Diffractive superresolution elements for radially polarized light

Generation of hollow beam with radially polarized vortex beam and complex amplitude filter

The generation of hollow beams with a long focal depth from a radially polarized Bessel-Gaussian beam with a second-order vortex phase and an amplitude filter is theoretically investigated by Richards-Wolf's integral. The null intensity on the optical axis is achieved by introducing the second-order vortex. The long focal depth is a result of the amplitude filtering based on the cosine function and Euler transformation. Numerical results indicate that the focal depth of a hollow beam is improved from 0.96λ to 2.28λ with a slight increase of the transverse size for the simplest amplitude filter design. The intensity distribution twist phenomenon of the x- and y-polarized components around the optical axis due to the introducing of the vortex phase is also discussed. It is believed that the proposed scheme can be used to achieve particle acceleration and optical trapping.

Longitudinal polarized focusing of radially polarized sinh-Gaussian beam

We consider the focusing performance of a radially polarized sinh-Gaussian beam. The sinh-Gaussian beam can be considered as superposition of a series of eccentric Gaussian beam. Based on the Richards-Wolf formulas, high beam quality and subwavelength focusing are achieved for the radially polarized incident sinh-Gaussian beam. Therefore, sinh-Gaussian beam can be applied in the focusing system with high numerical aperture to achieve focusing with superresolution.

Axial separation of orthogonally polarized focal field components due to a radially polarized beam

In this paper, we investigate the field distribution in the focal volume of an aberrated radially polarized beam. Using two different forms of the vectorial diffraction theory, we show that the presence of defocus in the beam displaces both the axially and the radially polarized fields parallel to the optical axis of the focusing lens, while the presence of spherical aberration primarily shifts the longitudinally polarized field only. This facilitates axial separation of the two orthogonally polarized field components, resulting in a significant boost to the ratio of the peak longitudinally polarized field to the peak laterally polarized field in the focal plane. We further show that with an appropriate combination of oppositely signed defocus and spherical aberration, the energy density in the focal volume due to the longitudinally polarized field can be caused to peak at the focal plane. The results obtained are expected to be beneficial to the applications requiring a stronger longitudinally polarized focal field relative to the laterally polarized focal field component.

Optimization of focusing of linearly polarized light

We show that, by adding a π-phase shift to one-half of a linearly polarized beam, the roles of the transversal and longitudinal field components of the focused beam are interchanged, resulting in better focusing of the longitudinal component in the direction perpendicular to the phase jump line. For this component the scheme produces a spot with FWHM >15% smaller than a spot generated with either linearly or radially polarized light for any NA. The scheme has a similar advantage when applied to circularly polarized light, and it holds for both a plane wave and a realistic case of a Gaussian incident beam. This technique may find applications when using recording media responsive to the longitudinal field only, particularly in read/write for optical storage where the resolution in one transverse dimension is most important.