Polarized Bessel Gaussian Beam Research Articles

Separating and transporting of particles using tightly focused radially polarized Bessel–Gaussian beam with conical phase

The intensity distributions near the focus for radially polarized Bessel–Gaussian beam with conical phase by a high numerical aperture objective are computed based on the vector diffraction theory. Results show that the circular focal spot can be changed from one to two on the focal plane by adjusting the truncation parameter β. By increasing the phase modulation parameter L, the focal pattern appeared focal shift. According to the intensity distribution, the forces acting on a particle are calculated. The stability of particle trapping is analyzed. It is shown that a tightly focused radially polarized Bessel–Gaussian beam with conical phase is applicable to trapping, separating and transporting of particles.

Focus shaping of linearly polarized Bessel–Gaussian beam modulated by Bessel gratings using a radial shift and a large numerical aperture

Focus shaping of linearly polarized Bessel–Gaussian beam modulated by Bessel gratings using a radial shift and a large numerical aperture

Attenuation characteristics of Bessel Gaussian vortex beam by a wet dust particle

The potential applications of complex optical fields for environmental detection have attracted a lot of attention. In this study, dusty medium is equivalent to a uniformly charged sphere and a non-uniform concentric layered sphere that satisfying the single scattering condition, respectively. The interaction between a high-order polarized Bessel Gaussian beam and a spherical particle is investigated using the generalized Lorenz–Mie theory and the angular spectrum decomposition method. The location of incident beam is considered for the first time. The extinction efficiency results of a wet charged particle are compared with those of a wet neutral particle. Simulations show that the difference in extinction between these two kinds of particles mentioned above is more evident in the smaller size parameter range, which is similar to the case of plane wave incidence. In addition, the influence of complex refractive index and size proportion of heterogeneous medium on the extinction effect is analyzed. The characteristic parameters of the incident beam are considered and find out that how they affect the differences in extinction is independent of the illuminated particle. This study lays the foundation for analyzing the transmission capacity of a Bessel Gaussian vortex beam with various parameters in a dust particle cluster.

Generation of ultra-long multiple optical tubes using annular Walsh function filters

The tight focusing properties of an azimuthally polarized Bessel Gaussian beam phase modulated by annular Walsh function filter is studied numerically by vector diffraction theory. It is observed that upon suitable optimization of order and annular obstruction ratio of an annular Walsh function filter, one can generate multiple sub wavelength scale optical tubes (optical holes) with super long focal depth. Such a focal system is usable for Nano-lithography, particle trapping and transportation, as well as confocal and STED microscopy, microstructure fabrication etc.

Design of pupil filter for scalable generation of uniform foci array

In this paper, the original focus under tightly focusing radially polarized Bessel–Gaussian beam is split into a foci array with a specially designed pupil filter modulation. With this method, foci in the array are precisely controlled at accurate positions, exhibiting almost identical intensities and weak side lobes. Furthermore, a compound modulation through superposition of several filters is theoretically investigated, and a method for scalable generation of uniform foci array on the basis of their subarrays is proposed, which greatly reduced the design complexity of the large-scale foci array. With this method, various kinds of uniform foci arrays with large amount of foci and attractive distributions are well modulated, which may find potential applications in multifocal multiphoton microscopy and parallel laser fabrication.

Creation of super-resolution hollow beams with long depth of focus using binary optics

In this letter, we propose a method for designing super-resolution hollow beams (SHBs) with long depth of focus (DOF) using an M-ring 0-π pure-phase binary optical element (BOE) and a focusing lens when a linearly polarized Bessel–Gaussian beam incident. We also introduce a custom-made method for SHBs with long DOF to iteratively obtain optimal 0-π phase distribution. Moreover, it is shown that the hollow beams can provide great flexibility by controlling spot size and DOF through adjustment of the BOE parameters, including different ring numbers and positions, and also have significant potential for particle trapping.

The minimum number belts of DOE for Bessel–Gauss beams to generate a strong longitudinally polarized beam

In this paper, we minimize the number of belts on the diffractive binary optical element (DOE) to generate a strong longitudinally polarized beam by focusing a radially polarized Bessel–Gaussian beam. Based on a combination of the three-belt DOE and a high-numerical aperture parabolic mirror focusing system, a needle of strong longitudinally polarized beam can be achieved. The transverse full width at half maximum of this longitudinally polarized beam is 0.40 λ and the longitudinal field power fraction reaches 85%. In alternative focusing elements, three belts are the minimum number of the DOE for Bessel–Gauss beams.

