearity. The model uses full-wave dipole equation by employing all time-dependent fields and introduces the concept of nonlinear radiation impedances. Analytical expressions for the nonlinear radiation (internal and external) impedances are derived and used for the first time to get the close-form expression of nonlinear (NL) scattering cross-sectional area using voltages, currents and circuit elements. The effects of nanoparticle parameters i.e. radius, intensity and dielectric function of surrounding medium on cubic nonlinearity are analyzed using impedance model. The validated close-form impedance model preserves the macroscopic properties to give intuitive understanding of NL behavior necessary in facilitating next-generation nanophotonics applications.