Reconfigurable chaos in electro-optomechanical system with negative Duffing resonators

Leisheng Jin,Xincun Ji,Yufeng Guo,Lijie Li

doi:10.1038/s41598-017-05020-w

Abstract

Generating various laser sources is important in the communication systems. We propose an approach that uses a mechanical resonator coupled with the optical fibre system to produce periodic and chaotic optical signals. The resonator is structured in such a way that the nonlinear oscillation occurs conveniently. The mechanical apparatus in the configuration is the well known resonating system featured by the negative stiffness. The mechanical resonance is converted to reflected optical signal with the same dynamic properties as the mechanical oscillation, subsequently interacting with the optical signal within the optical fibre. The optical radiative force on the mechanical structure is also considered in the analysis. The coupled electro-optomechanical system has been analysed, and results show that the mechanical resonator has the capability to control the dynamics of the optical signal precisely. The system will have potential applications in tunable laser sources.

Highlights

Thanks to the state-of-the-art fabrication techniques, in recent years various optomechanical systems using, e.g., microtoroids[1], microspheres[2], microdisks[3], suspended mirrors[4] and cavities with membrane in the middle[5], have been fabricated and investigated theoretically and experimentally, opening up new possibilities in research ranging from fundamental physics, such as ground state cooling[6] and quantum entanglement[7], to practical applications, such as quantum-limited detection of forces and displacements[8]
Typical examples are optomechanical systems that are coupled by an extra microwave LC resonator, in which the generated chaos can be modulated by electrical signals[20]
We propose a new design of EMOS by changing the mechanical oscillator in conventional optomechanical systems with a Duffing osccillator with a negative stiffness

Summary

Model Construction

Where Hm and Ho describe mechanical and optical mode, respectively, and Hmo represents the coupling between the two modes These sub-Hamiltonians terms can be written as: Hm = ωm(p2 + q2)/2; Ho = ∆0a†a; Hmo = −Goa†aq; Hd = i (Ee−iω0ta† − E⁎eiω0ta),. G0 and Δ0 represent the coupling strength between the mechanical and optical modes, and the laser detuning, respectively. According to the established theory[21], the force and couple can be given by: F = M · ∇B0; C = M × B0, where B0 is magnetic field and M is magnetization induced by B0 In this case, a magnetic energy potential can be found by using Galerkin approximation, which is written as: W = −(1/2) ∫ M ⋅ B0dν, and this potential is nonlinear in terms of beam’s modal amplitude q and can be expanded in a Tayler series in q, as:. Quantum noises will be neglected in the following numerical study

Numerical Simulation

Conclusion

Additional Information