CONTINUOUS-WAVE MODE-LOCKED SOLID-STATE LASERS WITH ENHANCED SPATIAL HOLE-BURNING .2. THEORY

Part I of this paper [1] experimental results were presented and discussed. In this part, we investigate theoretically the dynamics of end-pumped solid-state lasers due to enhanced spatial hole burning. This becomes possible by a fast numerical implementation of the saturated gain in the presence of strong spatial hole burning that allows to treat the multimode case for an arbitrary pumping level. We find for a wide range of laser parameters that the mode spacing of the cw running modes is essentially determined by the length of the gain medium and only weakly depends on the absorption depth of the pump transition. It is shown that spatial hole burning can lead to a completely flat saturated gain profile over half of the gain bandwidth. In mode-locked lasers, the flat gain due to spatial hole burning results in shorter pulses. But the pulses are neither Gaussian-nor sech-shaped as they are in actively or passively mode-locked lasers without: spatial hole burning. Further, we show that soliton-like pulse shaping can be used to restore a transform-limited sech-shaped pulse in an end-pumped solid-state laser while exploiting the full gain bandwidth of the laser material.