Universal output directionality of single modes in a deformed microcavity

We have investigated the characteristics of quasibound states of a quadrupole-deformed microcavity both experimentally and theoretically. Five distinct single-mode groups are observed in the cavity emission spectra with their cavity quality factors varied by several orders of magnitude. Although the corresponding mode wave functions show qualitatively different geometrical shapes, these single modes exhibit almost identical far-field emission patterns, which contradicts a common understanding that the emission direction is usually associated with the geometry of the mode wave functions. The observed universal directionality is explained by a subtle manifestation of unstable manifolds of classical chaos in the formation of quasibound states.

Figure 1

Schematic of our experimental setup for measuring the cavity-mode spectrum and single-mode far-field emission pattern of a QDM.

Figure 2

Cavity-modified fluorescence and lasing spectra of our QDM with $\eta =16\%$ for a pump power of $54\mathrm{mW}$ and $112\mathrm{mW}$. Inset: five distinct mode groups are identified and labeled as $l=1,2,3,4,5$ with increasing order of FSR. The positions of these mode groups are marked as vertical ticks below the spectra.

Figure 3

Observed far-field emission pattern of individual single-cavity modes. The observed single modes are labeled from bottom as $l=1,2,3,4,5$. The base line for each curve is denoted by dotted lines.

Figure 4

(Color) Calculated Husimi plots of quasieigenmodes with (a) $nkr=232.27$ and (b) $nkr=226.29$, corresponding to $l=2$ and 4 modes, respectively. Distributions below the critical line $(=1∕n)$ in (a) and (b) are enhanced 100 times in intensity in (c) and (d), respectively.

Figure 5

Calculated far-field distributions associated with quasieigenmodes with $nkr=228.87$, 232.27, 226.29, 227.65, and 230.87, which belong to mode groups labeled as $l=1$, 2, 3, 4, and 5, respectively. Curves are smoothed over 5° intervals to match the experimental angular resolution.