Linear least-square regression model to predict supercontinuum generation in χ⁽³⁾ waveguides

Supercontinuum-based optical frequency comb sources (OFCs) have become an essential tool for various scientific and technological applications. Typically, these OFCs are generated by nonlinear optical interactions using high peak-power femtosecond lasers in χ⁽³⁾ waveguides. The spectral-temporal profile of these supercontinuum OFCs often dictates the application limitations. Thus, to gain insights into supercontinuum generation, the generalized nonlinear Schrodinger's equation (GNLSE) is employed as an efficient mathematical model. With known optical and waveguide parameters like the nonlinear coefficient, effective length, and higher-order dispersion coefficients, the GNLSE can accurately simulate the evolution of the supercontinuum spectral broadening. However, the complete dispersion profile, including higher order terms, is often difficult to obtain, especially when the material properties and geometries are proprietary. In such cases, complex numerical simulations are required to determine the higher-order dispersion coefficients. To overcome this, we demonstrate a linear least squares regression model to estimate the higher-order dispersion coefficients using limited datasheet information or dispersion-parameters for χ⁽³⁾ waveguides and simulate the supercontinuum broadening using the GNLSE. We validate our simulation with experimental results from a silica photonic crystal fiber using a femtosecond laser as a pump source. We also compare the model with supercontinuum generated from a 7 mm long silicon nitride waveguide. The simulations closely match the experimental observations spanning approximately a 2-octave optical bandwidth.