Magnetic spectral Stokes singularities of stochastic electromagnetic beams through an astigmatic lens

Abstract

Much interest has been aroused in the polarization singularities. A new technique for metrology called singular Stokes polarimetry based on the detection of polarization singularities has been recently developed and used to detect deformations and displacements of samples on a submicron scale, to measure the topology of polarized speckle field and to study the biomedicine as well. The polarization singularities have been extensively studied theoretically, numerically and experimentally. However, most of the studiesare restricted within the frameworks of the fully coherent wave-fields. By using the spectral Stokes parameters introduced by Korotkova and Wolf[Korotkova O, Wolf E 2005 Opt. Lett. 30 198], Yan and L[Yan H, L B 2009 Opt. Lett. 34 1933] have extended the concept of the polarization singularities from fully coherent beams to partially coherent beams. On the other hand, Hajnal[Hajnal J V 1990 Proc. R. Soc. Lond. A 430 413] studied the electric and magnetic polarization singularities in free-space propagation experimentally with microwaves and confirmed that the electric and magnetic polarization singularities are not coincident in general. In this paper, taking the partially coherent edge dislocation beam for example, the explicit magnetic propagation expression for stochastic electromagnetic beam through an astigmatic lens is derived based on the representation of cross-spectral density matrix propagation. Using the spectral Stokes parameters the magnetic spectral singularities are studied in detail. It is shown that there exist magnetic spectral s12, s23 and s31 singularities of stochastic electromagnetic beams through an astigmatic lens. The magnetic spectral Stokes singularities correspond to the zero points of complex Stokes fields sij=0. s12 singularity corresponds to the circular polarization (C-point) of partially coherent beam, and s3 0(s30) means right-(left-) handedness, where the orientations of the major and minor axes of the polarization ellipse become undefined. s23 and s31 singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined (linear polarization). By suitably varying a control parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, and astigmatic coefficient or propagation distance, the motion, creation, and annihilation of magnetic spectral Stokes singularities may appear. It has been shown that a pair of C-points with equal but opposite topological charges and with similar handedness may be created or annihilated. The V point and handedness reversal of C point may take place. Compared with the electric spectral Stokes singularities of stochastic electromagnetic beams, the positions are not the same, and the left- and right-handedness spaces do not coincide. The results obtained in this paper would be useful for an in-depth understanding of polarization singularities of stochastic electromagnetic beams.