Fig. 1. Schematic diagram of the proposed compact ultrahigh-$Q$ MRR. (a) 3D view and (b) top view.

Fig. 2. Design of the compact ultrahigh-$Q$ microracetrack resonator. (a) Cross section of the ${\mathrm{Si}}_3{\mathrm{N}}_4$ optical waveguide of the resonator; (b) relationship between the scattering loss and the waveguide core width based on $n\text{-}w$ model; (c), (d) simulated mode profiles when the waveguide widths are 1 and $3\mu \mathrm{m}$, respectively; (e), (f) calculated respective MERs of the higher-order TE modes excited by ${\mathrm{TE}}_0$ mode and MERs of the higher-order TM modes excited by ${\mathrm{TM}}_0$ mode, in the waveguide consisting of an input MSW, a 180 deg Euler MWB, and an output MSW, when $R_{\min }=100\mu \mathrm{m}$, $R_{\max }=4000\mu \mathrm{m}$; (g) simulated ${\mathrm{TE}}_0$ mode propagation in the designed 180 deg Euler MWBs; (h) simulated ${\mathrm{TE}}_0$ mode profile at the input (top), the quadrant MRR ($R=R_{\min }$) (middle), and the output (bottom) of the 180 deg Euler MWBs; and (i) FDTD simulations of the light coupling in the MSW DC.

Fig. 3. False color images of the fabricated ultrahigh-$Q$${\mathrm{Si}}_3{\mathrm{N}}_4$ racetrack resonator. (a) Global view of the fabricated device; (b) modified Euler bend; (c) adiabatic taper; and (d) coupling waveguides of DC.

Fig. 4. Experimental setup for characterizing the $Q$ factor of the compact ultrahigh-$Q$${\mathrm{Si}}_3{\mathrm{N}}_4$ racetrack resonator based on VNA.

Fig. 5. Measured results of the MRR (height $0.8\mu \mathrm{m}$ × width $3.0\mu \mathrm{m}$). (a) Measured transmission of the resonator when TE and TM mode resonances exist; (b) measured transmission spectrum when only TE mode resonance exists; (c) histogram of intrinsic linewidth of the MRRs; and (d) representative resonance with critical coupling.