Research · Publication & note
Chaotic dynamics in coupled resonator sequences
IEEE Group IV Photonics · Conference paper · 27 August 2014
Abstract
We report on the generation of chaotic signals in sequences of integrated coupled silicon resonators at telecommunication wavelengths. These can pave the way to on chip all optical random bit generators naturally compatible with silicon photonics.
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Research fields
Top-down
A sequence of silicon microrings is fabricated in a SCISSOR architecture with each cavity coupled to common straight waveguides. The topology preserves strong optical feedback even when fabrication disorder shifts individual resonances.
Simulations & fits
Coupled nonlinear rate equations include intracavity power, free carriers and temperature for every ring. Numerical time traces and phase-space diagnostics identify the transition from periodic self-pulsing to deterministic chaos as more resonators participate.
Characterization
Continuous-wave excitation is monitored simultaneously through temporal output signals and top-scattered-light images of the ring chain. Correlating waveform complexity with the number of heated cavities demonstrates that the aperiodic response originates inside the coupled system.
RESEARCH TOPICS
CouplingThe experiment uses a SCISSOR sequence of silicon microrings side-coupled to a common bus, with a 300 nm gap. Light dropped by one resonator continues through the circuit and the thermal/free-carrier state of several rings becomes dynamically linked through the shared optical signal. Power scans from 5 to 23 mW over 1542.5–1545 nm show regimes in which two, three or six resonators become hot. The collective response is therefore not equivalent to repeating an isolated bistable ring.
InterferenceChaos is diagnosed from temporal data, not from an irregular-looking trace. The drop signal is embedded into a reconstructed phase space using delayed copies with an 8 ns lag, following Takens' theorem. Dense trajectories and sensitivity to initial conditions are compared with simulations, and Lyapunov exponents provide the quantitative test. Figure 4 shows that the reconstructed experimental attractor and the model occupy similar regions, connecting the observed fluctuations to deterministic nonlinear dynamics rather than detector noise.
MultimodeThe relevant degrees of freedom are the optical and thermal/free-carrier states of many nominally similar resonators in the chain. At low complexity, one or two hot rings produce periodic outputs; as more rings participate, the coupled state space expands and the motion becomes aperiodic. Spatially resolved simulations in Figure 2 identify which resonators are hot at each operating point. This distributed behaviour is why a resonator sequence can reach a chaotic regime unavailable to a single, slowly responding cavity under the same continuous-wave drive.
NonlinearContinuous-wave excitation activates two delayed silicon nonlinearities: free carriers generated by two-photon absorption change the index, while absorption heats the rings and shifts their resonances in the opposite direction. Their different time scales create bistability, self-pulsing and, when several rings interact, chaos. The study maps these regimes against wavelength and coupled power rather than invoking an instantaneous Kerr response. That distinction matters because the chaotic bandwidth and attractor are set by carrier recombination and thermal relaxation.
ResonatorsEach microring is a wavelength-selective cavity, but the sequence behaves as a dynamical network. The SCISSOR topology preserves access to the individual drop responses and avoids some propagation constraints of inline CROW or photonic-crystal chains. Experiment and coupled equations show periodic states when only a small subset is thermally shifted, followed by deterministic chaos as additional resonators join. The architecture links standard silicon resonators to functions such as optical memory, neuromorphic dynamics and physical random-signal generation.