Polarization And Spin Of Vector Beams

Since the pioneering work of Allen et.al.on the orbital angular momentum of paraxial scalar light beams in 1992 [Phys.Rev.A 45,8185(1992)],the optical angular momentum has become an important research hot topic in optical physics.At about the same time,Jordan and Hall's theoretical study on azimuthally polarized light beams [Opt.Lett.19,427(1994)] opened the research area of vector light beams.In 1998,Berry pointed out in a paper on the spin angular momentum of paraxial light beams [Proc.SPIE 3487,6(1998)] that the spin of a light beam cannot completely describe its polarization state.The main task of this dissertation is to investigate the relationship between polarization and spin by analyzing the way of characterizing the polarization state of general vector light beams.First,we generalize the Stokes vector characterizing the polarization of a plane wave to a general vector beam in the momentum space.Analysis shows that the Stokes vector of the vector beam at any momentum(called the generalized Stokes vector)depends on the choice of the transverse local coordinate system at that momentum.To determine the generalized Stokes vector of a general vector beam,we used a method proposed by Stratton to characterize the degree of freedom of local coordinate system selection using a constant unit vector(called a Stratton vector).Further research has found that although the polarization vectors of any given beam correspond to different generalized Stokes vectors in different local coordinate systems,once the Stratton vector is selected(or once the local coordinate system is determined in the momentum space)has a one-to-one correspondence between the polarization vector and the generalized Stokes vector.That is to say,once the Stratton vector is selected,the generalized Stokes vector can characterize the polarization state of the vector beam in this sense.We also compare the degrees of freedom revealed here—the similar relationship between the Stratton vector and the electromagnetic potential specification degrees of freedom.On this basis,we analyze the relationship between the spin and polarization of a general vector beam in momentum space and find that the spin is only the longitudinal part of the generalized Stokes vector that characterizes the polarization.This result is not only consistent with the well-known fact that the spin of light lies entirely along its direction of propagation,but also explains why the spin of light does not fully describe its polarization state.The spin of light is as familiar as the common sense of physics,but Bliokh et al.recently published an article in Nature Communications [Nature Communications 5,3300(2014)] claiming that they found a so-called transverse spin perpendicular to the direction of propagation in the evanescent wave that occur during total reflection.The second part of this thesis proves that such a spin does not exist.