Secondary Coupling Effect Of Photodynamic System

The general coupling between nanomechanical oscillators and optical fields is the radiation pressure coupling which is a linear coupling that is proportional to the field intensity I and oscillator’s displacement x. The nonlinear spatial coupling effect will become obvious and important in a strong cavity field with large oscillating amplitudes, and then the nonlinear effect with quadratic coupling in opt-mechanical devices takes a significant meaning. In this article, two typical effects of the quadratic coupling in optomechanical system have been studied and the other effects on this topic are briefly summarized. The dissertation includes four parts:In the first chapter, the significance and the prospect of the recent research on cavity optomechanics and the related applications are introduced. Furthermore, the main research results of the scholars from both home and abroad are summarized in this chapter. The main concepts for cavity optomechanics such as the compositions of optomechanics system as well as the basic characteristics of optical cavity and mechanical oscillators, the attenuation coefficients of the optical cavity and mechanical oscillator, the radiation pressure and its application in cavity optomechanics system are discussed in details. Meanwhile, the mechanisms of different couplings between optical and mechanical objects are reviewed. A typical Hamiltonian and the linearized approximation method on this model are presented in order to give a basic background of optomechanics for the following studies.In the second chapter, the typical opto-mechanical systems with quadratic couplings are introduced to derive a generic model under quadratic coupling. The study on this model shows that these systems will produce a stable self-sustained oscillation when the energy injected by external driving equals to that of dissipations in a certain parametric region. The semi-classical equation of motion of the system is numerically solved and the results reveal a high-dimensional limit circle in phase space under the controls of driving and damping. The numerical study verifies the existence of the high dimensional limit circle by finding the stable closed orbits in all the projective3-dimensional phase spaces and demonstrates a highly controllable topological structure of the phase orbit which is very similar to Lissajous figures formed in a2-dimensional case. The shape twisting and splitting of the limit circles in phase space are due to variations of the locked frequency and the amplitude of vibrator’s motion which subsequently change the topology of the limit cycles. In addition, by adjusting the control parameters, the amplitude bifurcation of the self-oscillation will occur above a critical pumping power. The responses of the oscillator to the light show a discrete characteristic and have a high sensitivity under quadratic couplings. The self-sustained oscillation of the driving resonator with controllable amplitudes and frequencies not only demonstrates a reliable physical application of opto-mechanical system under quadratic coupling, but also provides a mathematical model for the study of limit cycle in a high dimension for the nonlinear differential equations.In the third chapter, the modification on static responses of a linear coupling nano-oscillator by quadratic optomechanical couplings is studied. A quadratic coupling enabled parametric oscillation in an optomechanical system is used to modify the nonlinear static responses of a mechanical oscillator along with the normal linear coupling. The mean value study shows that the modification of the static response on a mechanical oscillator is extremely sensitive and useful, which can readily enhance or suppress the nonlinear displacement response from a bistability case to singlet or triplet well case, freely bifurcating the equilibrium position from one to two or three. The static equilibria structure and the stability regions for mean-value controls on nano-oscillator are analyzed under the possible modification parameters.In the fourth chapter, the other effects of the quadratic coupling in opto--mechanical system are summarized and the prospective topics beyond this thesis are provided. Based on a typical membrane-in-the-middle system, the non-demolition detection on the energy or photon number of the oscillator, the squeezed states generation and the nonlinear photon tunneling modified by the mechanical oscillation are discussed. The classical dynamical behavior and the quantum dynamics behavior of the system under quadratic optomechanical couplings are missed in this thesis and they are certainly the challenging problems which need to be studied further in the future.