Scattering of polarized non-diffracting Lommel beams by nonspherical homogeneous particles

We report a detailed study of the scattering from nonspherical homogeneous particles illuminated by non-diffracting Lommel beams with different states of polarization. Based on the scalar expression of Lommel beam, by introducing vector potential and using the Lorentz gauge, a full vector-wave derivation for the electric and magnetic field components of non-diffracting Lommel beams with linear, circular, radial, and azimuthal polarizations is provided. The surface integral equations method (SIEM) is applied to characterize the scattering problems involving nonspherical homogeneous dielectric particles. As an example, the effects of various parameters characterizing the feature of the Lommel beams on the differential scattering cross section (DSCS) for a spheroid are examined. The results show that the DSCS strongly affected by the states of polarization, asymmetric constant, half-cone angle, and order of the incident beam, which indicates that appropriate selection of these parameters can enhance or suppress the scattering by particles. The DSCSs for the scattering of a Lommel beam with different states of polarization by a cylinder, a cone, and a hexagonal prism are also presented. These results will be useful to reveal the scattering mechanism of the non-diffracting Lommel beams and provide useful references for optical diagnosis, measurement and manipulation of nonspherical particles.