Study On Propagation Of Singular Beams In Gain And Absorbing Media

Singularity optics is a new branch of modern optics,which studies the light field with singularity.In the transmission process,the field can maintain the existence of optical singularities,where the light intensity is zero.Optical singularity refers to the point in the light field where the physical parameters cannot be defined,so that the light intensity or amplitude of the point must be zero in order to have a reasonable physical existence.Phase singularities are the most initial and extensive research objects in singularity optics.Generally,the light field carrying phase singularities is called vortex beams.Vortex beam is a light field that spirals in the direction of propagation.From the perspective of the wave of light,the phase of the center point of the vortex beam is uncertain due to the characteristic of spiral advance,which leads to the light intensity is zero and point in the center of the light field,namely the dark field.Therefore,it can be seen that singularity beam has unique optical properties,which make this kind of beam have important application value in the capture and control of particles,material processing,laser communication and other fields.This paper will mainly study the propagation of singularity beam in gain and absorption medium,which is divided into the following three parts:Firstly,We made some theoretical analysis and derived the field distributions of Gaussian vortex beams in the gain and absorption media.The intensity distribution and phase evolution of Gaussian vortex beams propagating in gain and absorbing media are studied,the effects of the real part of wave number k_r,the imaginary part of wave number k_i and the topological charge m on beams propagation properties are analyzed in detail.The results show that the larger the real part of the wave number k_r and the larger the topological charge m,the intensity of Gaussian vortex beams decreases more slowly,it always keeps the characteristic of hollow beam distribution and has good stability.The gain effect of beams propagation becomes more obvious with the increase of the imaginary part of wave number k_i,the absorbtion effect of beams propagation becomes more obvious with the decrease of the imaginary part of wave number k_i.The phase distribution of Gaussian vortex beams is affected by the topological charge m,The number of optical vortices of Gaussian vortex beams with different topological charge m are different at the source and during transmission.Secondly,we investigated the propagation of the partially coherent vortex beams in the gain and absorption media.The intensity distribution,phase evolution and spectral coherence of the partially coherent vortex beams in the gain and absorption media are studied.The effects of topological charge m,coherence length?₀,real part k_r(related to refractive index)and real part k_i(related to gain and absorption characteristics)on the propagation of partially coherent vortex beams are analyzed.The results show that the larger the topological charge m,the larger the coherence length?₀,the larger the real part of the wave number k_r,and the larger the propagation distance of the partially coherent vortex beams with hollow distribution.The smaller the coherence length?₀ is,the more obvious the loss effect of the beam in the transmission is.The larger the coherence length?₀ is,the more obvious the gain effect of the beam in the transmission is.In the gain media,the optical power increases continuously,while in the absorbing media,the optical power decreases continuously.The coherent vortices with a topological charge of+m at the source will split into m coherent vortices with a topological charge of+1in both the gain and absorption medium transmission and new coherent vortices with a negative topological charge will be generated at the same time.The larger the coherence length?₀ is,the larger the corresponding distance of coherent vortices splitting and the larger the corresponding transmission distance when new coherent vortices appear.The larger the coherence length?₀ is,the slower the spectral coherence attenuation is and the larger the minimum value appears in t he attenuation.In addition,k_r and k_i of different media have different effects on the evolution of spectral coherence.Finally,the influences of the gain media on partially coherent circular edge dislocation beams are derived.The reference point?₁=(x₁,y₁),real part of wave number k_r,the number of circular edge dislocations n and coherence length?₀on the phase distribution of spectral coherence of partially coherent circular edge dislocation beam are analyzed.Results show that the larger value of reference points x₁and y₁,the larger corresponding transmission distance when new coherent vortices appear,but the selection of reference points has no effect on the overall law of phase evolution.In addition,by comparing the phase distribution of k_r in the real part of different wave numbers,it can be seen that the larger k_r is,the less likely it is for coherent vortices to split and generate during transmission.When the beam with n propagation through the gain medium,the circular edge dislocation will disappear and be transformed into n pairs of coherent vortices.With the further increase of the transmission distance,new n pairs of coherent vortices will be generated,that is,there are at most 2n pairs of coherent vortices in the transmission process.In addition,the greater the coherence length?₀,the greater the distance of new coherent vortices.When?₀ tends to infinity,the partially coherent circular edge dislocation beam degenerates into a(completely coherent)circular edge dislocation beam,and the phase distribution of the circular edge dislocation is always maintained,and no new coherent vortices are generated.In all phase distributions,the position of the coherent vortices shifts with transmission,but the position of each pair of coherent vortices is symmetric about the axis y=x.