Pump-Induced Dynamical Tunneling in a Deformed Microcavity Laser

Pump-induced dynamical tunneling has been observed in free-space resonant optical pumping of a deformed microcavity by employing excitation spectroscopy. A focused-pump beam was injected into the cavity by refraction and then coupled to a high-$Q$ cavity mode via dynamical tunneling. Pump-coupling efficiency as high as 50% and an effective coupling constant responsible for the tunneling were obtained from the observed pumping efficiency with a mode-mode coupling model.

Figure 1

(a) Mode spectrum of our microcavity. (b) Magnified view around 600 nm. (c) Pumping-efficiency spectrum obtained by the excitation spectroscopy explained in the text. Each data point represents an averaged value over several measurements with about 15% error.

Figure 2

Pumping-efficiency spatial distribution in $\theta \mathrm{\text{−}}X$ space with the pump wavelength fixed at $l=3$ $P$-mode resonance indicated by a blue arrow in Fig. 1c. The left-hand figure shows the cross section of the liquid jet.

Figure 3

Phase space (Poincaré surface of section) for our deformed microcavity is presented in the Birkhoff’s coordinates, in which a ray is reflected off the cavity boundary at polar angle $\varphi$ with an incidence angle $\chi$. Husimi distributions of $l=1$, 2, 3 modes are shown in purple, orange, and green, respectively. The red-filled circle indicates the initial bundle of rays and blue lines represent the subsequent pump-beam trajectories. Inset: real-space pump-beam trajectories.

Figure 4

(a) Mode-mode coupling model. Uncoupled chaotic mode ${\mathcal{E}}_n$, excited by refractively injecting a pump laser $E_0$, can couple to an uncoupled regular mode ${\mathcal{E}}_r$ with a coupling constant $g_n$ by dynamical tunneling. (b) Decay rate ${\gamma }_r$ and the effective coupling constant $\overline{g}$ obtained from the pumping-efficiency data for each high-$Q$ cavity mode.