Method for measuring the nonlinear index n₂ in optical microresonators

The nonlinear refractive index n₂ is a fundamental parameter in photonics, governing essential third-order nonlinear optical processes, such as self-phase modulation, cross-phase modulation, four-wave mixing, optical parametric oscillation, Kerr frequency comb generation, and supercontinuum generation. While several established techniques exist for measuring n₂, many are unsuitable for fabricated photonic devices or require complex setups. In this work, we present a simple yet highly definitive method to determine n₂ in integrated microresonators. This is accomplished by comparing the optically induced resonant frequency shifts of two modes within the same mode family. We demonstrate this approach using four silicon nitride microring resonators with varying Si/N stoichiometries. The measured relationship between χ⁽³⁾ and χ⁽¹⁾ agrees well with Miller's rule.