Class-A mode-locked lasers: Fundamental solutions

Abstract

We consider a delay differential equation (DDE) model for mode-locked operation in class-A semiconductor lasers containing both gain and absorber sections. The material processes are adiabatically eliminated as these are considered fast in comparison to the delay time for a long cavity device. We determine the steady states and analyze their bifurcations using DDE-BIFTOOL [K. Engelborghs, T. Luzyanina, and D. Roose, ACM Trans. Math. Softw. 28, 1 (2002)]. Multiple forms of coexistence, transformation and hysteretic behavior of stable steady states and fundamental periodic regimes are discussed in bifurcation diagrams.Lasers operate in a certain range of discrete optical frequencies known as longitudinal modes. Lasing modes may synchronize and provide pulse trains with fixed time separation between pulses, a phenomenon known as mode-locked laser operation. Mode locking (active or passive) finds application in a diversity of fields in physics, chemistry, biology and engineering. The passive technique is based on intracavity nonlinearities, and, in particular, on a saturable absorber. In this paper, we report the bifurcation analysis of a single delay differential equation suitable to describe a class-A semiconductor laser with saturable absorber. We analyze the conditions required for generation of a fundamental solution, i.e. periodic pulses equally spaced by the cavity round trip time. The appearance of the fundamental solution relates to a multiple folding phenomenon, but results from a Hopf bifurcation.