Investigation Of Optical Rogue Waves And It's Magnetic Control In Coherent Atomic Media

Rogue waves,firstly appeared in the ocean.Because it has sudden ap-pearance,large amplitude and strong destructive force for ships and oil drilling platforms,it is also known as "sail killer".In recent years,The study of Rogue waves,has long been not limited to the ocean,but also extends to the plasma system,fiber and resonator cavity,Bose Einstein condensate,finance and other fields.Among them,optical rogue waves have attracted a great of interests be-cause of their potential applications.optical rogue waves was firstly produced by Solli in nonlinear optical fiber.They use a novel dispersive Fourier trans-form technique to capture high-speed events in the time domain and observed extraordinarily high amplitude peaks at certain wavelengths in the chaotic spec-trum from the supercontinuum.Compared with rogue waves in the ocean,they described these large amplitude waves as "optical rogue waves".It is very difficult to produce optical rogue waves in traditional media,be-cause the nonlinearity in those media such as optical fibers and waveguides is very weak,and hence large input power or very short pulse duration is needed in order to bring out the nonlinear effect required for the rogue wave formation.On the other hand,although the nonlinear effect can be enhanced by the use of some resonant mechanisms,there is however a significant optical absorption,which leads to serious attenuation and distortion of optical pulses.Electromagnetically induced transparency(EIT)posing brought a turn for overcoming the above dif-ficulties.The mechanism of EIT is to introduce a control laser fields,so that the absorption of the atomic medium to probe laser fields is suppressed,its core is through the introduction of control laser fields make coherent atoms destructive interference in the absorption channel for probe laser fields.In this paper,we propose the use of EIT and incoherent optical pumping to realize the generation and propagation of Peregrine optical rogue waves in coherent atomic medium as well as the new mechanism of Akhmediev and Kuznetsov-Ma breathers,and study the propagation path of the optical rogue wave and the breathers how to deflect with the gradient magnetic field.Particularly,the design of the gradient magnetic field can make the optical rogue wave and the breathers move around the obstacle to realize the active control of the optical nonlinear localized states.In recent years,the research on rogue waves has been extended from sin-gle component to double component(vector field).In this paper,a double EIT mechanism is proposed to realize vector Peregrine rogue waves,Akhmediev and Kuznetsov-Ma breathers.We also study the deflection of different polarization components of high dimensional vector breathers in gradient magnetic field by analogy with Stern-Gerlach effect.In contrast with the previous work,the maxi-mum of the breather intensity is much larger than that of the solitons,and hence it is more easily to be measured in experiments.This work is valuable for the precise measurement of gradient magnetic fields.The research work of this paper is mainly focused on the following two aspects:1.Optical rogue waves,breathers,and their active control in A-type three-level atomic gas via electromagnetically induced transparency.Firstly,we use the semi-classical theory of the light and atom,electric-dipole,rotating-wave approximations and slowly varying envelope approximation,derive the op-tical Maxwell-Bloch equations of the atomic system.Secondly,under the EIT condition,we can solve the Maxwell-Bloch equations of the atomic system or-der by order by means of the standard method of multiple scales,obtain the nonlinear propagation equation of the probe-field envelope(i.e.the nonlinear Schrodinger equation),Peregrine rogue waves,Akhmediev and Kuznetsov-Ma breathers solutions of the nonlinear Schrodinger equation are obtained.Then we take Peregrine rogue waves,Akhmediev and Kuznetsov-Ma breathers solutions as the initial condition to simulate,the power is estimated and we want to know whether the incoherent optical pumping have an effect on the formation of rogue waves.The results show that,(1)the system can support stable propagation of optical rogue waves,Akhmediev and Kuznetsov-Ma breathers;(2)due to reso-nance enhancing the nonlinear effect of the system,the input power of the optical rogue wave and the breathers is very low;(3)since incoherent optical pumping can further suppress the optical absorption of atomic systems,the propagation of rogue wave and breathers will be more stable with incoherent optical pump-ing.Finally,under the action of the external magnetic field,the trajectory of the breather is parabolic,and even can bypass obstacles.This has potential applications in the transmission of optical signals.2.Vector optical Rogue waves,as well as Akhmediev,Kuznetsov-Ma breathers and their analogy study with atomic Stern-Gerlach effec-t in five-level double EIT atomic gas via electromagnetically induced transparency.Firstly,we use the theory and method of the first part to derive the Maxwell-Bloch equations of light atom interaction system,obtain the non-linear propagation equation of the probe-field envelope in the atomic medium under the EIT condition(i.e.,the coupled nonlinear Schrodinger equation)and get Peregrine rogue waves,Akhmediev and Kuznetsov-Ma breathers solutions of the coupled nonlinear Schrodinger equation.Then,the resulting vector rogue wave solutions and the breathers solutions are taken as initial conditions for nu-merical evolution,and estimate the power generation.It is found that the input power of the vector optical rogue wave and the breather is very low.In addition,the interaction between a pair of Peregrine rogue waves and the Kuznetsov-Ma breathers is investigated,and found that the interaction(attraction or repulsion)depends on the relation phase.Finally,study the deflection of different polariza-tion components of Kuznetsov-Ma vector breathers with gradient magnetic field to analogy with atomic Stern-Gerlach effect.The results show that the deflec-tion angles of two components of the vector Kuznetsov-Ma are different due to the different velocity.Because the peak intensity of the breathers is far greater than the peak intensity of the background wave,deflection angle of breathers is more easily measured in the experiment,which helps to estimate the value of the gradient magnetic field accurately.The system has potential application value in the field of precise measurement of magnetic field.