Fig. 1. Illustration of the working principles of two-point coupling for waveguide resonators shows the tunable bus-resonator coupling expressed by κ2(ϕ)=4κ02(1−κ02)cos2(ϕ/2), and the tunable bus-resonator coupling rate expressed by γc=cκ2(ϕ)/ngL. Panels (a) to (e) show two-point-coupled ultra-high Q resonators for various applications, such as (a) critically-coupled ultra-high-Q reference resonators for PDH lock and laser stabilization, (b) over-coupled resonators for increased feedback and output power in self-injection locked lasers, (c) squeezed light generation in over-coupled resonators, (d) multi-wavelength coupling design for efficient OPO processes, and (e) dual-mode (TE-TM) coupling. TE, transverse electric. TM, transverse magnetic. SIL, self-injection locked laser. PDH, Pound–Drever–Hall. OPO, optical parametric oscillation.

Fig. 2. Two-point-coupled 10-meter-coil resonator with 340-million intrinsic Q. (a) The measured resonator linewidth from 1550 nm to 1630 nm shows resonator coupling tuning with respect to wavelength with a tuning period of 5.6 nm, where critical coupling can be found across the wavelength range from 1550 nm to 1630 nm. The purple dashed line is a sinusoidal function fitted to the blue-dot data points based on the tunable coupling model by κ2=4κ02(1−κ02)cos2(ϕ/2), and the green dashed line is merely a trend line interpolated from the green-dot data points. (b) The loaded and intrinsic Q of the critically coupled resonances show an intrinsic Q of 200 million at approximately 1550 nm and 340 million at 1630 nm. Inset shows a picture of the 10-meter-coil resonator and a zoomed-in view of the two-point coupler section. (c) The resonance gradually changes from being under-coupled to critically coupled and over-coupled from 1558.6 nm to 1561.3 nm corresponding to data points labeled as (1)–(5). (d) The spectral scan of the critically coupled resonance at 1630 nm measures a loaded Q of 184 million and an intrinsic Q of 340 million, corresponding to a waveguide propagation loss of 0.074 dB/m.

Fig. 3. Tunable two-point-coupled visible resonator with in-situ thermal tuning of two-point coupling. (a) Measurements of the resonator intrinsic and coupling linewidths for the TM0 mode at 698 nm show that the thermal tuning of the two-point coupling tunes the resonator coupling while the resonator intrinsic loss stays constant and the waveguide loss is measured to be 0.83 dB/m, corresponding to a 71-million intrinsic Q. Inset shows a picture of the visible-wavelength ring resonator device on the testing stage with a zoomed-in illustration of the thermally tuned two-point coupling section. (b) Measured resonator intrinsic and coupling linewidths for the TE0 mode at 780 nm while thermally tuning the two-point coupling show the two-point coupling tuning and a waveguide loss of 1.20 dB/m, corresponding to a 44-million intrinsic Q. (c) When thermally increasing the two-point coupling, the 698-nm TM resonance translates from being under-coupled to critically coupled and over-coupled. (d) Tuning the two-point coupling changes the 780-nm TE resonance coupling from weak coupling to under-coupling.

Fig. 4. Laser stabilization and frequency noise reduction at multiple wavelengths in the C and L bands using a two-point-coupled 10-meter-coil resonator with a 340-million intrinsic Q. (a) Photograph of the 10-meter-coil resonator. (b) At 1554 nm, 1585 nm, and 1600 nm, the 10-meter-coil resonator is critically coupled and used for laser stabilization, which shows frequency reduction of six orders of magnitude at 1 kHz offset and three orders of magnitude at 10 kHz offset.

Fig. 5. (a) Silicon nitride waveguide loss spectrum measured in the two-point-coupled 4-meter-coil waveguide resonator shows the absorption loss peaks near 1385 nm and 1520 nm related to hydrogen impurities. (b) SIMS depth profiling measures the hydrogen impurity level at different depths and layers, revealing ∼6×1019  atoms/cm3 hydrogen impurity level in the silicon nitride layer. The SIMS spot is on a 2 mm by 2 mm area of the fill pattern with 50% nitride and 50% TEOS oxide upper cladding.

Fig. 6. Bending loss, S-bend point loss, S-bend mode conversion simulation in 6-μm and 80-nm silicon nitride waveguides at 1550 nm. (a) The TE0 mode has negligible bending loss at bending radii above 1.0 mm. (b) The TE0 mode has a 0.2–0.8  dB point loss at the S-bend center with a bend radius from 1 mm to 2 mm. (c) Mode conversion between the TE0 and TE1 modes due to mode mismatches where the S-bending direction turns in the opposite direction.

Fig. 7. Waveguide taper design for edge coupling. (a) Coupling loss between TE0 and three types of fibers with different mode field diameters (MFDs)—SMF28, UHNA1, and UHNA3—shows that a 1.5-μm taper can achieve coupling loss below 1.0 dB. (b) Waveguide effective index (neff) simulation shows that the tapered waveguide is single mode below 2.2 μm in taper width.

Fig. 8. Measured intrinsic resonator waveguide loss comparison between one-point-coupled and two-point-coupled 10-meter-coil silicon nitride waveguide resonators. (a) The measured intrinsic, coupling, and total resonator linewidths in a one-point-coupled 10-meter-coil resonator show the critical coupling wavelength region from 1580 nm to 1610 nm. (b) The measured waveguide loss in both the one-point-coupled and two-point-coupled 10-meter-coil resonators shows almost identical loss spectra.