Global bifurcations and homoclinic chaos in nonlinear panel optomechanical resonators under combined thermal and radiati
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ORIGINAL PAPER
Global bifurcations and homoclinic chaos in nonlinear panel optomechanical resonators under combined thermal and radiation stresses E. Hollander . O. Gottlieb
Received: 15 March 2020 / Accepted: 22 September 2020 Ó Springer Nature B.V. 2020
Abstract In this paper, we investigate the nonlinear interaction and time-evolution of confined optical, thermal and mechanical modes in a three-dimensional optomechanical resonator. We model a high-finesse cavity with a thin thermo-elastic panel placed at the center of two highly reflective mirrors that is subjected to an incoming continuous-wave electromagnetic field. The latter is constructed by constraining the light-structure interaction to a first-order scattering phenomenon in the classical interpretation modeled as a spatio-temporal perturbation around a time-harmonic field. We employ a Galerkin-based separation of variables decomposition on the resultant fields and replace them with their nonlinear modal counterparts. The resulting dynamical system is thus governed by the combined effects of thermal and radiation stresses which yield a complex spatially dependent selfexcited bifurcation structure where Hopf bifurcations give rise to periodic limit-cycle solutions. In regions where coexisting solutions are found, homoclinic connections ensue codimension-two Bogdanov–Takens and Double-Hopf bifurcations and that for a range of control parameters a global homoclinic Shilnikov bifurcation culminates with a distinct period-doubling route to chaos. We note that the current formulation demonstrates the essential contribution of coupled E. Hollander O. Gottlieb (&) Department of Mechanical Engineering, Technion – Israel Institute of Technology, 32000 Haifa, Israel e-mail: [email protected]
thermal and radiation stresses to the bifurcation structure of nonlinear light-structure interaction systems and may shed light to modal energy transfer mechanisms and scattering phenomena. Keywords Optomechanical resonators Lightstructure interaction Radiation pressure Photothermal effect Codimension-two bifurcations Homoclinic chaos Shilnikov bifurcation
1 Introduction Nonlinear optomechanical resonators (OMRs) which span across macro-, micro- and nano- scale dimensions have been studied in the past three decades as an alternative for traditional electromechanical resonators [1, 2] due to their relative simplicity and advantages for non-intrusive, non-contact and lowpower applications. These resonators harness the influence of various effects, such as the photothermal effect, the transfer of momentum (referred to as radiation pressure) or the photostrictive phenomenon [3]. In the absence of external modulation, self-excited oscillations in these systems refer to the conditions where in response to a continuous wave (CW) laser, periodic limit-cycle oscillations (LCOs) emerge in the proximity of an equilibrium state stability threshold.
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E. Hollander, O. Gottlieb
Devices based on the photothermal effect mak
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