Multi-timescale frequency-phase matching for high-yield nonlinear photonics

Integrated nonlinear photonic technologies, even with state-of-the-art fabrication with only a few nanometer geometry variations, face significant challenges in achieving wafer-scale yield of functional devices. A core limitation lies in the fundamental constraints of energy and momentum conservation laws. Imposed by these laws, nonlinear processes are subject to stringent frequency and phase matching (FPM) conditions that cannot be satisfied across a full wafer without requiring a combination of precise device design and active tuning. Motivated by recent theoretical and experimental advances in integrated multi-timescale nonlinear systems, we revisit this long-standing limitation and introduce a fundamentally relaxed and passive framework: nested frequency-phase matching. As a prototypical implementation, we investigate on-chip multi-harmonic generation in a two-timescale lattice of commercially available silicon nitride (SiN) coupled ring resonators, which we directly compare with conventional single-timescale counterparts. We observe distinct and striking spatial and spectral signatures of nesting-enabled relaxation of FPM. Specifically, for the first time, we observe simultaneous fundamental, second, third, and fourth harmonic generation, remarkable 100 percent multi-functional device yield across the wafer, and ultra-broad harmonic bandwidths. Crucially, these advances are achieved without constrained geometries or active tuning, establishing a scalable foundation for nonlinear optics with broad implications for integrated frequency conversion and synchronization, self-referencing, metrology, squeezed light, and nonlinear optical computing.