Abstract

Mode-locking is a very efficient technique to generate short optical pulses with high repetition rates used in many applications. A conventional approach to model semiconductor mode-locked lasers is based on the use of the so-called traveling wave equations, a system of partial differential equations governing the space-time evolution of the amplitudes of counter-propagating waves and the carrier density in the semiconductor medium. On the other hand, simpler and efficient approach to model mode-locked lasers exploiting a system of delay differential equations (DDEs) was proposed in [1]. In particular, a modification of the DDE model was used to describe the dynamics of frequency swept Fourier domain mode-locked (FDML) [2] and sliding frequency mode-locked [3] lasers used in optical coherence tomography. However, despite of its considerable success in modelling the dynamics of mode-locked, frequency swept, as well as other types of multimode semiconductor lasers, the DDE model does not account for such important physical factor as non-resonant second order intracavity dispersion. In order to fill this gap, we have developed a new model of a multimode semiconductor laser that takes into account non-resonant chromatic dispersion. This model satisfies automatically the causality principle and, in addition to fixed delay, contains a distributed delay term with explicit analytical expression for the response function. The distributed DDE model can be reduced to an infinite chain of delay differential equations with a single fixed delay which can be truncated in the case when the non-resonant dispersion is sufficiently small.

© 2017 IEEE