Long-path formation in a deformed microdisk laser

An asymmetric resonant cavity can be used to form a path that is much longer than the cavity size. We demonstrate this capability for a deformed microdisk equipped with two linear waveguides, by constructing a multiply reflected periodic orbit that is confined by total internal reflection within the deformed microdisk and outcoupled by the two linear waveguides. Resonant mode analysis reveals that the modes corresponding to the periodic orbit are characterized by high-quality factors. From measured spectral and far-field data, we confirm that the fabricated devices can form a path about 9.3 times longer than the average diameter of the deformed microdisk.

Figure 1

(a) Deformed microdisk with two linear waveguides attached at $V_0$ and $V_{11}$ and a half-circular scatterer at $V_{12}$. (b) The stable periodic orbit that appears when the scatterer at $V_{12}$ is absent. (c) The contact area (gray region), where currents are injected.

Figure 2

Stability diagram for the open-star-polygonal periodic orbit, where $\varepsilon$ is the deformation parameter and $d_{11}$ is the scaled length of the waveguide at $V_{11}$, i.e., $d_{11}=\overline{V_{11}{V}_{11}^{\prime }}/r_0$ (note that the scaled length of the waveguide at $V_0$ is fixed at $d_0=1.90565\times d_{11}$). The open-star-polygonal periodic orbit is linearly stable in the gray regions (i.e., $\left|\text{Tr}M\right|<2$ with $M$ the monodromy matrix). In this work, the parameter values are fixed at $(\varepsilon ,d_{11})=(0.005,0.2)$ (indicated by an arrow).

Figure 3

The distribution of the resonances, where the star modes are plotted with filled circles ($•$). The star modes appear regularly with the average mode spacing $\mathrm{\Delta }k{r}_0=0.0512$. The wave functions corresponding to (a) and (b) are shown in Figs. 4 and 4, respectively.

Figure 4

(a) and (b) show the intensity distributions of the wave functions for the resonances: (a) $k{r}_0=224.165-i0.011$ and (b) $k{r}_0=224.430-i0.010$, where a lighter color indicates a higher intensity. (c) and (d), respectively, show far-field emission patterns for the mode shown in Fig. 4 (black curves) and for the mode shown in Fig. 4 (gray curves).

Figure 5

Far-field patterns (normalized) for a device with $r_0=30\mu \text{m}$: (a) emission to the left side of the cavity and (b) emission to the right side. The direction of the waveguide is $\theta =0$ deg in (a), while it is $\theta =27.7$ deg in (b). Experimental data for a pumping current of 90 mA are plotted with black curves, while numerical data obtained with the BEM calculation are plotted with gray curves.

Figure 6

Far-field patterns (normalized) for devices with $r_0=30$ and $50\mu \text{m}$: (a) emission to the left side of the cavity and (b) emission to the right side. The direction of the waveguide is $\theta =0$ deg in (a), while it is $\theta =27.7$ deg in (b). Experimental data for $r_0=30\mu \text{m}$ are plotted with black curves, while those for $r_0=50\mu \text{m}$ are plotted with gray curves. The pumping current is 90 mA in all cases.

Figure 7

Optical spectra: (a) $r_0=30\mu \text{m}$ and below the threshold, (b) $r_0=30\mu \text{m}$ at 90 mA, (c) $r_0=50\mu \text{m}$ and below the threshold, and (d) $r_0=50\mu \text{m}$ at 90 mA. In (a) and (c), respectively, equidistant vertical dotted lines with 0.154- and 0.101-nm spacings are plotted as an eye guide.

Figure 8

Long-path formation by coupling nine identical deformed disks with $Q=10$ and an average radius $r_0$. The total path length is about $107\times r_0$, whereas the entire system length is about $6\times r_0$.