Studies On The Focusing Characteristics Of Ince-Gaussian Vectorial Beams

Vector fields can provide both spatial and polarization degrees of freedom,which have attracted wide attention.It has advanced potential applications in many fields of optics.However,the diversity of the transverse mode pattern of the Ince-Gaussian(IG)modes laser has more degrees of freedom,and the vector fields composed of the IG modes are expected to show rich phenomena under the condition of tightly focusing.This paper mainly studies the tightly focusing characteristics of the IG vectorial(IGV)beams,including the changes of light intensity,polarization state and spin angular momentum during the focusing process.In this paper,we first introduce the IGV light field which is composed of two orthogonal polarized IG even and odd modes,and focus it tightly according to Richards-Wolf vector diffraction theory.Through the comparison of the distribution of the intensity and polarization state of the theoretical calculation of IGV incident light fields and focusing fields in two cases under different orders,the stability of its transverse structure under the condition of high numerical aperture focusing is revealed,and the corresponding satisfying conditions are given.Then,we focus the vortex phase loaded by x-component of the incident field of IGV tightly.We find that the symmetry of the longitudinal component of the focused field will be broken when the topological charge number is odd,which results in that the total intensity of the focused field is no longer symmetrical.We analyzed the reason of this phenomenon.When two components of IGV incident light fields are simultaneously loaded with vortex phase,the intensity of the focused field remains symmetrical again.It should be noted that the transverse field of IGV is no longer stable when the vortex phase is loaded.In addition,we take IGV(e441,o423)as an example to investigate the focusing stability when the lens is at the non waist position of the beam.In addition,the spin angular momentum in the focusing process is also discussed when the initial phase delay of IGV field is 0 and-? / 2.We find that there is a ? / 2 phase difference between the longitudinal component and the transverse component of the focusing field similar to the cylindrical vector beams.This leads to the generation of transverse spin angular momentum.