Classical Chaos And Synchronous Behavior Of Cavity-Coupled Photodynamic Thin Film Oscillators

The field of optomechanics, which deals with the interaction between radiation and nano-or micromechanics motion. The light matter coupling and other system parameters can be adjusted over large scales, optomechanics provides a genuine opportunity to access the classical and quantum dynamics of mesoscopic driven dissipative systems in a variety of different regimes. The semiclassical optomechanical system which is high-dimensional nonlinear dynamical system, we observe the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. Here we analyze the route from regular self-induced cantilever oscillations into the chaotic regime by two ways of increasing the pump power ? and changing quadratic coupling strength ?2. Then We show that many micromechanical resonators interacting with a common mode of cavity field, synchronize to a single mechanical mode Which includes chaos synchronization.Chapter one introduces briefly the history and the current developments of the optomechanicals theory. The one focuses on the investigation history, current situations of cavity optomechanicals.Then describe the chaos fundamental theory in dynamical systems. At last, generalize the synchronization of optomechanicals system and chaos synchronization.In chapter two, we presents a simple but general study on the coupled cavity optomechanical system as well as some other similar systems based on the adiabatic approximation theory. The basic theoretical model and the relevant mathematical method are provided in this chapter. We adopts the adiabatic theory and the transfer matrix method instead to investigate the coupled Fabry-Perot cavities with the membrane-in-the-middle scheme, and gives a universal calculation on the Fabry-Perot cavities mode frequency and the transmission rate modulating by the collective motion of the membranes.In chapter three, We describe the sequence of period-doubling bifurcations (PDBs) that leads to chaos and a chain of inverse of period-doubling bifurcations (IPDBs) that lead to order. In fact, the transition of the system behavior from period to chaotic with variation of parameter, i.e. as the system parameter is changed, a chaotic attractor appears. The process of PDBs and IPDBs verified by the numerical calculation of characteristic signatures in the optomechanical system. The dynamicaltransition can easily be traced or detected by the power spectrum of the cavity field.Chapter five show that Optomechanical systems are based on the nonlinear coupling between the electromagnetic (EM) field in a resonator and one or more bulk mechanical resonators can display synchronization. We present various types of synchronization. Besides we find a chaotic synchronization which includes complete synchronization and phase synchronization. At last, we introduce invariant manifolds and transverse Lyapunov exponent which can be used to identify the complete synchronization in Optomechanical systems with multiple mechanical reasonators.At last summery the work and points out some aspects to be further studied on optomechanical systems.