Exploring Multistability in Semiconductor Ring Lasers: Theory and Experiment

We report the first experimental observation of multistable states in a single-longitudinal mode semiconductor ring laser. We show how the operation of the device can be steered to either monostable, bistable, or multistable dynamical regimes in a controlled way. We observe that the dynamical regimes are organized in well-reproducible sequences that match the bifurcation diagrams of a two-dimensional model. By analyzing the phase space in this model, we predict how the stochastic transitions between multistable states take place and confirm it experimentally.

Figure 1

Experimental SRL setup. Four waveguide contacts are depicted of which only the one denoted by $I_w$ is biased.

Figure 2

Bifurcation diagrams of Eqs. (1, 2) for (a) ${\varphi }_k=0.2$ and (b) ${\varphi }_k=1.5$ Stable solutions of Eqs. (1, 2) are marked in black, unstable ones in gray. Dashed lines are used to indicate periodic solutions. The Roman numbers I–V indicate different dynamical regimes.

Figure 3

Phase space portraits of Eqs. (1, 2) for different values of $J$ and ${\varphi }_k$. The notation is as defined in the text. (a) ${\varphi }_k=0.2$, $J=1.05$, (b) ${\varphi }_k=1.5$, $J=0.75$, (c) ${\varphi }_k=1.5$, $J=0.5$, (d) ${\varphi }_k=1.5$, $J=0.66$.

Figure 4

Simulations vs experiments for a sequential transition $U_1\to B_1\to U_2$ for the phase space described in Fig. 3b. (a) Projection on the phase space; (b) numerical time series; (c) experimental data. The model parameters for (a),(b) are $J=1.05$, ${\varphi }_k=1.02$, $\alpha =3.5$. The experimental conditions for (c) were $I_p=45.31\mathrm{mA}$ and $I_w=9.81\mathrm{mA}$.

Figure 5

Experimentally measured time series for different bias currents $I_p$ and $I_w$ corresponding to the dynamical regimes of Fig. 3. (a) $I_w=9.81\mathrm{mA}$, $I_p=44.35\mathrm{mA}$; (b) $I_w=9.81\mathrm{mA}$, $I_p=45.21\mathrm{mA}$; (c) $I_w=9.81\mathrm{mA}$, $I_p=46.39\mathrm{mA}$; (d) $I_w=12.0\mathrm{mA}$, $I_p=40.23\mathrm{mA}$; (e) $I_w=12.0\mathrm{mA}$, $I_p=44.34\mathrm{mA}$; (f) $I_w=12.0\mathrm{mA}$, $I_p=45.94\mathrm{mA}$. The insets show a zoom on relevant segments of the time series.