Abstract
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale.
Highlights
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport
Note the characteristic timescales of the optomechanical oscillation (OMO) and the photonic crystal carrier dynamics are made comparable through our designed mechanical modes and intrinsic free-carrier diffusion times, enabling the coupled equations of motion to have sufficient overlap and degrees of freedom for chaos generation
We demonstrate chaos generation in mesoscopic silicon optomechanics achieved through single-cavity coupled oscillations between radiation-pressure- and two-photon-induced free-carrier dynamics
Summary
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. We report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. In the toroidal whispering-gallery-mode microcavity, stochastic resonance and chaos have been transferred between two optical fields[23] with the chaotic physical basis through a strong nonlinear optical Kerr response from the nonlinear coupling of the optical and mechanical modes This is complemented by recent theoretical studies on chaos including electro-optomechanical systems and potential routes into chaos[24,25]. Our photonic crystal implementation is based on a slot-type optomechanical (OM) cavity with sub-wavelength [E0.051(l/nair)3] modal volumes V, and high quality factor-to-volume ratios Q/V (refs 26,27) This provides strong optical gradient oscillation[26,28] to achieve operating intracavity energies of B60 fJ and enables near-singlemode operation. Our first-principles numerical modelling, including coupled oscillations in seemingly unrelated degrees of freedom (two-photon-induced free-carrier and thermal dynamics with radiation pressure dynamics) capture the experimental observations, the multi-period orbits and the trajectory divergence into chaotic states
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