Excitability in a Quantum Dot Semiconductor Laser with Optical Injection

We experimentally analyze the dynamics of a quantum dot semiconductor laser operating under optical injection. We observe the appearance of single- and double-pulse excitability at one boundary of the locking region. Theoretical considerations show that these pulses are related to a saddle-node bifurcation on a limit cycle as in the Adler equation. The double pulses are related to a period-doubling bifurcation and occur on the same homoclinic curve as the single pulses.

Figure 1

Experimental microwave mask (a) and parameter space mapping (b). Slave laser currents are 45 mA and 60 mA, respectively. Master power on left is 4 mW; fits on right are included as guides for the eye.

Figure 2

Experimental single (a) and double (b) excitable intensity pulses. $P_m$ is 3 mW and 4 mW, respectively; slave current is 80 mA, $\Delta =9\mathrm{pm}$ and 12 pm, respectively. Switching between locked state and limit cycle (c) with zoom of the limit cycle oscillations (d). $P_m$ is 4 mW, slave current 45 mA, $\Delta =9\mathrm{pm}$.

Figure 3

($S_m$, $\Delta$) parameter space of Eqs. (1). The master power is plotted along the $x$ axis and the detuning along the $y$ axis. Regions 1 and 2 are unlocked; region 3 is stably locked; region 4 is bistable between two fixed points of different phase; region 5 is bistable between a stable fixed point and a limit cycle; in region 6 the laser exhibits excitable pulsing.

Figure 4

Parameter space mapping of part of region 6 exhibiting excitable pulses. Single excitable pulses are found in region 6S; double excitable pulses are found in 6D. The regions above SN contain stable limit cycle (LC) and stable double limit cycles (DLC). A period-doubling line (PD) separates LC from DLC. The shaded set is bounded by limit-cycle fold-bifurcation boundary LCF. Numerically obtained single and double pulses are inset in regions 6S and 6D, respectively.