Fig. 1. Symmetry breaking of counterpropagating light in a high-QSi3N4 resonator. (a) Schematic of the Kerr-nonlinearity-induced interaction of light in the Si3N4 resonator. Two counterpropagating light waves with the same frequency and power are injected from the left and right sides of the bus waveguide, which can support both TE00 and TM00 modes. (b) For bi-directional pumping, at low pump power, the two counterpropagating waves generate standing waves and the resonant transmission spectra of the two light waves are identical (left panel). At high power, the resonator enters a state with clockwise or counterclockwise circulating light. In this symmetry-breaking state, the optical modes in different directions have different resonance frequencies (middle panels). Increasing the optical power in the non-dominant direction enables switching between the counterpropagating light states. This switching behavior follows a hysteresis (right panel). (c) Microscope image of the Si3N4 resonator.

Fig. 2. Measurements of symmetry breaking at different powers for the TM00 resonance. (a) Experimental setup. The continuous-wave light from a tunable laser is amplified by an EDFA first and then split into two branches and coupled into the two sides of the bus waveguide. EDFA, erbium-doped fiber amplifier; VOA, variable optical attenuator; PC, polarization controller; C1, C2, circulators; PD1, PD2, photodetectors; OSC, oscilloscope. (b) Transmission spectrum of the TM00 mode at a wavelength of 1603 nm. Measured transmission spectra in CW and CCW directions at input pump powers of (c) 3.9 mW, (d) 6.2 mW, and (e) 15.7 mW, respectively.

Fig. 3. Measurement of symmetry breaking for the TE00 resonance. (a) Transmission spectrum of the TE00 mode at a wavelength of 1572.6 nm. Measured transmission spectrum in CW and CCW directions at input pump powers of (b) 16.8 mW and (c) 21.4 mW, respectively.

Fig. 4. Optical switching between CW and CCW light states. (a) Hysteresis measurement of the output powers in the two directions at different power ratios of the input power. (b), (c) Numerically simulated output power hysteresis with increasing input power. (d), (e) Simulated output power hysteresis with increased frequency detuning. (f) Hysteresis widths for different combinations of normalized average input power and detuning.

Fig. 5. Calculated spectra of symmetry breaking under different powers for TM00-mode resonance. Simulated transmission spectra from CW and CCW directions under input pump powers of (a) 3.9 mW, (b) 6.2 mW, and (c) 15.7 mW, respectively, shown by the solid lines. Corresponding analytical solutions are depicted by the dashed lines.