Self-Switching Kerr Oscillations of Counterpropagating Light in Microresonators

We report the experimental and numerical observation of oscillatory antiphase switching between counterpropagating light beams in Kerr ring microresonators, where dominance between the intensities of the two beams is periodically or chaotically exchanged. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging, which restores the broken symmetry on average. Self-switching of counterpropagating light is robust for realizing controllable, all-optical generation of waveforms, signal encoding, and chaotic cryptography.

Figure 1

(a) Schematic of a ring resonator. Two identical input beams enter the resonator, via a coupling mechanism, to then circulate in opposing directions. They each complete many round-trips before eventually leaving the resonator to continue to their respective outputs. The inset shows a glass microrod resonator (the bulge in the middle of the rod). (b) Example of antiphase periodic switching. “Slow time” refers to a timescale much larger than the round-trip time of the resonator.

Figure 2

Stationary and oscillatory intensities, described by Eqs. (1), under a forward detuning scan, with $|E_{\mathrm{in}}{|}^2=4.0$. The blue and black lines indicate the symmetric and symmetry-broken stationary solutions, respectively, with solid lines indicating stable states and pale dashed lines indicating unstable states. The red dots denote Poincaré sections: a red dot is placed at each local minimum and maximum of an oscillation. Also shown, in semitransparent yellow and blue, are the full ranges of the oscillations. The yellow and blue shading results in a green colouring where the oscillations overlap. One observes three distinct regions: In zones (1), the oscillations in intensity do not overlap. In zones (2), they partially overlap, but this does not cause switching. In zone (3), switching occurs between the intensities of the two counterpropagating modes.

Figure 3

(a) Schematic of the experimental setup. Fiber amplifier (Ampli.), polarization controllers (PC), optical isolators (Iso.), photodiodes (PD), microresonator ($\mu$-res.), oscilloscope (Osc.). Power attenuation components are omitted for simplicity. (b)–(d) Examples of different experimentally observed self-switching behaviors under a detuning scan of a single cavity resonance—the traces depict fluctuations in optical power. (b) Intermittent switching where the modes do not exchange dominance every time their intensities approach similar values. (c) Transient synchronization phenomena in between transition events (circled). (d) Near-periodic switching dynamics approach regular periodicity (the amplitudes of the intensity oscillations reach similar minima and maxima for every mode exchange).

Figure 4

Time series and rf intensity spectra (FFT of $|E_{\pm }{|}^2$) of different switching states obtained by numerical integration of Eqs. (1). (a)–(b) Intermittent switching: the modes swap irregularly, with chaotic amplitude variations ($|E_{\mathrm{in}}{|}^2=5.8$, $\theta =6.984$). (c)–(d) Near-periodic switching approaches regular periodicity ($|E_{\mathrm{in}}{|}^2=5.8$, $\theta =7.1$). (e)–(f) Periodic switching (under imbalanced input powers), implying the disappearance of broadband chaos ($|E_{{\mathrm{in}}_1}{|}^2=4$, $|E_{{\mathrm{in}}_2}{|}^2=4.2$, $\theta =6.92$).

Figure 5

Heat maps when varying the pump power and detuning. (a) Characteristic frequencies (key changes in behavior are marked with black curves). (b) Various types of dynamics: A, steady state; B, regular oscillations; C, period doubled; D, period tripled; E, period quadrupled; F, chaotic, nonswitching; G, chaotic switching; H, periodic switching. The period-tripled state, like periodic switching, is associated with the total disappearance of chaos. The system reverts to steady-state behavior towards the right of the frames.