Excitability and self-pulsing in a photonic crystal nanocavity

Bistability, excitability, and self-pulsing regimes in an InP-based two-dimensional (2D) photonic crystal nanocavity with quantum wells as an active medium are investigated. A resonant cw beam is evanescently coupled into the cavity through a tapered microfiber. In such conditions, we show that the cavity exhibits class II excitability, which arises from the competition between a fast electronic nonlinear effect, given by carrier-induced refractive index change, and slow thermal dynamics. Multiple perturbation-pulse experiments allow us to measure the refractory time (“dead time” between two excitable pulses) of the excitable nanocavity system.

Figure 1

(a) Schematic of the PhC sample showing the L3 cavity. The InP is bonded onto a silicon substrate through a SiO${}_2$–benzocyclobutene (BCB) layer; the SiO${}_2$ is subsequently removed to obtain a suspended membrane. (b) Tapered fiber optical coupling scheme for transmission and reflectivity measurements. A Scanning Electron Microscopy (SEM) image of the L3 cavity is shown. (c) Sketch of the tapered fiber characteristics.

Figure 2

(a) Reflected signal for a probe power of $95\mu \text{W}$. Arrows ${\lambda }_A$ to ${\lambda }_I$ indicate the wavelength range for the bistability experiment. (b) Time traces of input [black (top) line (right vertical axis)] and reflected [blue, red, and green lines (left vertical axis)] signals for detunings of $\Delta \lambda =1.5$, $1.7$, and $1.9\text{nm}$, respectively. (c) Hysteresis cycles showing bistable behavior. Detuning values with respect to the cavity resonance are, from ${\lambda }_A$ to ${\lambda }_I$, $1.9$, $1.8$, $1.7$, $1.5$, $1.3$, $1.1$, $0.9$, $0.7$, and $0.4\text{nm}$. The input power is measured at the tapered fiber input. The durations of the switch processes is $\sim 6\text{ns}$ for the on and off switches.

Figure 3

Transient responses (bottom traces) for different detunings. The detunings (in nanometers) and the injected powers (in megawatts) are, from ${\lambda }_A$ to ${\lambda }_I$, $1.8$ and $2.9$; $1.7$ and $2.5$; $1.6$ and $2.2$; $1.5$ and $1.8$; $1.4$ and $1.6$; $1.3$ and $1.3$; $1.2$ and $1.2$; $1.1$ and $0.9$; 1 and $0.8$. The top trace corresponds to the perturbation signal (peak power $=$ $80\mu \text{W}$).

Figure 4

Excitable responses (bottom traces) to 130-ns width, 40-KHz repetition rate pulse perturbations (top trace) for different perturbation powers: $1\mu \text{W}$ is below threshold (black line); 20, 35, and $46\mu \text{W}$ are above threshold [red, blue, and green lines, respectively (gray lines)]. The injected signal power is set at $2.6\text{mW}$ and the detuning is $\Delta \lambda =1.5\text{nm}$.

Figure 5

(a) Output and perturbation signals (lower and upper traces) as a function of time for different delays ($\Delta t$) between $808\text{-nm}$ perturbation pulses; $\Delta \lambda =1.2\text{nm}$, injected power $2.8\text{mW}$, and perturbation power $255\mu \text{W}$. The refractory time is $\sim 2\mu \text{s}$, determined as $\Delta t$ just before the two output pulses take place (in between the two highlighted situations). (b) Refractory time as a function of the excitable pulse duration ($\Delta \lambda =1.2$, $1.1$, 1, and $0.9\text{nm}$ for increasing excitable pulse duration). (Red) line: linear fit.

Figure 6

Self-sustained oscillations. Reflected signals as a function of time for different detunings, from ${\lambda }_A$ to ${\lambda }_H$, $1.8$, $1.7$, $1.6$, $1.5$, $1.4$, $1.3$, $1.2$, and $1.1\text{nm}$. The input power, measured at the tapered fiber input, is $3.2\text{mW}$.