Nonlinear Optical Responses In Two-mode Optomechanics

Cavity optomechanics is a hot research topic that has been studied extensively inrecent years. The traditional cavity optomechanical system is composed of an optical cavityand a nanomechanical resonator. When the optical cavity is driven by a pump laser beam,the radiation pressure force imposed by the intracavity photons will lead to the coherentvibration of the mechanical resonator near its equilibrium position, thus the effective lengthand the resonance frequency of the cavity will be modulated, resulting in a series ofinteresting optical effects. In this thesis, we mainly investigate the nonlinear optical effectin the two-mode optomechanical system where two optical cavities are coupled to acommon mechanical resonator via radiation pressure force. The research contents mainlycontain the following three aspects: Electromagnetically induced transparency and slowlight effect, the bistable behavior of the intracavity photon numbers, and the resonantlyenhanced four-wave mixing (FWM) effect. This paper is divided into five chapters.In Chapter One, we first introduce the research background of cavity optomechanics,and then introduce working principle of typical optomechanical systems. We also introduceseveral cavity optomechanical systems that have been realized in experiments. In addition,this chapter also introduce the phenomenon of electromagnetically induced transparency(EIT) and four-wave mixing.In Chapter Two, we investigate the phenomenon of electromagnetically inducedtransparency (EIT) as well as slow light effect in two-mode optomechanical system. Ourinvestigate found that the broad cavity resonance splits into two dips and a narrowtransparency window appears when the probe beam is resonant with the cavity frequency.As the left pump power increase, the width of the transparency window also increase andthe transmission intensity tends to one. There is a transparency window combined with asteep positive phase dispersion at the cavity resonance, which will result in a tunable groupdelay of the transmitted probe beam and the maximum time delay can reach about4μs.In Chapter Three, we investigate controllable optical bistability based on photons andphonons in a two-mode optomechanical system. When the right cavity is driven at the redsideband, by adjusting the pump detuning, the left cavity photon number will affect thephoton number of right cavity by the vibration of the nanomechanical resonator, and thephoton number of right cavity is higher than the photon number of the cavity when the leftcavity is driven at the blue sideband. The single-mode optomechanical system would needmany more photons in the cavity in order to reach the bistable regime. Furthermore,bistability at low photon numbers below unity should be possible in such a coupled system.In Chapter Four, we investigate the phenomenon of resonantly enhanced four-wavemixing (FWM) based on the phenomenon of electromagnetically induced transparency.Under the low pump power, when the left cavity is driven at the red sideband and the rightcavity is driven at the blue sideband, four wave mixing intensity increases by three orders of magnitude. The FWM process will disappear immediately when the left pump beam isturned off or the optomechanical coupling between the left cavity and the mechanicalresonator equals to zero.In Chapter Five, it is the main conclusions and the prospect.