Frequency-Matched Optical Switching in Slow Nonlinear Media: A Spatiotemporal Design Framework

We introduce a frequency-matching design principle that overcomes speed limitations of slow optical nonlinearities. By matching the optical timescale via modulation frequency or pulse duration to the material's nonlinear response time τ, efficient all-optical switching becomes possible even in thermally dominated, free-carrier-based, or other slow nonlinear systems. The condition ωτ ∼ 1 maximizes switching efficiency and transforms the material response time from a limitation into a design parameter. Combined with spatial barrier engineering via propagation constant tuning, this provides a complete spatiotemporal framework for nonlinear photonic switches. Universal scaling laws and design guidelines are given for various material platforms.