טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentEyal Hollander
SubjectSelf-Excited Oscillations Bifurcations and Chaos in
Nonlinear Optomechanical Thermo-Visco-Elastic
Panel Resonators
DepartmentDepartment of Mechanical Engineering
Supervisor Full Professor Gottlieb Oded
Full Thesis textFull thesis text - English Version


Abstract

            Nonlinear macro-, micro- and nano- optomechanical resonators (OMRs) have been extensively studied in recent years due to their promising potential for non-intrusive sensing, quantum computing and optical tweezing. In a free-space OMR that is subjected to a continuous-wave laser, a thin mechanical panel is coupled to an optical cavity through induced Lorentz forces and bolometric heating. In the absence of external modulation, the interaction with these forces can lead to self-excitation of the resonator, where periodic limit-cycle oscillations emerge in the proximity of an equilibrium state stability threshold. These oscillations can lose their orbital stability to period-doubled and quasiperiodic oscillations culminating with non-stationary dynamics. Characterizing these thresholds, among other effects, is crucial in explaining observed phenomena such as hysteresis, mode-hopping and optical cooling. To date, the dynamics of OMRs have been described by nonlinear lumped-mass models that do not accurately incorporate the dispersion and spatio-temporal complexity of the coupled thermo-visco-elastic and electromagnetic (EM) fields. In addition, most researches have focused on cases in which only one of the forces (i.e. bolometric or radiation effects) is active and in the close vicinity of an optical resonance.

            Thus, we derive a continuum-mechanics-based nonlinear thermo-visco-elastic model for a thin panel under the influence of an EM field. The latter is constructed by constraining the light-structure interaction to a first order scattering phenomenon (in the classical interpretation) modelled 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 modal counterparts. It is shown that for a range of parameters the combined and separate effects of bolometric and radiation stresses induce a spatially-dependent complex dynamical response where Hopf bifurcations evolve into periodic, quasiperiodic and chaotic-like strange attractors that are sensitive to initial conditions. In regions where coexisting solutions are found, homoclinic connections ensue co-dimension two Bogdanov-Takens, Double-Hopf and Zero-Hopf bifurcations. We show that for a range of control parameters a homoclinic loop of a saddle-focus elicit a global Shilnikov bifurcation which culminates with a distinct period-doubling route to chaos. We investigate a limiting case of an adiabatic EM field in which a bolometric planar beam model is used to validate experimental results, including hysteresis effects and mechanical mode-switching that can lead to quasiperiodic breakdown and homoclinic chaos.