Semiclassical theory for plasmons in two-dimensional inhomogeneous media

The progress in two-dimensional materials has led to rapid experimental developments quantum plasmonics, where light is manipulated using plasmons. Although numerical methods can be used quantitatively describe plasmons spatially inhomogeneous systems, they are limited relatively small setups. Here, we present a novel semi-analytical method media within the framework of Random Phase Approximation (RPA). Our approach based on semiclassical approximation, which formally applicable when length scale inhomogeneity much larger than plasmon wavelength. We obtain an effective classical Hamiltonian for by first separating in-plane and out-of-plane degrees freedom subsequently employing Ansatz electrostatic potential. illustrate this general theory considering scattering radially symmetric inhomogeneities. derive expression differential cross section compute its values specific model inhomogeneity.