With the fast development and rapid adoption of all-optical data processing, integrated optical switches are expected to have an important impact on enhancing the speed, reducing power consumption, and minimizing the size of telecommunication systems and optical computing devices [1–3]. Integrated optical switches usually rely on mechanisms such as the thermo-optic effect or carrier dispersion effect to alter the refractive index of materials, allowing for switching between two discrete states. The Mach–Zehnder interferometer (MZI) [4], the microring resonator (MRR) [5], and the hybrid MRR and MZI [6] are the commonly employed structures. Over the last decades, considerable efforts have been made to improve the performance of integrated optical switches in terms of speed, power efficiency, bandwidth, compactness, and so on. Recently, phase change materials (PCMs) integrated with silicon devices have shown great potential as optical switches for further improving the speed performance. These materials can rapidly switch between two stable states and maintain them [7–9].

In the field of optical physics, it is known that spontaneous symmetry breaking (SSB) caused by the nonlinear Kerr effect can exhibit two different states from slight changes as optical switches, which have been revealed across numerous nonlinear optical systems, including nanolasers [10], nanophotonic Bose–Hubbard dimer [11], metamaterials [12], and microresonators [13–17]. In a single optical microresonator, SSB can be observed from the Kerr-interaction between two counterpropagating light waves [13,14,18,19] or polarization states [20–22]. In the context of bi-directionally pumped microresonators, SSB is caused by instability of the intracavity power. Beyond the threshold pump power, a small deviation between the counterpropagating light powers results in a large resonance frequency difference of the initially equal resonator modes in clockwise (CW) and counterclockwise (CCW) directions. This leads to a strong optical nonreciprocity in a symmetry broken resonator. The chirality with unbalanced CW and CCW modes has various applications that have been proposed for optical switches [23], gyroscopes [24], isolators [25–27], and single-particle detection [28–30]. However, until now, SSB-induced switches have not been reported on chips.

Here, we propose to utilize the SSB in a Si3N4 resonator for novel on-chip optical switches. With bi-directional pumping involving two counterpropagating light waves, we observe the emergence of the SSB at a threshold power of 3.9 mW. Every time we cross the nonlinear threshold power, we observe a switching selection of either the CW or CCW state being dominant. The Si3N4 resonator has an intrinsic quality (Q) factor of 9.4×106. Finally, a hysteresis loop in the two directions is experimentally investigated at different pump powers and frequency detunings, indicated for optical switches.

Symmetry breaking in a bi-directionally pumped Kerr resonator originates from the difference of Kerr resonance shift induced by the self-phase modulation for copropagating photons and the cross-phase modulation affecting counterpropagating photons [31]. If two counterpropagating light waves have identical frequencies but different intra-cavity powers inside a resonator, they will see different detunings with respect to the resonance frequency. Theoretically, for a resonator structure in Fig. 1(a), two light fields are injected with the same frequency and power from the left and right sides of the bus waveguide, i.e., PL and PR. The two light fields circulate in CW and CCW directions within the resonator and can interact with each other. As indicated in Fig. 1(b), when the powers of the two intra-cavity light fields are below the nonlinear threshold, the measured transmission spectra are identical in both directions with the resonance frequency of both directions being degenerated. However, if we increase the input powers, the different nonlinear refractive index changes for the two directions will lead to different resonance frequencies for the counterpropagating modes. Practically, the laser power and laser frequency unavoidably have small fluctuations, which can introduce slight differences in power and frequency between the two counterpropagation light waves. If a resonator has a high Q factor, the power difference will be strongly built up within the resonator through the Kerr symmetry breaking. Above the threshold power, the two counterpropagating resonator modes have different resonance frequencies. The resonator mode with higher power will see a smaller frequency shift and will be closer to the pump laser frequency, while the weaker resonator mode has a strong shift induced by cross-phase modulation and will be pushed away from the pump laser frequency [14]. This resonance frequency difference increases with increasing pump power. When the power fluctuations of the pump laser are random, the two light waves will randomly choose one of the two states, enabling the switching between the two light states which follows the hysteresis loop in the right panel of Fig. 1(b).

