Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (f_CEO) and experimentally investigate the static and dynamic f_CEO dependence on pump power. We find good agreement with the measured dependence of f_CEO on laser output power, showing a broad f_CEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157 dBc/Hz level leading to a tenfold reduction in f_CEO-linewidth.