Fig. 1. (a) Schematic of loss channels for standing-wave supermode microresonators with periodic radius modulation. (b) Normalized transmission spectra of the optical modes with the backscattering rate (g/2π) increasing from top to bottom, where κ0/2π=100  MHz and ΓR=0. Inset: optical field distributions of the two supermodes, with the red and blue colors representing the positive and negative maxima of the electrical field, respectively. (c) Normalized transmission spectra with various external coupling rates κex,0/2π. The blue, red, orange, purple, and green curves correspond to K=κex,0/κ0=0.01, 0.1, 1, 5, and 10 when κ0/2π=100  MHz, g/κ0=10, respectively. (d) Normalized on-resonance transmission of the optical mode, as a function of the total linewidth. The blue and green dots correspond to the cases with strong backscattering (g/κ0=10) and without backscattering (g/κ0=0), respectively. The black dashed and solid fitting curves correspond to the ideality of I=0.5 and I=1 cases, respectively.

Fig. 2. Characterization of SiO2 supermode microresonators. (a) Top: scanning electron microscopy (SEM) image of the microresonator. Middle: zoom-in on the periodic radius modulation. Bottom: optical microscopy image of the supermode microresonator coupled with a tapered fiber. (b), (c) Normalized transmission (blue) and reflection (orange) spectra of TE (b) and TM (c) modes of the supermode microresonator. (d), (e) Fine-scanned transmission (blue) and reflection (orange) spectra of modes marked in the black boxes in (b) and (c), respectively.

Fig. 3. Measurement of the coupling ideality of SiO2 supermode microresonators. (a), (b) Evolution of the normalized transmission (a) and reflection (b) spectra of the higher-frequency TE targeted mode (a+) with K=0.02, 0.17, 1.08, 3.39, 5.22. (c) Normalized on-resonance transmission of the mode a+ as a function of the total linewidth with a fitting ideality I of 0.5, where g/κ0=135. (d), (e) Evolution of the normalized transmission spectra (d) and reflection spectra (e) of a non-targeted mode with K=0.02, 0.16, 0.99, 3.26, 5.38, where the backscattering rate is determined to be zero. (f) Normalized on-resonance transmission of the non-targeted mode as a function of the total linewidth with a fitting ideality I of 1, where g/κ0=0.

Fig. 4. Experimental results of the coupling ideality of the supermodes and non-split modes as a function of g/κ0.

Fig. 5. Characterization of supermode microresonators. (a) Measured frequency splitting and (b) intrinsic quality factors of the optical modes as a function of the modulation amplitude for SiO2 microresonators with a radius of r0=20  μm, thickness of 1 μm, and modulation period of 2m=202.

Fig. 6. Measurement of the normalized transmission/reflection spectra and coupling ideality of SiO2 supermode microresonators. The parameter g/κ0 for the four modes in (a)–(d) are determined to be 260, 81, 0, and 0, respectively. The left (i), middle (ii), and right (iii) columns show the normalized transmission spectra, normalized reflection spectra, and coupling ideality, respectively.