The optical field amplitudes propagating in the CW (E+) and CCW (E−) directions in a resonator can be written as [32,33] ∂E±∂τ=κexEin,±−[κ2+i(δ−gk|E±|2−2gk|E∓|2)]E±,(1)where Ein,+ and Ein,− are the amplitudes of the input beams in CW and CCW directions, and δ is the frequency detuning between the input pump frequency and the resonance frequency. The total loss in the resonator is κ=κex+κ0, where κex is the coupling loss and κ0 is the internal loss. The Kerr nonlinear coefficient is gk=ℏω02cn2n02Veff, where ℏ is the Planck constant, ω0 is the frequency of the pump mode, c is the speed of light, Veff=2πRAeff is the mode volume of a resonator with radius R and effective mode area Aeff, n0 is the linear refractive index, and n2 is the nonlinear refractive index. The circulating powers in the CW and the CCW directions (PCW and PCCW) are proportional to the square of the fields, i.e., PCW∝|E+|2 and PCCW∝|E−|2. The threshold power of SSB is Pth=1.54πn02Veffηn2λQLQi, where η is the coupling efficiency, λ is the pump wavelength, and the QL and Qi factors are the loaded and intrinsic Q factors [14]. Aiming at low-threshold power SSB, the resonator is expected to have a small mode volume, high nonlinear refractive index, and high Q factor. Note that a higher Q factor especially helps to lower the threshold power because of the 1/Q2 dependence, which requires low-loss resonators.

The waveguide loss is determined by the material loss, scattering loss, and bending loss [34]. The scattering loss is related to the mode overlap with the sidewall roughness. A wide waveguide can reduce the mode overlap with the sidewall. Compared to the fundamental transverse electric (TE00) mode, the fundamental transverse magnetic (TM00) mode can have lower mode overlap, hence reducing the scattering loss and having a higher Q factor [34]. Here, we design the resonator with a waveguide width of 2 μm to support both TM00 and TE00 modes. To achieve a low bending loss, we select a bending radius of 100 μm for the resonator with 400-nm Si3N4 thickness, which can have a negligible bending loss according to our simulations. Details on the fabrication of Si3N4 resonators can be found in Refs. [35,36]. The fabricated Si3N4 resonator is shown in Fig. 1(c).

The experimental setup for investigating SSB in the Si3N4 resonator is shown in Fig. 2(a). Continuous-wave light from a tunable laser serves as the pump light for both CW and CCW modes. The pump light is amplified by an erbium-doped fiber amplifier (EDFA) and subsequently divided into two pathways, directed to the left and right sides of the resonator’s bus waveguide. Before coupling the pump light into the bus waveguide, two variable optical attenuators and polarization controllers (PCs) are used to control the pump powers and adjust the polarization state of the light. Two optical circulators are used to separately monitor the CW and CCW transmission spectra using two photodetectors (PDs). Both CW and CCW transmission spectra are recorded by an oscilloscope (OSC). In the measurement, we first align the light polarization into quasi-TM polarization. We choose one TM00 resonance at a wavelength of 1603 nm with a Qi factor of 9.4×106 as shown in Fig. 2(b) for the SSB measurement [37]. By applying extended coupled-mode theory to fit the resonance transmission at the pump mode [38,39], we find that the coupling rate between the CW and CCW modes is around 16 MHz, which is comparable to the intrinsic linewidth. This leads to an asymmetric resonance lineshape as shown in Fig. 2(b), deviating from the typical Lorentzian profile. Despite the comparable coupling rates between CW and CCW modes, the SSB remains happening. The calculated SSB threshold is 3.8 mW. We experimentally investigate the SSB with input powers of 3.9 mW, 6.2 mW, and 15.7 mW, respectively, as shown in Figs. 2(c)–2(e). Each figure is obtained by sweeping the laser frequency with identical pump powers and exhibits randomly one of the two counterpropagating light states. With increasing pump power, the transmission spectrum exhibits a larger shift of resonance toward a lower frequency. More detailed dynamics of the symmetry breaking in high-QSi3N4 resonators can be found in Appendix A, including theoretically calculated SSB spectra under different pump powers.

