Frequency-domain modelling of gain in pump-probe experiment by an inhomogeneous medium

Introduction of a gain medium in lossy plasmonic metamaterials reduces and compensates losses or even amplifies an incident light often with nonlinear optical effect. Here, optical gain in a pump-probe experimental setup is effectively calculated in the frequency-domain by approximating a gain material as an inhomogeneous medium. Spatially varying local field amplitudes of the pump and probe beams are included in the model to reproduce the inhomogeneous gain effect, in which population inversion occurs most strongly near the surface and decays along the propagation direction. We demonstrate that transmission spectra calculated by this method agree well with finite-difference time-domain simulation results. This simplified approach of gain modelling offers an easy and reliable way to analyze wave propagation in a gain medium without nonlinear time-domain calculation.