Focusing Of Cylindrical Vector Beam Research Articles

Toroidal polarization vortices in tightly focused beams with singularity

In this paper, we numerically investigated tight focusing of cylindrical vector beams of the sec-ond order using Richards-Wolf formulae. It was shown that intensity rings where the Poynting vector was equal to zero appeared not only in the focal plane but also in nearby planes. For example, a lens with numerical aperture NA=0.95 was shown to generate periodical toroidal vortices with a 0.8-mkm period along the z-axis at a distance of about 0.45 mkm from the axis. The vortices were generated pairwise, with the closest-to-focus vortex having clockwise helicity and the subsequent being anti-clockwise. The vortices were also characterized by saddle points. When focusing an optical beam passed through a narrow annular aperture, no toroidal vortices were observed.

Tight focusing of a cylindrical vector beam by a hyperbolic secant gradient index lens.

In this Letter, we investigate the tight focusing of a second-order cylindrical vector beam by a hyperbolic secant gradient index lens with a thickness of 10 µm, a radius of 9.43 µm, and a refractive index on the axis of 3.47 (silicon). It is shown that the lens forms the reverse energy flow near its shadow surface. Moreover, it was obtained that the spherical hole in the center of the shadow plane with a diameter of 0.3 µm allows us to localize the direct energy flow inside the lens material and with the reverse energy flow in an area of free space.

Subwavelength gratings for creation and focusing of cylindrical vector beams

In this paper we derive the equations for the subwavelength grating vector of polarization element that creates the arbitrary order radially polarized beam. We show that the element can be implemented with different shape for different orientations of the input and output polarization. There are under consideration different essential cases of the first and the second order polarization. The second-order element can be sun- or mira- shape and axicon shape. Intermediate shapes are also possible.

Longitudinal component of the Poynting vector of tightly focused cylindrical vector beam

We numerically investigated the tight focusing of cylindrical vector beam with wavelength of 532 nm by a diffractive lens with a numerical aperture 0.95. The simulation was carried out using the Richards-Wolf formulae. It was shown that the focusing of cylindrical vector beam by a wide-aperture lens can produce intensity distribution with a negative component of the longitudinal component of the Poynting vector in the center of the focal spot.

Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures.

The three-dimensional (3D) optical fields that arise from the focusing of cylindrical vector beams (CVB) with radial and azimuthal polarizations provide new sources of contrast for optical microscopy of nano-objects. So far, these demonstrations have been restricted to two-dimensional transversal scanning, i.e., along the focal plane of interest, or use of point-like objects, i.e., single molecules and nanoparticles. Here, we demonstrate the first application of CVBs for 3D imaging of 3D nano-objects. This technique is done by acquiring 3D image scans of the second-harmonic generation signal from vertically-aligned semiconductor nanowires, whose second-order response is primarily driven by the longitudinal electric field, i.e., the field component along the nanowire axis. Our technique provides a new way to study individual nano-objects in three dimensions through the unique combination of nonlinear microscopy and CVBs.

Focus modulation of cylindrical vector beams through negative-index grating lenses

A cylindrically symmetric negative-index grating lens composed of unitary material is proposed as an effective method to modulate the focusing of cylindrical vector beams (CVBs). The grating parameters are designed to obtain an appropriate negative index, and the lens profile is tailored to realize the constructive interference. The plano-concave lens is parameterized to achieve desired focal length and the plano-cone lens is proposed to obtain large depth of focus. An optical needle is generated with radially polarized incidence, and an optical tube is achieved with incidence of azimuthal polarization. Moreover, the presented modulation methods can be applied for any arbitrary polarized CVBs. This work offers a more flexible and effective approach to design negative-index lenses for subwavelength focusing of CVBs, which has potential application value in related areas, such as optical trapping, and other nano-optics fields.

Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect.

Sub-wavelength focusing of cylindrical vector beams (CVBs) has attracted great attention due to the specific physical effects and the applications in many areas. More powerful, flexible and effective ways to modulate the focus transversally and also longitudinally are always being pursued. In this paper, cylindrically symmetric lens composed of negative-index one-dimensional photonic crystal is proposed to make a breakthrough. By revealing the relationship between focal length and the exit surface shape of the lens, a quite simple and effective principle of designing the lens structure is presented to realize specific focus modulation. Plano-concave lenses are parameterized to modulate the focal length and the number of focuses. An axicon constructed by one-dimensional photonic crystal is proposed for the first time to obtain a large depth of focus and an optical needle focal field with almost a theoretical minimum FWHM of 0.362λ is achieved under radially polarized incident light. Because of the almost identical negative refractive index for TE and TM polarization states, all the modulation methods can be applied for any arbitrary polarized CVBs. This work offers a promising methodology for designing negative-index lenses in related application areas.

Subwavelength focusing of cylindrical vector beams by plano-concave lens based on one dimensional metallic photonic crystal

Cylindrical vector beams (CVB) can exhibit a unique optical field distribution and focusing characteristic, due to the cylindrical symmetry in polarization. They are widely used in optical micro-manipulation, super-resolution imaging etc. and can be extended to subwavelength scale applications rapidly. Usually, the focusing CVB in subwavelength dimensions is realized by using plasmonic lens. However, this method is restricted by the state of polarization of electromagnetic waves. Nevertheless, when the negative refraction effect of photonic crystals is utilized, subwavelength focusing or imaging can be achieved in orthogonal states of polarization simultaneously. In this paper, the one-dimensional metallic photonic crystal (1D-MPC) with stronger manipulation ability is discussed. The calculated band structure and equi-frequency surfaces show negative refraction for both orthogonal states of polarization in a specific wavelength band. A cylindrical 1D-MPC plano-concave lens is designed to simultaneously focus radially and azimuthally polarized beams to subwavelength dimensions in visible spectrum. This phenomenon is simulated using the finite element method. Furthermore, variation of the polarization components in CVB can directly modulate the spacial intensity and the polarization distribution in the focal field. In fact, subwavelength focusing of CVB with arbitrary polarization components can be achieved by using the 1D-MPC plano-concave lens. The scheme proposed in this paper can be taken as reference for other wavelength bands as well. This study is also valuable for optical micro-manipulation of small particle, super-resolution imaging, and other related areas.