Fig. 1. (a) Schematic and (b) outputs of an ideal ring resonator.

Fig. 2. (a) Illustration of the backcoupling in a 2×2 directional coupler. (b) Ring resonator with this backcoupling.

Fig. 3. (a)–(c) Simulations of an all-pass ring resonator with a lumped reflector inside and the backcoupling at the directional coupler. (d) Schematic. f is the ratio of backcoupling over forward-coupling, f=κ′/κ.

Fig. 4. Designed circuit in order to introduce manipulation backcoupling in a realistic way. An MZI is placed in front of a ring resonator to dynamically control the intensity of light in two inputs of a ring resonator. Each of the inputs will couple to one circulating mode in the ring.

Fig. 5. Schematics of the ring resonator with (a) a reflector inside and (b) the tunable reflector.

Fig. 6. Simulated results of the influences of manipulating backcoupling on the split resonance. These figures show the results of manipulating PS1 with PS2=0. (a) and (b) Output at out1. (c) and (d) Results at out2.

Fig. 7. When backcoupling equals forward-coupling (in1=in2), one of the two peaks in a split resonance can be suppressed. By adding either 0.5π or 1.5π phase shift to PS1, we can also choose which peak to be suppressed.

Fig. 8. We fix PS1=0.2π and vary PS2 to change the phase difference between backcoupling and forward-coupling. (a) and (b) Output at out1. (c) and (d) Results at out2.

Fig. 9. Schematic and spectra of a coupled-resonator circuit. They are identical at resonant frequency (wavelength). If both are lossy, we get standard resonance splitting, while, when one resonator has gain instead of loss, those sharp asymmetric Fano resonances are generated. This behavior is similar to that of our backcoupling manipulation.

Fig. 10. Microscopic images of the devices to manipulate backcoupling. (a) Circuit with a purely circular ring resonator, whose internal reflection is induced by stochastic backscattering. (b) Circuit with a ring resonator that has a tunable reflector inside.

Fig. 11. Demonstration of the tunability of resonance splitting caused by internal reflections using PS3 shown in Fig. 10(b). (a) and (b) Results of two devices with different coupling coefficients. In both cases, the splitting can be adjusted and eliminated using PS3.

Fig. 12. Without internal reflections and resonance splitting (by tuning PS3 to the correct condition), varying PS1 and PS2 do not have an impact on the resonance shape, which is consistent with former simulation results.

Fig. 13. Measured spectra at (a) out1 and (b) out2 for constant PS2=0 and varying PS1. They show good correspondence with simulation results plotted in Fig. 6. Peak splitting can be eliminated at both ports.

Fig. 14. Measured spectra at (a) out1 and (b) out2 at fixed PS1=0 with varying PS2. They show good correspondence with the simulation results plotted in Fig. 8.

Fig. 15. Measured spectra with varying PS1 and fixed PS2 of a circuit with a circular ring resonator at (a) out1 and (b) out2. Resonance splitting due to stochastic backscattering is present in both cases; it can be suppressed by varying PS1.

Fig. 16. Measured spectra with varying PS2 and fixed PS1 of a circuit with a circular ring resonator at (a) out1 and (b) out2.

Fig. 17. Details of measured resonances of a ring resonator with coupling gap at 400 nm. All resonances show a Q-factor larger than 300000 and satisfying ER. The FSR of such a resonator is about 2.5 nm. The calculated finesse is around 600.

Fig. 18. FDTD simulation of the transmission of the directional coupler consisting of a circular arc with 35 μm bend radius and a bus waveguide with 400 nm gap in between. The coupling coefficient is less than 0.003.

Fig. 19. Simulated resonances of a 35 μm bend radius circular ring with loss coefficient of 2  dB/cm and a coupling coefficient of 0.003.

Fig. 20. Simulated outputs of the circuit shown in Fig. 4 but with the same parameters in the simulation of a pure circular ring above. Manipulating the backcoupling can increase the extinction ratio of the resonance.