Single-parameter optimization of supercontinuum generation in bulk media based on effective interaction length

Optimizing supercontinuum generation (SCG) in bulk media usually requires empirical tuning of the pump power, focusing numerical aperture, and crystal length. Here, we show that these coupled parameters can be effectively described by an effective interaction length, L_eff defined by the nonlinear-focusing dynamics in the medium. Using 180 fs, 1030 nm pulses, we experimentally characterize SCG in bulk YAG and find that the infrared spectral bandwidth scales nearly linearly with L_eff. Because L_eff can be estimated analytically from the input beam parameters and material nonlinearity, this scaling provides a practical route for predicting and optimizing the SCG bandwidth. It also enables physically guided selection of experimental conditions for target infrared supercontinuum spectra.