Scattering matrix for chiral harmonic generation and frequency mixing in nonlinear metasurfaces

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 microscopic and macroscopic symmetries of the metasurface. 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 analyse chiral harmonic generation in nonlinear metasurfaces with various symmetries including rotational, 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.

arXiv comment16 pages, 7 figures, 3 tables, 46 references

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Cited by in corpus (3)

• Chiral Dichroism in Resonant Metasurfaces with Monoclinic Lattices
• Achiral nanostructures: perturbative harmonic generation and dichroism under vortex and vector beams illumination
• A Tensor Product Space for Studying the Interaction of Bipartite States of Light with Nanostructures