Mode Locking in the Few-Femtosecond Regime Using Waveguide Arrays and the Coupled Short-Pulse Equations

A new theoretical model is proposed for characterizing the ultrashort (few femtoseconds and below) propagation dynamics in a laser cavity that is mode locked with a waveguide array. The theory circumvents the standard and problematic center-frequency expansion methods that typically result in the nonlinear Schrödinger-based master mode-locking equation. The resulting short-pulse-equation framework, which is the equivalent of the nonlinear Schrödinger equation for ultrafast pulses, provides an asymptotically valid description of the electric-field amplitude, even if pulses are shortened below a single cycle of the electric field. Given the lack of theory in the ultrafast regime, the model provides the beginning theoretical framework for quantifying the pulse dynamics and stability, as pulsewidths approach the attosecond regime.