The role of nonlocal response in second harmonic generation at metasurfaces with triangular metaatoms

Abstract

Metasurface consisting of square array of obtuse isosceles triangle metaatoms is found to exhibit much more efficient second harmonic generation (SHG) compared to that of split ring resonators and its heptagonal modification, experimentally as well as numerically. All of them are designed to lack inversion symmetry in horizontal direction but to have vertical symmetry, and to meet the double resonance condition for vertically-polarized fundamental and horizontally-polarized SHG waves. SHG efficiencies were estimated numerically for each structure by evaluating an overlap integral of second order nonlinear polarization and field distribution at the SHG wavelength. The large overlap integral for the triangle metasurface is ascribed to the nonlocal response at the SHG wavelength. Current induced at the center of the triangle near the obtuse angle by horizontally polarized light at SHG wavelength flows toward two corners of acute angles. As a result, polarization charges oscillate in time at the surfaces of two acute corners, which results in strong field oscillation away from the center where the electric field is applied to majority of free electrons. Experimentally observed wavelength dependence of SHG efficiencies for the three metasurfaces are reasonably reproduced by a numerical estimation.