We demonstrate both second harmonic generation (with a normalized efficiency of 0.20 %W−1 cm−2 ) and, to our knowledge, the first degenerate χ (2) optical parametric amplifier (with an estimated normalized gain of 0.6 dBW−1/2 cm−1 ) using silicon-on-insulator waveguides fabricated in a CMOS-compatible commercial foundry.
Subwavelength grating (SWG) metamaterial structures are excellent platforms for guided-wave nonlinear optics, but their design and optimization are challenging due to the large number of geometric degrees of freedom and the need for compute-intensive 3D simulations. Here, we demonstrate inverse design of χ(2) SWG waveguides using an efficient and accurate differentiable plane-wave expansion (PWE) eigensolver. Our solver, which incorporates sparse iterative algorithms and subpixel smoothing, enables efficient eigensolution and end-to-end differentiation from geometric parameters to the SWG figure of merit, which depends both on the eigenvalues (first-order perturbation theory) and the eigenvectors and group indices (second-order perturbation theory), both in forward- and reverse-mode. We apply this solver to the design and optimization of metamaterial waveguides for two types of backward SHG: idler-reversed and pump-reversed. This approach may find use in designing periodic structures more generally, including nanobeam cavities, slow-light modulators, and vertically coupled resonators.
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