Influence of time-distribution in lasers subject to feedback from long FBGs

Fiber Bragg grating (FBG) feedback has initially been investigated as a promising approach to conceal the time-delay signature in optical chaos generation. It has been shown that the laser dynamics vary greatly with respect to the FBG properties, especially to the frequency detuning between the laser emission and the Bragg wavelength. As a result, adjusting the FBG features will lead to significantly different behaviour.

Here, we theoretically study the response of FBGs with different lengths but with similar reflectivity: this way, the impulse response is stretched over a longer period of time while its overall shape is maintained. This leads to a broadening of the FBG bandwidth and, thus, to a longer distribution of the feedback over time. In this work, we analyse the effects of the time-distribution variations for long gratings by simply tracking the first Hopf bifurcation and the feedback rate needed to destabilize the laser. The numerical results are generated using a modified version of the well-known Lang and Kobayashi equations. Our results show that the time-distribution of the feedback seem to have little effect in itself on the overall dynamics though it obviously affects the FBG spectra properties. We report stability oscillations of the laser behavior when long, narrow-bandwidth gratings are considered. The influence of the grating length on the specific dynamic details is investigated through the time delay signature (TDS) focusing especially on the implication of the stability oscillations on the TDS. We report that although variation of the TDS for long grating are observed the better TDS suppression is achieved with relatively short gratings.