Figure 1

(a) Relative intensity distributions ($I_B/I_A$) in two channeling waveguides as a function $\Delta n$. The inset shows the schematic of a two-channel quadruple cavity with $\varepsilon =0.08$, $\Delta {\varphi }_1=\Delta {\varphi }_2=0.1$, and ${\varphi }_{c1}={\varphi }_{c2}-\pi =0.633$. The overlap between the green circle (radius $r$) and the cavity represents the perturbed area with $n=n_0+\Delta n$. Here $r/R$ is 0.225. And no perturbation has been applied at port B. Panels (b)–(d) show the corresponding far-field patterns (FFPs) of modes marked i, ii, iii, respectively, in panel (a). Here the resonance is set at $kR=25.04$.Reuse & Permissions

Figure 2

Panels (a) and (b) show the clockwise Husimi maps of modes ii and iii from Fig. 1a. It is clear that the distribution of the chaotic layer has been changed by the perturbation $\Delta n$ at the joint position of port A.Reuse & Permissions

Figure 3

(a) The relative intensity ratio ($I_B/I_A$) at different resonances. All the cavity parameters are the same as for Fig. 1c. Except for the resonance coupling to nearby resonances, most of the resonances show similar FFPs. (b) Dependence of ($I_B/I_A$) of mode with $kR=25.04$ on size (blue squares) and shape (red circles, $a$ and $b$ are both axes of an ellipse in Cartesian coordinates) of perturbation area. Panels (c) and (d) show the resonant wavelength and intensity ratio along two ports as a function of shape-deformation parameter $\varepsilon$. The diamond mode maintain its far-field pattern (FFP) with $I_B\gg I_A$ for a wide range of $\varepsilon$ except that it couples to other resonances. The stars in panel (d) show the significant tolerance of the perturbed FFP on refractive index. The regions between the dashed lines in panels (a), (b), and (d) correspond to bidirectional emission. Except for the varied parameters, the others are the same as the parameters in Fig. 1.Reuse & Permissions

Figure 4

Panels (a) and (c) show the mode patterns of triangle and rectangle resonances at $\varepsilon =0.07$ and $\varepsilon =0.11$ (from Fig. 3), respectively. The corresponding FFPs are shown in the bottom panels (b) and (d). For comparison, the FFPs of nearby diamond resonances are shown in the upper panels of (b) and (d). It is clear that the FFPs of high-$Q$ modes are dominated by the low-$Q$ modes via mode coupling. Here and below, the basic parameters of cavities are $n_0=3.3$, $\Delta n=-0.05$, and $\varepsilon =0.08$, except where specifically stated otherwise.Reuse & Permissions

Figure 5

Panels (a) and (b) show the FFPs of mode 3 and mode 7 at $\varepsilon =0.095$ and $\varepsilon =0.07$, respectively. $I_B\gg I_A$ is recovered when the diamond modes are away from the crossing points.Reuse & Permissions

Figure 6

(a) Examples of FFP and corresponding field pattern off mode marked by arrow in panel (b). The perturbed area is the overlap between the quadruple cavity and the red circle. (b) Tolerance of new mechanism on the resonant wavelengths. As opposed to Fig. 3, here the refractive index $n_0$ is 2.4 for GaN or ZnO and $\Delta n=-0.05$. It is clear that the FFPs with $I_b\gg I_A$ can be obtained in a wide $kR$ range from 34 to 40. Several modes have bidirectional emissions between the dashed lines in panel (b) are formed by mode coupling as in Figs. 1 and 3.Reuse & Permissions

Figure 7

Control of FFPs of chaotic microcavities with small perturbation amplitude ($\Delta n_A=-0.005$ and $\Delta n_B=0.005$). The suppression of $I_A$ happens at both (a) $n_0=3.3$ and (b) $n_0=2.4$. All the other parameters are the same as in Fig. 3.Reuse & Permissions

Figure 8

(a) Schematic of four-channel quadruple cavity. There are four perturbation areas with amplitude $\Delta n_A$, $\Delta n_B$, $\Delta n_C$, $\Delta n_D$. Here $\varepsilon =0.08$, $r_A/R=r_B/R=r_C/R=r_D/R=0.225$, $\Delta {\varphi }_A=\Delta {\varphi }_B=\Delta {\varphi }_C=\Delta {\varphi }_D=0.1$, and ${\varphi }_A=\pi -{\varphi }_B={\varphi }_C-\pi =2\pi -{\varphi }_D=0.633$. The selected resonance has $kR=45.835$, which is around two times that of the modes in Figs. 1, 2, 3 to illustrate the robustness. (b) Possible unidirectional output along port B. Here $\Delta n_A=\Delta n_B=-0.05$, $\Delta n_C=-0.03$, and $\Delta n_D=0.02$. Panels (c)–(e) show directional outputs in two ports. The perturbations with $\Delta n=-0.05$ are applied on the other two ports. (f) Directional outputs in three ports simultaneously except port A. Here $\Delta n_A=-0.05$, and $\Delta n_B=\Delta n_C=\Delta n_D=0$. Due to the symmetries, the directional emission in one and three ports can be converted to all the other ports.Reuse & Permissions