Complex dynamics of nano-mechanical membrane in cavity optomechanics

• Published in: Nonlinear dynamics Vol. 83; no. 1-2; pp. 963 - 970
• Main Authors: Akram, Muhammad Javed, Saif, Farhan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2016; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Computer simulation; Control; Digital mapping; Displays; Dynamic stability; Dynamical Systems; Dynamics; Engineering; Harmonic oscillators; Holes; Mathematical models; Mechanical Engineering; Membranes; Nanostructure; Nonlinear dynamics; Opto-mechanics; Original Paper; Radiation pressure; Stability analysis; Vibration; Survival probability; Stability; Optomechanics; Driven system; Lyapunov exponent
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-015-2380-y

Theoretical analysis of a suspended nano-mechanical membrane subject to an optical driving field in an optomechanical cavity is presented, which is confirmed through numerical simulations. In the presence of an optical field between its mirrors, the high-finesse optomechanical resonator acts as an oscillator driven by a radiation pressure force. The periodic nature of the radiation pressure force makes the nano-mechanical membrane in the optomechanical system as a kicked harmonic oscillator. Mathematically the physical system displays a stochastic web map that helps to understand several properties of the kicked membrane in classical phase space. We find that our web map is area preserving and displays quasiperiodic symmetrical structures in phase space which we express as q -fold symmetry. It is shown that under appropriate control of certain parameters, namely the frequency ratio and the kicking strength, the dynamics of kicked membrane exhibits chaotic dynamics. We provide the stability analysis by means of Lyapunov exponent and survival probability.