Characterization Of The Vectoriality Of Light Beams And Its Application

Vectoriality is one of the most important properties of laser beams. The researchon the vectoriality of light beams has developed new study methods, enriched andexpanded the content of paraxial laser optics, and became the fundamental researchsubject in laser optics. It has been a long time for the research on the vectoriality oflight beams in laser optics. Traditionally, the paraxial light beams were alwaysdescribed as the uniformly polarized light beams (or named scalar light beams),whose polarization is uniform on the cross section. During the past years, theresearch on the vectorial light beams has been a hot subject with fast progress. Themajor difference between the vectorial light beams and the scalar light beams is thepolarization of the vectorial light beams is non-uniform on the cross section. Inrecent twenty years, the well-known vectorial light beams are cylindrical vectorbeams, whose polarization is rotationally symmetric about its propagation axis. Infact, due to the assumed paraxial approximation, there exists an inconsistenceparadox in the conventional theory of laser optics, and in practical work, because ofthe large far field divergence angle of non-paraxial light beams, the paraxialapproximation theory is invalid. Then many kinds of methods have been intrigued toexactly express the transmission of non-paraxial light beams, such as perturbationpower series method, angular spectrum representation, longitudinal componentmethod, and virture source method. But since the advent of laser, the existedrepresentation theory of finite light beams is far from perfect, one of themanifestations is that there exist disputes on the vectorial nature of light beams whenthe Imbert-Fedorov effect is analyzed. And more and more properties, such as thebarycenter of light beams, the spin Hall effects of light beams, the spin and orbitalangular momentum of light beams, and the vectorial feature and the transmissionrule of non-paraxial light beams, will be revealed when the vectoriality of lightbeams is considered. So it is valuable to build and perfect the representation theory of light beams, and to explore the vectorial nature of light beams.In2008, on the basis of the plane-wave spectrum expansion, Chun-fang Liproposed a representation formalism for finite light beams by the introduction of aglobal characteristic unit vector, and he found out that the characteristic unit vectorcan characterize the vectoriality of finite light beams. He pointed out that, when thecharacteristic unit vector is perpendicular to the optical axis, one has the vectorbeams whose polarization is uniform on the cross section in the paraxialapproximation; when the characteristic unit vector is parallel to the optical axis, onehas the vector beams whose polarization is non-uniform on the cross section; whenthe characteristic unit vector is neither perpendicular nor parallel to the optical axis,one has another kind of vector beams. These vector beams are exactly satisfied to theMaxwell’s equations.Due to the characteristic unit vector can be treated as an index to characterizethe vectoriality of finite light beams, so the research on the role of this characteristicunit vector is the main content of this thesis. The purpose of this thesis is to study therole of the characteristic unit vector by analyzing several specific issues associatedwith the vectoriality of light beams, such as the characterization theory of vectordiffraction-free beams, the properties of the barycenter and the angular momentumof light beams, and the different vectorial properties of two light beams which havethe same paraxial approximation. The main research work and innovativeachievements are as following:Firstly, based on the characteristic unit vector introduced in the representationtheory of light beams, the field expression of vector diffraction-free beams is givenout, and the intensity distribution of vector diffraction-free beams affected by threeparameters, such as the characteristic unit vector, the cone angle of diffraction-freebeams and the helicity, are discussed. And it finds out that, the characteristic unitvector can be treated as an index to characterize a complete orthonormal set withdifferent polarization vectors, and the vector diffraction-free beams can be treated as a complete orthonormal set to represent an arbitrary vector beams.Secondly, photon position operator is given out, and it finds out that the positionoperator is not only related to the helicity but also to the characteristic unit vector.With the help of this position operator, the relationship between the barycenter ofvector diffraction-free beams and the characteristic unit vector is studied. And byanalyzing the change of the characteristic unit vector of diffracted light beams, thespin Hall effect of diffracted light beams is perfectly explained.Thirdly, the decomposition of optical angular momentum is introduced. Photonspin and orbital angular momentum operators are given out, and it gives the reasonwhy the optical angular momentum cannot simply be divided into the spin angularmomentum which has the relation with the helicity and the orbital angularmomentum which does not have the relation with the helicity. And it points out thatthe vector beams whose characteristic unit vector is parallel to the optical axis arethe eigenstates of the total angular momentum in the propagation direction.Fourthly, by choosing two different characteristic unit vectors, field expressionsof two different kinds of vector diffraction-free beams which have the same paraxialapproximation are given out. After analyzing and comparing the vector structure andthe angular momentum features of the two beams, it finds out that, although the twovector beams have the same paraxial approximation, they belong to two kinds oflight beams which have different vectoriality. And it points out that there exists aproblem in the generation of cylindrical vector beams.