Fig. 1. (a) Schematic illustration of the Friedrich–Wintgen quasi-BIC formed by external strong coupling in a shared leaking continuum. (b) SEM image of the Limaçon microdisk coupled with a bus waveguide supporting Friedrich–Wintgen quasi-BIC. The scale bar is 50 μm. (c) Poincaré surface of the section of the Limaçon microcavity (without bus waveguide) at deformation parameter ϵ=0.35 and neff=1.649. The side pictures show the ray trajectories of quasi-WGMs (blue) and six-bounce (red) modes, respectively. Not all supported modes are plotted for clarity. (d) Normalized survival probability after 1500×2000 uniformly distributed rays bouncing 200 times inside the Limaçon microcavity, where rays with intensity above 0.1 are extracted. (e) Wave-optics simulation results of the normalized far-field spectrum of the WGM-like and six-bounce modes. The inset pictures show the field distributions of the quasi-WGMs (top) near kr=106, quasi-WGMs (middle) near kr=59, and six-bounce modes (bottom) near kr=106, respectively.

Fig. 2. Internal and external strong mode coupling in a microcavity. (a) and (b) Real and imaginary parts of the eigenenergies of the Hamiltonian derived in Eq. (2) as a function of detuning parameter Δ. Inset in (a) shows the real eigenvalue difference. To demonstrate internal strong mode coupling, we set E1=1538.5+Δ−0.0025i, E2=1538.5+2Δ−0.005i, and κ1κ2=0.0006 as an example. (c) Corresponding Q factors. (d) to (f) Strong external coupling case, where E1=1538.5+Δ−0.023i, E2=1538.5+2Δ−0.023i, and κ1κ2=0.00084i.

Fig. 3. Transmission spectrum near the avoided resonance crossing region. (a) Wide-range transmission spectrum of the Limaçon microdisk with ϵ=0.35. (b) Zoom-in view of spectra in (a) before, near, and after the strong coupling regions. Clear variations in resonant wavelength difference and resonant linewidths are observed. Each spectrum in (b) has a fixed wavelength range of 0.4 nm.

Fig. 4. Formation of Friedrich–Wintgen quasi-BIC. The resonant wavelength difference in (a) and Q factors of Mode A and Mode B in (b) are extracted from the spectrum in Fig. 2(a) by Lorentzian fitting. Mode number 0 corresponds to resonances at a wavelength of 1538.48 nm. Avoided resonance crossing along with the significantly enhanced Q-factor of Mode A indicates the formation of Friedrich–Wintgen quasi-BIC.

Fig. 5. Fine tuning of the Friedrich–Wintgen quasi-BIC at Mode number 0. (a) Resonant wavelength difference and (b) Q-factor of Mode A as a function of substrate temperature.

Fig. 6. Formation of Friedrich–Wintgen quasi-BIC in a single Limaçon microcavity with ϵ=0.4. (a) Wide-range transmission spectrum of the Limaçon microcavity with ϵ=0.4. (b) Zoom-in view of spectrum in (a) before, near, and at strong coupling. Each spectrum has a fixed wavelength range of 0.4 nm.

Fig. 7. Resonance fitting and Q-factor extraction. (a) Transmission spectra near the quasi-BIC region, with green arrows indicating the Fabry–Pérot background caused by reflections at the bus waveguide edges. (b) and (c) Fitting results for Mode B and Mode A, respectively. (d)–(g) Fitting results for additional resonances.