Effective linear regimes in plasmonic three-wave mixing

Abstract

The theory of parametric resonances induced by three-wave mixing processes in planar plasmonic structures coupled to second order nonlinear crystals is investigated in detail. The system under study involves a pump field interacting with two counterpropagating surface plasmon polaritons (SPPs), where the permittivity of the dielectric medium is modulated by the pump field’s amplitude. Two distinct linear regimes are identified: linearity in time at the onset of the parametric resonance and linearity with respect to the pump amplitude in the steady state. The former emerges at the onset of the parametric resonance but is suppressed over longer time intervals due to second order interactions that lead to nonlinearity. Conversely, the latter rises thanks to the induction of an effective third order nonlinearity that forces the SPPs’ amplitudes to have a linear relationship with the pump amplitude.