TY - JOUR

T1 - From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

AU - Paulau, P. V.

AU - Gomila, D.

AU - Colet, P.

AU - Malomed, B. A.

AU - Firth, W. J.

PY - 2011/9/23

Y1 - 2011/9/23

N2 - We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m = infinity, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.

AB - We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m = infinity, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.

KW - vortex solitons

KW - dissipative solitons

KW - optical solitons

KW - stability

KW - 2-component active systems

KW - Ginzburg-Landau model

KW - frequency-selective feedback

KW - lasers

U2 - 10.1103/PhysRevE.84.036213

DO - 10.1103/PhysRevE.84.036213

M3 - Article

VL - 84

JO - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1539-3755

IS - 3

M1 - 036213

ER -