title: Analytic theory of self-similar mode-locking.
abstract: A theoretical model is developed to quantify the experimental observations of self-similar parabolic pulses in a mode-locked laser cavity with net-zero dispersion. The averaging procedure used shows the pulse amplitude to be governed by the porous media equation that has the well-known Barenblatt similarity (parabolic) solution, suggesting that it is a viable theoretical description of temporal profiles observed in mode-locked cavities. To the best of our knowledge, this is the first analytic model proposing a mechanism responsible for generating temporal parabolic pulses.
authors.affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-2420, USA.
authors.forename: Brandon G
authors.initials: BG
authors.lastname: Bale
authors.forename: J Nathan
authors.initials: JN
authors.lastname: Kutz
authors.forename: Frank
authors.initials: F
authors.lastname: Wise