Cage solitons of the Haus Master Equation

Laser mode-locking is traditionally explained in the framework of the Haus Master Equation [1] . Eigensolutions of this partial differential equation propagate without changing their shape on time scales long compared to the cavity roundtrip, that is, these solutions are fundamental solitons of the equation. While there are several different solved Master Equations, the fast saturable absorber variant [1] is probably the most universal, describing Kerr-lens, additive pulse, and nonlinear polarization mode-locking. Chirped hyperbolic secants are known as the fundamental solitons of this Equation and were initially found to describe experimental findings very well. This agreement was challenged by the advent of few-cycle lasers, which showed deviating pulse shapes that rather seemed to agree with unexplainable sinc-like or Bessel-like functional shapes. Here we discuss a generalization of the Haus formalism [2] , solving the Master Equation as a set of coupled ordinary differential equations entirely in the frequency domain. From this differential equation, an algebraic discriminant can be derived that allows determining the complete set of fundamental solitons of this equation. These solitons agree very well with the experimentally reported few-cycle pulse shapes and the corresponding concave spectra. These solutions result whenever the mode-locked laser spectrum starts to encompass the entire available gain bandwidth, which acts like a spectral cage. Consequently, we termed these solutions "cage solitons."