Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers

We investigate both theoretically and experimentally the stochastic switching between two counterpropagating lasing modes of a semiconductor ring laser. Experimentally, the residence time distribution cannot be described by a simple one-parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. In order to elucidate the origin of these two time scales, we propose a topological approach based on a two-dimensional dynamical system.

Figure 1

(a) Optical setup. SRL: semiconductor ring laser cavity; WG: bus waveguide; OUT CW and CCW: optical outputs. Each of the outputs can be coupled to an oscilloscope through an optical fiber. (b) Measured RTD in the CCW mode for a laser current of $J_{\mathrm{ring}}=39.92\mathrm{mA}$; the waveguide is biased at 8.22 mA and the temperature is $21.55°\mathrm{C}$. (c) RTD obtained by simulating Eqs. (1, 2) with the following parameters: $\mu =1.59$, $\alpha =3.5$, $s=0.005$, $c=0.01$, $k=0.44{\mathrm{ns}}^{-1}$, ${\varphi }_k=1.5$, $D=6.5\times {10}^{-5}{\mathrm{ns}}^{-1}$. Best fitting lines are shown in white.

Figure 2

Comparison between measured time series (a)–(c), simulated time series (d)–(f), and phase space trajectories (g)–(i) for different kinds of transitions. In the experiment the ring was biased at $J_{\mathrm{ring}}=39.86\mathrm{mA}$, the waveguide was biased at 8.22 mA, and the temperature was $21.55°\mathrm{C}$. In the numerical simulation the following parameters were used: $\mu =1.59$, $\alpha =3.5$, $s=0.005$, $c=0.01$ $k=0.44{\mathrm{ns}}^{-1}$, ${\varphi }_k=1.5$, $D=6.5\times {10}^{-5}{\mathrm{ns}}^{-1}$. The notation of (g)–(i) is as follows: CW, CCW are the stable states, $S$ is the saddle; solid line: stable manifold of $S$; dashed line: unstable manifold of $S$; gray: projection of the time series (d)–(f).