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

Integrated nonlinear photonics struggles to deliver wafer-scale functional device yields. Nanometer-level fabrication variations compromise the strict frequency-phase matching mandated by energy- and momentum-conserving nonlinear processes. We introduce nested frequency-phase matching, a passive scheme that relaxes these constraints, and implement it in a two-timescale lattice of commercially available silicon nitride (SiN) coupled ring resonators for harmonic generation. The nested lattice simultaneously generates ultrabroad bandwidth light in the fundamental-, second-, third-, and fourth-harmonic bands and achieves 100 percent multifunctional wafer-scale device yield, all passively and without geometry fine-tuning. Distinct spatial and spectral signatures confirm the predicted relaxation of frequency-phase matching, establishing a scalable route for chip-scale nonlinear optics. Our approach provides possibilities for integrated frequency conversion and synchronization, self-referencing, precision metrology, squeezed-light sources, and nonlinear optical computing.