Nonlinear wave phenomena in delay differential models of multimode lasers

Andrei Vladimirov
Weierstrass Institute, Mohrenstrasse 39, D-10117 Berlin, Germany
Multimode lasers are widely used in medical, industrial, and technological applications. In particular, mode-locked semiconductor lasers are low cost, compact, and efficient sources of short optical pulses with high repetition rates suitable for application in telecommunication networks. A conventional technique to the theoretical studies of these lasers is based on numerical integration of a system of partial differential equations for the electric field envelope and carrier density. Here we use an alternative approach to describe multimode lasers, based on the use of delay differential equations (DDEs). We investigate DDE models of different multimode laser devices, - nonlinear mirror mode-locked lasers generating short optical pulses, frequency swept lasers with a long dispersive fiber delay line, and broad area external cavity semiconductor lasers. In addition to numerical simulations of these models we perform an analytical linear stability analysis that reveals modulational, Turing-type, and flip instabilities of CW regimes. We demonstrate the existence of bistability, chaotic regimes, square waves, as well as temporal and spatio-temporal (light bullets) localised structures of light and discuss their properties and interaction.