Research On Transverse Focal Shift And Polarization Properties In Optical Fields

Recently,vortex beams and partially coherent beams become important parts of optical and electromagnetic field theory.Some related works on the vortex beams have been widely used in the fields of optical tweezers,quantum communications and optical image processing.Consequently,research on the properties of vortex beams has became a hot topic.Partially coherent beams describe the light field of an actual light source.They are widely used in space optical communications,material heat processing and dark field imaging.With the development of partially coherent beam,researching on the principle and tunable polarization properties of partially coherent beam turns to be important.Hence,we focus on the transverse focal shift of vortex beams and polarization properties of partially coherent beams in this dissertation.The main contributions of this dissertation are outlined as follows:1.The propagation properties of vortex Gaussian beams in a strong focusing system: The electric field of an off-axis linearly polarized vortex beam in the focusing area is derived.The intensity and phase distribution in the focusing area are obtained.The phenomenon of electric field intensity changes in the focal plane and the singularity “producing-annihilationproducing”during the propagation are further analyzed.In addition,the Gouy phase of the beam in a strongly focused field is studied and the main factors affecting the Gouy phase are explored.The results lead to some conclusions,firstly,the “Z”shape of the propagation trajectory of the beam is mainly because of the topological reaction.Secondly,the position of the vortex beams influence the transverse focus,but has no influence on the Gouy shift.Thirdly,the Gouy phase becomes smooth when increasing aperture angle or decreasing the beam width.2.The transverse focal shift of vortex Gaussian beams in a strong focusing system: Based on the phenomenon of intensity changing of an off axis vortex beam in a high numerical system,the analytical expressions of the electric field of four typical vortex beam models through the strong focusing system are derived.The electric field intensity and phase distribution in the focal plane are numerically calculated.Firstly,we introduced the term ―“transverse focal shift”.Then,the effects of parameters such as lens aperture angle,vortex position,topological charge and beam waist width on the transverse focal shift are further studied.The results show that: Firstly,the intensity maximum can move from the y-axis,x-axis to the geometrical focus,or move from +y axis to-y axis in different cases.Secondly,there are three main parameters,the topological charge,the initial positions of the vortices,and the semiaperture angle mainly influencing the transverse focal shift.3.The polarization properties of partially coherent beam in a paraxial system: The electric field and the degree of polarization in the focusing region of partially coherent beam through lens are derived.Based on the optical fourier theory,we propose a 4f focusing system and obtain the formula of the electric field and degree of polarization in the fourier plane and exit plane respectively.Finally,the method for adjusting the degree of polarization in the exit plane is obtained.The results show that a low numerical aperture lens can considerably enhance the degree of polarization at its geometrical focus.The degree of polarization of a beam can be tailored by using amplitude masks in the Fourier plane located in the middle of the two lenses.4.The polarization properties of a circular partially coherent beam in a high numerical system: The expression of 3D degree of polarization in the strong focusing system is derived.The changing of the degree of polarization in the focal plane are also analyzed.The method for adjusting the degree of polarization of this novel partially coherent beam is proposed.The results show that for an unpolarized,partially coherent incident beam,the field in the focal plane can go from almost unpolarized state to almost fully polarized state along a radial distance.Secondly,through adjusting the width of the annular pupil,the Do P on average can be reduced or enhanced significantly.Thirdly,for the very narrow annulus,the approximation expression of the Do P is derived,from which the accurate positions of the peak values of the Do P can be calculated easily.