Bifurcation analysis of a semiconductor laser with filtered optical feedback

We study the dynamics and bifurcations of a semiconductor laser with delayed filtered optical feedback, where a part of the output of the laser reenters after spectral filtering. This type of coherent optical feedback is more challenging than the case of conventional optical feedback from a simple mirror, but it provides additional control over the output of the semiconductor laser by means of choosing the filter detuning and the filter width. This laser system can be modeled by a system of delay differential equations with a single fixed delay, which is due to the travel time of the light outside the laser. In this paper we present a bifurcation analysis of the filtered feedback laser. We first consider the basic continuous wave states, known as the external filtered modes (EFMs), and determine their stability regions in the parameter plane of feedback strength versus feedback phase. The EFMs are born in saddle-node bifurcations and become unstable in Hopf bifurcations. We show that for small filter detuning there is a single region of stable EFMs, which splits up into two separate regions when the filter is detuned. We then concentrate on the periodic orbits that emanate from Hopf bifurcations. Depending on the feedback strength and the feedback phase, two types of oscillations can be found. First, there are undamped relaxation oscillations, which are typical for semiconductor laser systems. Second, there are oscillations with a period related to the delay time, which have the remarkable property that the laser frequency oscillates while the laser intensity is almost constant. These frequency oscillations are only possible due to the interaction of the laser with the filter. We determine the stability regions in the parameter plane of feedback strength versus feedback phase of the different types of oscillations. In particular, we find that stable frequency oscillations are dominant for nonzero values of the filter detuning. © 2007 Society for Industrial and Applied Mathematics

Pure frequency oscillations of semiconductor lasers with filtered optical feedback

A semiconductor laser subject to delayed filtered optical feedback can show pure frequency oscillations with a period of the order to the delay time, while the power remains practically constant. This is remarkable in light of the strong self-phase modulation in semiconductor lasers that couples frequency and power. It turns out that the dynamics of the filter plays an essential role in this behavior, because it changes the instantaneous amount of feedback in response to the instantaneous laser frequency. By using numerical bifurcation techniques we show how frequency oscillations bifurcate in Hopf bifurcatious from the continuous wave solutions known as external filtered modes

Dynamics of a filtered-feedback laser: influence of the filter width

The behavior of a semiconductor laser subject to filtered optical feedback is studied in dependence on the width of the filter. Of special interest are pure frequency oscillations where the laser intensity is practically constant. We show that frequency oscillations are stable in a large region of intermediate values of the filter width, where the dispersion of the filter is able to compensate for the well-known phase-amplitude coupling of the semiconductor laser. Our stability diagram covers the entire range from a very narrow filter, when the system behaves like a laser with monochromatic optical injection, to a very broad filter, when the laser effectively receives conventional (i.e., unfiltered) optical feedback. (C) 2007 Optical Society of America

Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback

We investigate the dynamics of a semiconductor laser subject to coherent delayed filtered optical feedback. A systematic bifurcation analysis reveals that this system supports two fundamentally different types of oscillations, namely relaxation oscillations and external roundtrip oscillations. Both occur stably in large domains under variation of the feedback conditions, where the feedback phase is identified as a key quantity for controlling this dynamical complexity. We identify two separate parameter regions of stable roundtrip oscillations, which occur throughout in the form of pure frequency oscillations