Characterization Of The Vector Beams And Vector Diffraction-free Beams

This thesis is concerned mainly with one of the hot topics, the characterization ofvector light beams. First of all, the form of Jones vector for arbitrary vector beams isstudied on the basis of the accurate representation theory for the light beams and thecylindrical vector beams with a helical phase structure are analyzed carefully; Then,the characterization and properties of general vector diffraction-free beams arestudied and the condition of the diffraction-free beams to expand a finite vectorbeam as a complete orthonormal set is discussed here; In addition, a recentlyadvanced parameter, called degree of paraxiality, is refined; Finally, the power-seriesexpansion of the electromagnetic beams is investigated. The main results andinnovations are as follows:First, the generalized Jones vector in Li’s representation theory is analyzedcarefully and the form of Jones vector for arbitrary vector beams is studied. Also, themisunderstanding of the polarization ellipticity in the previous work is corrected. Itshows that cylindrical vector beams with a helical phase structure are the eigenstatesof total angular momentum in the propagation direction.Second, the characterization and properties of general vector diffraction-freebeams are studied here. And the condition of the diffraction-free beams to expand afinite vector beam as a complete orthonormal set is discussed here. The importanceof the so-called characteristic unit vector I for the complete orthonormal set isinvestigated. Also, the I-dependence of the longitudinal component of thediffraction-free beam is analyzed. The relative strength of the longitudinalcomponent with the total component for the electric field can reflect its vectorialproperty. At last, the transverse displacement and angular momentum for thenon-diffracting beams are given.Third, a recently advanced parameter given by Gawhary and Severini, calleddegree of paraxiality, is refined. By examining the property of the energies originatingfrom the longitudinal as well as the transverse components, we can define the parameter. It is shown that this parameter is determined by the magnitude of theangular spectrum, without depending on the vectorial feature of it. Its value rangesfrom0to1. A larger value stands for a more paraxial beam. As an application, twoexamples, the family of diffraction-free beams and a class of beams that has aGaussian-like angular spectrum are examined. Also, this definition can be generalizedto polychromatic beams without any difficulty.Fourth, from the representation theory, power-series expansion according to aparameter s for all kinds of beams can be obtained by choosing differentparameters I, and the scalar angular spectrum f. When the characteristic unitvector is vertical to the propagation direction, the consistent result is achieved withthe previous work. The transverse component of the electric field involves only evenpowers of s, while the longitudinal component of it involves only odd powers of s.When the characteristic unit vector is parallel to the propagation direction, there isno high-order correction to the longitudinal component of the electric field, still thetransverse component of it involves only even powers of s. It is found that theelectric field of the azimuthally polarized beam has no longitudinal component.When the characteristic unit vector is neither vertical nor parallel to the propagationdirection, in the first-order approximation, it is noticed that the transverse componentof it contains not only the even powers but also the odd powers of s.