Approaching Upper Bounds to Resonant Nonlinear Optical Susceptibilities with Inverse-Designed Quantum Wells

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We develop a unified framework for identifying bounds to maximum resonant nonlinear optical susceptibilities and for “inverse designing” quantum-well structures that can approach such bounds. In special cases (e.g., second-harmonic generation) we observe that known bounds, a variety of optimal design techniques, and previous experimental measurements nearly coincide. But for many cases (e.g., second-order sum-frequency generation, third-order processes), there is a sizable gap between the known bounds and previous optimal designs. We sharpen the bounds and use our inverse-design approach across a variety of cases, showing in each one that the inverse-designed QWs can closely approach the bounds. This framework allows for comprehensive understanding of maximum resonant nonlinearities, offering theoretical guidance for materials discovery as well as targets for computational design.