Abstract

There is considerable interest currently, in achieving stable, phase-locked operation of semiconductor laser diode arrays. While this has recently been achieved for linear arrays using novel resonant antiguide devices,^[1] the problem remains unsolved for 2-D surface emitting structures. In particular, concern has been growing over the temporal stability of both 1-D and 2-D arrays which through experimental and limited theoretical studies, have indicated that unstable and often chaotic behaviour is the norm.^[2] Mainly through cpu limitations, the numerical work has necessarily been limited ≤10 devices. In this paper we propose certain physically reasonable assumptions which, although restricting applicability, at least allows progress to be made on arrays consisting of much larger numbers of devices. The particular methods used have also allowed a restricted analytic analysis to be carried out, based on coupled nonlinear oscillator theory in the thermodynamics limit of N→ ∞.^[3] Our specific assumptions are: (i) The field in each device can be described by a single modal field, the spatio-temporal dynamics of which is governed by coupled mode equations. It is recognized that this is a gross simplification for many structures, although because of superior modal properties, index guided arrays (for which the approach is valid) have always been preferred where technologically feasible. Current spreading and anti-guiding effects are therefore ignored in our model, (ii) Experimentally it is observed that instabilities occur on sub-ns timescales,^[2] the power emitted over longer times being roughly constant. The difference between the photon (10⁻¹²s) and carrier (10⁻⁹s) lifetimes suggests that the complex dynamics arises purely due to coupled optical fields and to first order is not influenced by the carrier dynamics, which we assume to be constant. From the numerical viewpoint, this provides a model in which the differential equations are not stiff. Despite the restrictiveness of these assumptions, we show that the resulting model gives rise to instabilities which are consistent with those observed in practise (Fig. 1). With a large number of devices, the statistical variations between device parameters is important and is explicitly included in our model. Also, we allow for more general coupling schemes other than nearest neighbour evanescent coupling, reflecting the diversity of available structures.

© 1992 IQEC