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.

Figure 1

Experimental setup with the laser and the feedback loop with a Fabry-Pérot, beamsplitter (BS), optical isolator (ISO), mirrors (M), and electrical spectrum analyzer (ESA) for measuring the laser (ESA 1) and feedback light (ESA 2).

Figure 2

Time series of $I_L$, $I_F$ ${\dot{\Phi }}_L$, and ${\dot{\Phi }}_F$ of ROs (a), FOs (b), and quasi-periodic FOs (c). From (a) to (c) $(\kappa ,C_p)$ takes the values $(0.02,-8∕3\pi )$, $(0.07,-6\pi )$, and $(0.014,-6\pi )$.

Figure 3

Regions of different dynamics in the $(\kappa ,C_p)$-plane with stable EFMs (light gray) and stable FOs or ROs (dark gray). Bifurcation curves are saddle-node (SN), saddle-node of limit cycle (SL), Hopf (H), and torus (T) bifurcations. Codimension-two points are Bogdanov-Takens (BT), saddle-node Hopf (SNH), degenerate Hopf (DH), 1:1 resonance (1:1), and double Hopf (HH) points. The points (a)–(c) indicate the parameter values of the time series of Fig. 2. The inset shows an enlarged view at the tip of the lower FO region.

Figure 4

Experimental RIN spectra of FOs: Intensity (a) and frequency measured as the feedback intensity (b) of the laser.