Next, we investigate the SSB behavior of TE00 resonance. We fabricate another resonator with a slightly wider waveguide width (3.45 μm) to reduce the TE00 mode overlap with the sidewall roughness to further increase the Q factor of the TE00 mode. Figure 3(a) shows a transmission spectrum of a TE00 mode at a wavelength of 1572.6 nm with a Qi factor of 4.5×106. This leads to the SSB threshold power of 14.8 mW. Experimentally, we start to observe the spontaneous symmetry broken CW and CCW states when the pump power increases to ∼15mW. Two examples of the SSB spectra at pump powers of 16.8 mW and 21.4 mW are shown in Figs. 3(b) and 3(c). Compared to the TM00 mode based SSB spectra in Fig. 2, the SSB spectrum of the TE00 mode is much broader. We attribute this to the lower Q factor and increased heating of the resonator due to optical losses. The full width at half maximum (FWHM) of the TE00 mode is about two times larger than that of the TM00 mode. Theoretically, unequal power distribution between the CW and CCW modes will result in one dominant state, which is suitable for optical isolation [25,26]. However, during the measurement, the presence of noise in the laser causes small fluctuations in the optical power. Thus, SSB can still occur with slight input power differences between CW and CCW modes.

An important feature of the Kerr-nonlinearity-induced symmetry breaking is the hysteresis property when changing the power ratio between PCW and PCCW, used as optical switches. Experimentally, employing the same experimental setup as in Fig. 2(a), we fixed the power of the CCW input and varied the power in the other direction up and down in steps of 0.05 dB. The hysteresis loop of the output powers is observed in the two directions at different power ratios of the input power, as shown in Fig. 4(a). In addition, we numerically investigate the SSB-based optical switching by increasing the average input power and frequency detuning as shown in Figs. 4(b)–4(e). Higher average input power and larger frequency detuning yield a broader stability range before the switching takes place, as summarized in Fig. 4(f).

For the spectra in Fig. 4, more optical power couples into the direction that has access to higher input power initially (CCW direction). This causes more shifts in the resonance in the other direction due to cross-phase modulation. Therefore, less optical power couples into the other direction (CW direction). Gradually increasing the input power in the CW direction only causes a slight increase in the coupled power as the resonance is shifted away from the cold resonance position. This continues even after the point when the input powers in the two directions become equal. However, after crossing the threshold power, the coupled optical power in the CW direction increases swiftly and eventually becomes equal to the coupled power in the opposite direction. Just a tiny increment of the input power in the CW direction after this point shifts the CCW resonance by a great amount, causing a sudden jump of the coupled powers and inversion of the dominant light state. When reversing the direction of the input power scan, the jump will occur far beyond the point of equal input powers. This causes a hysteresis in the coupled powers in the two directions and can be used for optical memories [23].

In summary, we report a novel approach for on-chip optical switches based on the first, to the best of our knowledge, experimental demonstration of on-chip spontaneous symmetry breaking of both TE and TM polarizations in high-Q single Si3N4 resonators. The Q-factors of the TM00 modes and TE00 modes are 9.4×106 and 4.5×106. Taking advantage of the high Q factor of the TM00 mode, the threshold power is measured as low as 3.9 mW. By further increasing the pump power to 6.2 mW, and 15.7 mW, we observe significant broadening of the laser detuning range that supports symmetry breaking. A hysteresis loop is also observed in high-QSi3N4 resonators, used for optical switches. The influence of different pump powers and frequency detunings on the optical switches is investigated. Spontaneous symmetry breaking of the TE00 mode is observed at slightly higher pump powers of 15 mW. Based on the demonstrated symmetry breaking effect, the add–drop resonators in Fig. 2 can also be used for optical isolators [25–27]. In future research, the memory could be heterogeneously integrated with a semiconductor laser for optical computing [26]. Our demonstrated on-chip spontaneous symmetry breaking can also be applied to optical gyroscopes [24], random number generation [40,41], and optical neural networks [42,43].

Acknowledgment. We thank Dr. Olga Lohse for the help with EBL exposure, Dr. Florentina Gannott for the help with the etching process, and Dr. Irina Harder and Mr. Alexander Gumann for useful discussions about device fabrication.