Scattering matrix for chiral harmonic generation and frequency mixing in nonlinear metasurfaces
Kirill Koshelev, Ivan Toftul, Yongsop Hwang, Yuri S. Kivshar
Abstract
Abstract We generalize the concept of optical scattering matrix ( S -matrix) to characterize harmonic generation and frequency mixing in planar metasurfaces in the limit of undepleted pump approximation. We show that the symmetry properties of such nonlinear S -matrix are determined by the metasurface symmetries at the macroscopic and microscopic scale. We demonstrate that for description of degenerate frequency mixing processes such as optical harmonic generation, the multidimensional S -matrix can be replaced with a reduced two-dimensional S -matrix. We show that for metasurfaces possessing specific point group symmetries, the selection rules determining the transformation of the reduced nonlinear S -matrix are simplified substantially and can be expressed in a compact form. We apply the developed approach to analyze chiral harmonic generation in nonlinear metasurfaces with various symmetries including rotational, inversion, in-plane mirror, and out-of-plane mirror symmetries. For each of those symmetries, we confirm the results of the developed analysis by full-wave numerical calculations. We believe our results provide a new paradigm for engineering nonlinear optical properties of metasurfaces which may find applications in active and nonlinear optics, biosensing, and quantum information processing.