Study Of Optical Transmission And Its Nonlinear Effects In Quadratically Coupled Optomechanical Systems

With the rapid development of nanotechnology,cavity optomechanics based on nanophotonics and nanomechanics has become an important branch of quantum optics and nonlinear optics.Its main research object is the optomechanical system which is formed by the coupling between the mechanical motion and the optical cavity field via optical radiation pressure force.In recent years,many research results show that the optomechanical system has important application in sideband cooling of mechanical oscillator,gravitational-wave detection,precision measurement of weak forces,and so on.Most of the researches focus on the physical properties of the linearly coupled optomechanical system,while the researches based on the quadratically coupled optomechanical system are very limited.It has been demonstrated that the two phonon process involved in the quadratically coupled optomechanical system can bring many interesting physical phenomena,such as photon blockade,preparation of quantum superposition states,the squeezing of the mechanical oscillator,etc.Based on the study of the quadratic coupling,we can further expand the research scope of cavity optomechanical system in the fields of quantum and nonlinear optics.In this thesis,we study the optical transmission and its nonlinear effects of quadratically coupled optomechanical systems,including optomechanically induced amplification,Fano resonance,slow light,sum sideband,and difference sideband.Our research content can be summarized as the following three aspects:1.By studying the transmission characteristics of the probe field in the quadratically coupled optomechanical system driven by two control fields,we propose an effective method to realize optomechanically induced amplification under the coupling of a single mechanical oscillator and two cavity modes.The results show that the control field on blue detuning has an obvious amplification effect on the transmission of the probe field,that is,optomechanically induced amplification,and the amplification effect becomes more significant with the increase of the control field power.Compared with the single cavity mode quadratically coupled optomechanical system,the amplification effect of this system is more remarkable.In addition,we can realize the amplification of the output probe field by adjusting the power of the other control field and the reflectivity of the mechanical oscillator.This research is used to realize the conversion and amplification of weak probe signals,which promotes the application of cavity optomechanical system in classical optical communication and quantum information processing.2.By studying the transmission characteristics of the probe field in the double membranes(treated as mechanical oscillators)quadratically coupled optomechanical system,we propose a feasible scheme to obtain the Fano resonance and slow light under the coupling of a single cavity mode and two mechanical oscillators.The results show that the generation of Fano resonance is closely related to the frequency detuning between the cavity field and the control field,and the number and line shape of Fano resonance can be effectively controlled by adjusting the resonant frequency and reflectivity of mechanical oscillators.The results also reveal that the asymmetry of Fano resonance line shape is particularly sensitive to the change of environment temperature,and the group delay of the probe field depends sensitively on the detuning between the cavity field and the control field,and the power of the control field.This study provides theoretical guidance for the precise measurement of temperature and the design of optical buffers,and has potential application in the fields of optical switches and sensors.3.By studying the nonlinear effects of quadratically coupled optomechanical system driven by two probe fields,we propose a theoretical scheme to induce the generation and enhancement of sum sideband via using the quadratically coupled optomechanical system assisted by an optical parameter amplifier.Also,we propose a theoretical method to induce the generation and selective enhancement of difference sideband via using the quadratically coupled optomechanical system assisted by a weak coherent mechanical driving field.The results show that the generation of sum sideband and difference sideband can be effectively enhanced(about three orders of magnitude)by adjusting the nonlinear gain of the optical parameter amplifier and the amplitude and frequency of the weak coherent mechanical driving field under the condition of weak driven fields(at low input power with a few to tens of nanowatts).The results also show that the enhancement of sum sideband and difference sideband can be obtained by adjusting the power of the control field and the frequency detuning of the probe fields.This study can further deepen the understanding of the nonlinear optomechanical interaction in a quadratically coupled optomechanical system,and has important potential applications in precision measurement and optical transmission operations.