Integrating efficient second-order (χ(2)) optical nonlinearity into topological integrated photonic systems presents a fundamental challenge: frequency-dependent topological bandgaps inherently impede simultaneous, robust edge states at cross-octave frequencies required for second-harmonic generation (SHG). We overcome this limitation by introducing, based on theoretical modeling and numerical simulations, dual-frequency topological bandgap engineering in a square lattice of nonlinear microresonators with synthetic magnetic fluxes. Our design achieves unidirectional edge states for both fundamental and second-harmonic frequencies. It enables efficient SHG with flux-programmable chirality, a unique consequence of χ(2) nonlinearity-induced topology transitions in the system. The topological array yields an SHG efficiency enhancement of two orders of magnitude compared to a single resonator. Our design can be readily implemented by using χ(2) integrated photonic platforms like thin film lithium niobate, which would unlock novel functionalities such as nonreciprocal SHG diodes, optical logic gates, and a pathway to topology-protected entangled photon sources. Photonic topological insulators guide light robustly, but not at multiple colors needed for applications like frequency doubling. The authors theoretically demonstrate a broadband nonlinear resonator array that overcomes this, hosting topological edge states for two colors to achieve efficient nonlinear light conversion and programmable chirality.
Wang et al. (Wed,) studied this question.