Experimental Demonstration of Spontaneous Chirality in a Nonlinear Microresonator

Chirality is an asymmetric property widely found in nature. Here, we propose and demonstrate experimentally the spontaneous emergence of chirality in an on-chip ultrahigh-$Q$ whispering-gallery microresonator, without broken parity or time-reversal symmetry. This counterintuitive effect arises due to the inherent Kerr-nonlinearity-modulated coupling between clockwise and counterclockwise propagating waves. Above an input threshold of a few hundred microwatts, the initial chiral symmetry is broken spontaneously, and the counterpropagating output ratio exceeds $20:1$ with bidirectional inputs. The spontaneous chirality in an on-chip microresonator holds great potential in studies of fundamental physics and applied photonic devices.

Figure 1

(a) A toroidal microcavity is evanescently side coupled by two tapered fiber waveguides. Inset: A typical transmission spectrum collected by port $B$. TDL, tunable diode laser; PLC, polarization controller; VOA, variable optical attenuator; PS, phase shifter; C, circulator; OSA, optical spectroscope analyzer; PD, photodetector. (b) Scanning electron microscope image of the silica microtoroid. (c) Schematic illustration of the CW to CCW intensity ratio for a standing-wave mode (blue line) and a CW chiral state (red line), as the input power increases.

Figure 2

(a)–(d) CW (blue curve) and CCW (red curve) output spectra collected by the drop fiber under the inputs of 70, 150, 265, and $297\mu \mathrm{W}$ from port $A$ only. (e) The experimental intensity ratio $\mathfrak{R}=P_{\mathrm{cw}}/P_{\mathrm{ccw}}$ versus the input power, with ${\kappa }_{\mathrm{in}}/{\kappa }_{2,0}\approx 0.15$, 0.20, and 0.30, from top to bottom. (f) The theoretical $\mathfrak{R}$ (blue curve) and the scaled effective coupling strength $|g_{\mathrm{eff}}/g|$ (red curve) under the same experimental conditions in (e). Parameters: $2g/2\pi =11.67\mathrm{MHz}$, ${\kappa }_{2,0}/2\pi =2.93\mathrm{MHz}$, and $M=3.64\times 10^{11}{\mathrm{J}}^{-1}$. In (e) and (f), the shaded regions indicate the standing-wave-mode regime (gray), chiral state regime (orange), and four-wave mixing regime (green).

Figure 3

Dependence of chirality thresholds on the coupling rates ${\kappa }_{\mathrm{in}}$. Blue stars and red curves show experimental data and analytical results, respectively. The parameters are the same as in Fig. 2.

Figure 4

(a) Typical drop-port spectrum of the antisymmetric mode, with a total input power of $103\mu \mathrm{W}$ from ports $A$ and $B$. A chiral symmetric state is observed. (b),(c) The same as (a) but with a total input power of $338\mu \mathrm{W}$. The CW and CCW chiral states are observed, respectively. (d) Dependence of $\log \mathfrak{R}$ on the total input power. The solid curves are theoretical results for a lossy resonator with the bifurcation, and the black dots are the corresponding experimental data. Parameters: ${\kappa }_{\mathrm{in}}/{\kappa }_{2,0}\approx 0.33$, and the rest are the same as in Fig. 2. The inset shows the statistics of 71 events of spontaneous symmetry breaking measured under different powers.

Figure 5

(a),(b) Trajectories of state evolutions for $M{A}^2=0$, 3 in the phase space. States dominated by the CCW (CW) wave components lie in the upper blue-shaded area (lower orange-shaded area), with $\pi /2<\theta \le \pi$ ($0\le \theta <\pi /2$). Red dots (blue cross) mark stable (unstable) states. (c),(d) Patterns of the antisymmetric standing-wave mode and the chiral state obtained from two-dimensional numerical simulations [25]. In (c), there is only linear coupling between CW and CCW components, while in (d) the nonlinear coupling is present.