Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain

Abstract

The ABCD-matrix formalism is generalized for the description of self-focusing and radially varying pump power in a nonparabolic approximation. This extended formalism is used for the investigation of the operation and for the optimization of the saturable aperture loss, the power-dependent average gain, and the resonator magnification of Kerr-lens mode-locked lasers with as well as without an internal aperture. The calculated amplitude modulation parameters are compared with the necessary condition for self-starting and for the shortest possible pulse duration limit.