Fig. 1. (a) Schematic showing energy diagrams of ATS realized in a two-element photonic molecule. (b) Schematic showing an on-chip integrated waveguide-coupled size-mismatched photonic molecule. Refractive-index tuning can be realized by the integrated microheater covering half part of the inner ring.

Fig. 2. (a) Optical microscope image of a waveguide-coupled size-mismatched photonic molecule. The radii of the inner and outer rings are 47 and 50 μm, respectively. The gap spacing between the two rings and the spacing between the waveguide and the outer ring are both 300 nm. (b) Summarized resonant wavelengths λi and λo as a function of estimated azimuthal mode order of the outer ring Mo. λo and λi were determined by identifying the corresponding transmission dip. For the case of discernable mode splitting, λi was determined by averaging the wavelengths of two transmission dips. λi−o equals λi−λo. Dots: data. Lines: fits. (c)–(f) Measured transmission spectra around different Mo, including Mo=781 (c), 789 (d), 791 (e), and 793 (f). Insets: (i) schematic showing the geometry of the photonic molecule; (ii) extracted |Δλi−o| as a function of Mo; (iii),(iv) zoomed-in views to show the split modes.

Fig. 3. (a) Tracked resonant spectra upon an increased injection power from 0 to 70 mW. For better visualization of the key spectral features, the spectra were not plotted in the scale of absolute wavelength, but the corresponding δλ. The red dashed lines are visual aids of the upper branch (UB) and lower branch (LB). (b) Numerically modeled resonant spectra upon an increase δλ from −0.047 to 0.058 nm. The key parameters κi, κo, g, γo, and γi were adopted as 2.9, 0.3, 5.5, 1, and 1 GHz, respectively. (c), (d) Summarized splitting width of the inner ring Δλi as a function of the discerned splitting width of two main branches Δλi−o, including the cases with inter-cavity coupling gap spacing of 300 nm (c) and 380 nm (d). Here the wavelength of the split branch was adopted by averaging the two values of split modes. Dots: data. Curves: modeling.

Fig. 4. (a) Calculated eigenvalue surfaces in the frequency domain summarized in g–δω parameter space, including the real part standing for resonant frequency detuning (top) and the imaginary part standing for linewidth detuning (bottom). (b)–(d) Calculated tuning of eigenvalues, including the real (top) and imaginary (middle) parts, and also the intra-cavity ATS for two rings (bottom). The calculation was performed upon different inter-cavity coupling regimes, including (b) g=1.5  GHz, (c) 1 GHz, and (d) 0.5 GHz. Insets in (b)–(d): zoomed-in views to reveal the anti-crossing region (b) and crossing points (c), (d).

Fig. 5. (a) Captured scattering microscope image showing two bright spots due to the local bulges as Mie scatterers. There are in total four identically designed Mie scatterers (depth of 100 nm, length of 200 nm) located at the azimuthal angles of 45°, 135°, 225°, and 315°. For imaging of out-of-plane scattered light, a long-working-distance microscope objective lens (10× Mitutoyo Plan Apo, NA=0.28) and a monochrome sCMOS camera (CS2100M-USB, Thorlabs) were employed. The absence of bright scattering in the lower half of the inner ring is due to the blocking of the integrated microheater. Insets: schematics showing two bulges acting as Mie scatterers. (b) Summarized splitting width of the inner ring Δλi as a function of Δλi−o. Dots: data. Curves: modeling. (c), (d) Measured resonant spectra at varying injection power of 45 mW (c) and 15 mW (d). Dots: data. Solid curves: Lorentzian fits. Dashed curves: individual Lorentzian fits indicating three discernable supermodes.

Fig. 6. Schematic showing the modeled microring dimer system coupled through a bus waveguide. Here the input laser light from port 1 mainly excites the CCW lightwave components in both rings.