Abstract

Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal, and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for self-focusing and self-phase modulation, a general transverse gain profile, and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications include the temporal pulse dynamics in gain fibers and the beam propagation or spatiotemporal pulse evolution in bulk gain media. As an example, the steady-state spatiotemporal Gaussian pulse dynamics in a Kerr-lens mode-locked laser resonator is studied.

© 2006 Optical Society of America

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