Regular Article

Semiconductor mode-locked laser with external feedback: emergence of multi-frequency pulse trains with an increasing number of modes^★

¹ Institute of Theoretical Physics, Technische Universität Berlin, 10623 Berlin, Germany
² Dodd Walls Centre for Photonic and Quantum Technologies, Department of Mathematics, University of Auckland, Auckland, New Zealand

^a e-mail: B.Krauskopf@auckland.ac.nz

Received: 12 November 2018
Received in final form: 26 February 2019
Published online: 23 April 2019

Abstract

We investigate a mode-locked laser with optical feedback and a spectral filter that limits the number of lasing modes. For up to around ten modes the laser effectively behaves as a single-mode laser: it may generate Q-switched pulses but does not mode lock. When the number of modes is increased we observe the emergence of multi-frequency pulsing associated with invariant tori and multistability. We model this system with a delay differential equation system for the electric field, the gain and the absorption, and present a bifurcation analysis of the route to this type of pulsing. For increasing spectral filter width we present bifurcation diagrams in the plane of delay time and strength of the external feedback loop. The associated dynamics are represented by means of 2D period-roundtrip diagrams and 2D spectral plots. We illuminate the emergence of dynamics on different tori and the corresponding frequencies involved.