Fig. 2: Working principle for arbitrary chirality of TH radiation.

A The amplitudes (solid lines) and phases (dashed lines) of the x- and y-components of the superposition of forward TH radiation induced by the x and y components of the uncoupled field \({{{{\bf{E}}}}}_{0}^{(3\omega )}\) “x uncp” and “y uncp” (top two panels), and the amplitudes (solid lines) and phases (dashed lines) of the main component (y component for mode 1, and x component for mode 2 and 3) of the forward radiation of three expanded eigenmodes (bottom 3 panels) at the TH wavelength 731.98 nm, which are excited differently at different polarization angle θ. B The electric field amplitude (|E|) of three eigenmodes at 734.6 nm, 731.7 nm, and 731.2 nm, respectively. The fields are taken from the x-y plane in the middle of trapezoid nanopillar, and their corresponding forward radiation polarization are shown in the top-right boxes. C and D are the real (gray solid arrow) and imaginary (gray dotted arrow) parts of vector sum of all components at θ = 83.5^o and θ = 96.5°, respectively, marked by the corresponding vertical dashed-dotted lines I and II in (A). All expanded components are plotted in the same colors as in (A). Their individual real and imaginary parts are also denoted as solid arrows and dotted arrows, respectively. A slight change in the incident polarization state leads to a complete reversal of the THG helicity in (C) and (D).