Relative Refractory Period in an Excitable Semiconductor Laser

We report on experimental evidence of neuronlike excitable behavior in a micropillar laser with saturable absorber. We show that under a single pulsed perturbation the system exhibits subnanosecond response pulses and analyze the role of the laser bias pumping. Under a double pulsed excitation we study the absolute and relative refractory periods, similarly to what can be found in neural excitability, and interpret the results in terms of a dynamical inhibition mediated by the carrier dynamics. These measurements shed light on the analogy between optical and biological neurons and pave the way to fast spike-time coding based optical systems with a speed several orders of magnitude faster than their biological or electronic counterparts.

Figure 1

Sketch and scanning electron microscope (SEM) image of the micropillar laser with saturable absorber (see text). Pump light (red arrow) is incoming from the top and is partially reflected from the remaining part of the lower Bragg mirror.

Figure 2

(a) Amplitude of the response $R_1$ to a single pulse perturbation versus perturbation energy $E$ for varying bias pump $P$ relative to the self-pulsing threshold $P_{\mathrm{SP}}=694\mathrm{mW}$. (b) Theoretical response amplitude $R_1$ to single input $\delta$-perturbation pulse ${\mu }_{\delta }$ for different bias pumps ${\mu }_1$ ranging from 2.8 to $-42.2$. Note that the curves are offset by ${\mu }_1$ for clarity. (c) Dependance of the excitable threshold $E_{\mathrm{th}}$ (red circles) with reduced bias pump $P/P_{\mathrm{SP}}$ and linear fit (blue line). (d) Excitable threshold ${\mu }_{\delta }$ versus bias pump ${\mu }_1$. The blue line is the theoretical appproximation given by $-{\mu }_1+1+{\mu }_2$.

Figure 3

(a) Recorded time traces for different delays and their Gaussian fits. Upper traces are the input perturbations and the lower traces are the system’s response. The bias pump is set to 71% of the SP threshold. (b) Amplitude of the response $R$ to the first (black) and second (red or gray) perturbation pulses for a double-pulse perturbation with variable delays. $R_{\mathrm{th}}$ is the response amplitude at the excitable threshold. Lines are linear fits in selected ranges and are guides for the eye.

Figure 4

(a) Experimental measurements of the amplitude of the response to a second perturbation pulse after a first pulse has been sent at $t=0$ whose amplitude is 20% above the excitable threshold and has triggered an excitable response, for different delays between the two pulses. Bias pumping is $0.71P_{\mathrm{SP}}$. (b) Same as (a) according to the model [Eqs. (1)]. Time is rescaled to photon lifetime.

Figure 5

Intensity $I(t)$, recovery dynamics of carriers $G(t)$, $Q(t)$ and net gain $\mathrm{\Gamma }(t)$ for a double delta perturbation at $t_0=0$ and $t_1=250$. The first perturbation has amplitude ${\mu }_{\delta }(t_0)=3.5$ while the second perturbation is below (a), ${\mu }_{\delta }(t_1)=1.0$, and above (b), ${\mu }_{\delta }(t_1)=1.5$, the excitable threshold. Other parameters are unchanged. The initial state is the steady state.