Cavity soliton properties and dynamics in a VCSEL with frequency-filtered feedback

Cavity soliton lasing was recently demonstrated in VCSELs with feedback from a grating [1]. In this paper we discuss the basic underlying theory of such cavity soliton lasers. Introduction of frequency-dependent losses is shown to allow stabilization of dissipative solitons in a complex Ginzburg-Landau model with simple cubic or saturable nonlinearity. Analytic solutions are found for the former case in one dimension (ID), and robust solitons are found numerically in two dimensions (2D), and for the saturable case. Separation into spectral and spatial-nonlinear problems is an effective and flexible technique to guide analysis, numerics and experiment.