A new type of radially polarized (RP) cosine-Gaussian (CG) field is proposed. Through the analytical model, it is found that such RP CG beam exhibits completely different focusing properties from the reported RP plane waves. More importantly, a stable three-dimensional trap of Rayleigh particle accompanied by a subwavelength spin motion can be easily achieved using this RP CG beam.

Since the invention of optical tweezers, optical manipulation has advanced significantly in many applications, including atomic physics, biochemistry and soft matter physics. Here, we propose a method to trap metallic particles with adjustable trapping range in the transverse plane with the help of customized field. By tailoring the polarization state of the incident field, the focal field with elongation in the direction perpendicular to optical axis can be turned in the 4π focusing system. As a result, optical trapping with tunable trapping range is possible when the metallic particle is interacted with such customized field.

Nonzero transverse energy flow, which describes phenomenon in which the energy flux of localized light propagates in a plane perpendicular to the optical axis, has attracted enormous interest recently due to its useful application in micromanipulation. We show that the appearance of transverse energy flow in the focal plane of an aplanatic high numerical aperture focusing system is possible. We demonstrate our approach by specially tailoring the input state of polarization. Calculations reveal that number of transverse energy flow rings is controllable and depend on azimuthal index of the input field, thereby giving rise to tunable manipulating locations in optical trapping.

We propose a simple method to control the move and elongation of focus along the optical axis in a high-numerical aperture focusing system. By introducing the optical degree of freedom of polarization in the radial direction, a tunable focal shift and elongation of focus are achieved simply by tailoring the polarization index and the topological charge of vortex phase, without the need of additional modulations of amplitude or diffractive optical elements. These findings may be of help in the applications like optical micro-manipulation, laser processing, and imaging.

As an intrinsic attribute of light, the spin angular momentum (SAM) of photons has aroused considerable attention because of the fascinating properties emerging from light–matter interactions. We show that a diffraction-limited focal field with a steerable photonic spin structure in three dimensions can be produced under a 4π microscopic system. This is achieved by focusing two counter-propagating configurable vector beams produced in the coherent superposition of three different beams with x-polarization, y-polarization, and radial-polarization. By altering the amplitude factors of these resultant beams, the ratios between the three mutually orthogonal polarized components can be freely tuned within the focal plane, thereby allowing dynamic control over the spin orientation and ellipticity of the tightly focused optical field. The results demonstrated in this paper may find applications in spin-controlled nanophotonics.

We show that elongating a tightly focused field in the direction perpendicular to the optical axis is possible. We demonstrate our approach by specially shaping the Pancharatnam–Berry (PB) phase. Moreover, the analytical formulae required to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields near the focus of an aplanatic optical system are derived using the Richards and Wolf vectorial diffraction methods. Calculations reveal that the transverse enhancement is controllable and depend on the phase index in the PB phase, thereby giving rise to a focus with tunable length and subwavelength width in the focal plane.

With dual two-dimensional Airy-like waveforms, we demonstrate the creation of highly confined electromagnetic fields in the transverse plane and circular or elliptical propagation trajectories in the longitudinal plane by using specially designed Pancharatnam-Berry (PB) phases. Applying the Richards and Wolf vectorial diffraction methods, the explicit expressions are obtained to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields. Calculations reveal that the nanointerferometric structures of such highly confined fields highly depend on the indexes γ₁ and γ₂ determining the PB phase, thereby enabling the engineering of highly confined fields with tunable size, spacing, and propagation trajectories.