We experimentally study a semiconductor laser subject to two optical feedbacks in a free space setup. We show that control over the feedback phase is essential to adjust the time delay signature in the chaotic output intensity while affecting also the chaotic bandwidth. By optimizing the feedback phase, the time delay signature can be reduced by a factor of more than 2 while maintaining a large chaotic bandwidth.

I. INTRODUCTIONSemiconductor lasers subject to one optical feedback have been extensively studied for their dynamical behavior 3,4 . A wide range of feedback induced dynamics are possible: linewidth narrowing or broadening, periodic and quasiperiodic behavior, low frequency fluctuations or fully developed chaos in the output intensity, to name a few [3][4][5][6] . Adding another optical feedback, thereby subjecting the laser to two distinct optical delays, further increases the complexity. The additional feedback has been shown to either stabilize or further destabilize the laser depending on the feedback parameters 1,7-9 , to suppress chaotic dynamics 10 , to significantly reduce the laser linewidth 11,12 , and to make the chaos more irregular 13 . Towards applications, it could be used for reservoir computing system 14 , chaos control 7,15 , or secure communication [16][17][18][19] . This system has also been considered for improving self-mixing interferomety [20][21][22] . Moreover, in photonic integrated circuits there is no practical optical isolator, hence on-chip lasers could easily be subject to multiple a) Also at

In simulating a semiconductor laser subject to two feedback loops, we observed the dynamics to be dependent on both feedback phases. Even for very low second feedback strength, the second phase has a visible influence.