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Coherent modulation in coupled electro-optomechanical photonic crystal resonators : Floquet dynamics and chaos

Abstract : Nanomechanical systems are useful to inspect some fundamental aspects of physics such as the relations between the elastic, thermal and electromagnetic properties of solid-state objects. As many other nanometer scale systems, they are interestingly subjected to strong nonlinearities that can guide the emergence of ubiquitous phenomena - like synchronization and chaos – or be exploited for manipulating and processing information. Such nanomechanical systems can be put in interaction with an optical cavity or coupled to an electrostatic-actuator. These two approaches are embedded in the wide topic of electro-optomechanics. This work takes advantage of photonic crystal versatility to investigate the nonlinear optical and mechanical dynamics of such electro- or optomechanical systems under coherent modulation.The first experiments use a nanophotonic platform combining a suspended InP membrane and an underneath integrated silicon waveguide. The membrane is etched with a 2D photonic crystal embedding several evanescently coupled defect cavities. These latter constitute a photonic molecule whose electromagnetic eigenmodes can be driven with a laser, via the waveguide, thus enabling a sensitive access to the mechanical noise spectrum of the membrane. Using a coherent modulation of the input laser field, we show how the input modulation sidebands are transferred to the mechanical frequency domain via the optomechanical interactions. The presence of thermo-optic nonlinearities further leads to a desymmetrization of the noise spectrum features. The experiment is described theoretically via Floquet theory. Relying on thermo-optic bistability, a bistable photonic mode is finally used to amplify a small signal by vibrational resonance.In a second part, we study two mechanically coupled electro-optomechanical photonic crystal nanocavities. Here the system is probed via an optomechanical scheme and driven with an integrated electro-capacitive actuation to drive the system's mechanical normal modes. Under low-power drive, the system can be robustly studied and calibrated using simple model of coupled damping harmonic oscillators. The use of higher power excitation reveals the strong intrinsic nonlinearities of the system which can be modeled by two driven coupled Duffing oscillators. The use of coherent modulation of the input force now reveals interesting period-doubling cascade route to chaos dynamics. The simultaneous excitation of both normal modes in their nonlinear regime makes them couple such that synchronization can be studied. As chaotic system can be used to generate chaos, this bichromatic synchronized chaotic dynamics could be exploited in novel multispectral data encryption protocols.This work open the way toward the exploration of large optomechanical arrays, in which collective dynamics could be studied.
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Guilhem Madiot. Coherent modulation in coupled electro-optomechanical photonic crystal resonators : Floquet dynamics and chaos. Optics / Photonic. Université Paris-Saclay, 2020. English. ⟨NNT : 2020UPASP076⟩. ⟨tel-03106105⟩

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