Directional Laser Emission from a Wavelength-Scale Chaotic Microcavity

We demonstrate directional output from a deformed disk laser of dimensions comparable to the emission wavelength. Unlike larger deformed cavity lasers, which exhibit universal output directionality determined by chaotic ray dynamics, the far-field patterns differ between lasing modes. The directional emission results from weak coupling of isotropic high-quality modes to anisotropic low-quality modes, combined with chiral symmetry breaking of clockwise and counterclockwise propagating waves. This mechanism makes it possible to control the output properties of wavelength-scale lasers.

Figure 1

(a) Inset: Top-view SEM image of a GaAs disk. The scale bar is $1\mu \mathrm{m}$. Main panel: Measured laser emission spectrum at the incident pump intensity of $191\mathrm{W}/{\mathrm{cm}}^2$. (b)–(d) Measured FFPs for the lasing modes 1, 2, and 3 shown in (a). The red dashed curve in (b) is the FFP obtained by a ray-tracing model [4] applied to the cavity in the inset of (a).

Figure 2

(a) Calculated $Q$ values for the HQMs (blue dots) and the LQMs (red squares) in the same cavity as that in Fig. 1. Modes marked 1, 2, and 3 correspond to the three lasing modes in Fig. 1. (b) Calculated values of directionality $U$ for the HQMs and LQMs versus $kR$. Crosses are $U$ values of three lasing modes in Fig. 1. Inset: Calculated FFPs for modes labeled 4 (black solid line) and 6 (red dashed line) in (a).

Figure 3

(a),(d),(e) Calculated magnetic field intensity for the TE cavity modes labeled 1, 4, 5 in Fig. 2a; red arrows in (e) indicate high emission directions based on chiral symmetry; however, the dashed arrows denote emission which is not observed in the experiment (see below). Panels (b),(c),(f) show their Husimi projections (incident) onto the Poincaré SOS. The horizontal axis $S$ is the arc length along the cavity boundary from the point $\theta =0$ normalized by the cavity perimeter, the vertical axis is $\sin \chi$. The red dashed lines mark the critical angle for total internal reflection. The bouncing points of a diamond orbit (or triangle orbit), drawn in (a) or (e), are marked by “+” (or “×”) and labeled in (a) and (b) or (e) and (f). Panel (g) compares the incident and emergent Husimi projections of mode 5 for CW waves; the shift of the emergent waves to smaller $S$ and higher $\sin \chi$ directly demonstrates the GHS and FF effects in our device. (h) Two distinct periodic pseudo-orbits (gray and black) for CW and CCW waves which give rise to unidirectional emission instead of the tridirectional emission expected from the periodic triangle ray orbit shown in (e).