Focus shaping of cylindrically polarized Bessel–Gaussian beam modulated by Bessel gratings by a high numerical aperture objective

The focus-shaping technique of the cylindrically polarized Bessel–Gaussian-like beam, referred to the cylindrically polarized Bessel–Gaussian beam modulated by Bessel gratings, propagating through a high numerical-aperture lens is investigated theoretically and numerically in this paper, using the vector diffraction theory method. Results show that the intensity distribution in the focal region can be influenced considerably by: the beam topological charges (m, n), the beam parameter β and the polarization angle ϕ0. The intensity distribution in focal region can be tailored considerably by appropriately adjusting the polarization angle. Peak-centered, donut and flattop focal shapes with extended focal depth which are potentially useful in optical tweezers, material processing and laser printing can be obtained using this technique.

Multifocal array with controllable orbital angular momentum modes by tight focusing

Multifocal spots arrays with controllable three-dimensional (3D) position, orbital angular momentum (OAM) and the number of focal planes along longitudinal direction have been proposed and investigated by using a special designed phase-only multi-zone plate at the back aperture of a high numerical aperture (NA) objective. By using Debye diffraction integral, the focusing field could be rewritten as a fast Fourier transform (FFT), which is the theory and principle for generating the controllable OAM-modes focusing spots. According to this theory, a hybrid multi-zone plate at the back aperture of a high NA objective is designed for the illuminations of the radially polarized Bessel–Gaussian beam. Each focusing spot in the focal plane is generated by independent parts, so the multiplexing OAM-modes could be realized by focusing two or more spots at the same position with different orthogonal eigenstates. It is a practical and flexible OAM multi-focus technique with dynamically controllable 3D position, number of focal planes, corresponding topological charges and focal lengths to meet different requirements, such as 3D optical data storage, air-core fiber coupler and parallel optical manipulation.

Creation of super-length optical tube by phase modulated azimuthally polarized beam with multi-zone phase filter

We suggest a new approach to utilize a multi-zone phase filter along with a high NA lens axicon to accomplish a subwavelength focal hole with large uniform focal depth by means of azimuthally polarized Bessel–Gaussian beam. The intensity distributions are obtained and calculated based on the vector diffraction theory, the recommended system generates a subwavelength super-length optical tube with a sub diffraction beam size of 0.494 λ and long focal depth is approximately 63.6 λ in free space. We also established that the focal depth and sub diffraction beam size is dependent relative on focusing condition of the numerical aperture. The authors presume such a high intense tube beam may perhaps find the applications in atom optics, optical manipulations, optical trapping and optical processing technologies.

Generation of sub wavelength focal spot with large depth of focus generated by radially polarized beam

We investigate the focusing properties of a radially polarized Bessel Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal spot of 0.42λ having large uniform focal depth of 6.45λ. The authors expect such a long depth of focus have great potential for use in optical, biological, high-resolution and atmospheric sciences.

Sub wavelength multiple focal spot generation of high NA objective lens using diffractive optical element

In this article, based on the vector diffraction theory, the effect of specially designed phase modulating optical element by means of an incident tightly focused azimuthally polarized Bessel Gaussian beam in the focal region of high NA lens is investigated numerically. It is observed, that a specially designed diffractive optical modulation element (DOE) can generate multiple focal spot segment of transversely polarized in the focal region by controlling the angles of DOE. Such kind of sub wavelength transversely polarized focal spots segment may find wide applications in multiple optical traps and optical manipulation technology.

Improving the trapping capability using radially polarized narrow-width annular beam

A novel optical-trap method for improving the trapping capability using a radially polarized narrow-width annular beam (NWAB) has been proposed. In this paper, we theoretically study the tight focusing properties of a radially polarized NWAB, formed by subtly blocking the central portion of a radially polarized Bessel–Gaussian beam (the original doughnut beam), through a high-numerical aperture objective. It is shown that a sub-wavelength focal spot () with a quite long depth of focus (about ) can be formed in the vicinity of the focus. Furthermore, the optical trapping forces acting on a metallic Rayleigh particle are calculated for the case where a radially polarized annular beam is applied. Numerical results show that the radially polarized NWAB can largely enhance the transverse trap stiffness and broaden the longitudinal trap range compared with the usage of the original doughnut beam. The influence of the annular factor δ on the focusing properties and the trap stiffness is investigated in detail.

Generation of multiple sub wavelength focal spot segments using radially polarized Bessel Gaussian beam with complex phase filter

We propose a new approach for generating multiple focal spot segment of sub wavelength size, by tight focusing of phase modulated radially polarized Bessel Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observed that focal segment with multiple focal spots structure separated with different axial distance can be generated by properly tuning the phase of the incident radially polarized Bessel Gaussian (BG) beam. Potential applications of this focal shaping technique are also discussed.

Effect of annular obstruction and numerical aperture in the focal region of high NA objective lens

In this article, based on the vector diffraction theory, the effect of annular apodization and numerical aperture in the focal region of tightly focused azimuthally polarized Bessel Gaussian beam by high NA lens is investigated numerically. The results show that our proposed system generates a longitudinally polarized beam in sub wavelength focal spot having large uniform focal depth of incident beam with annular aperture for lower NA. Such kind of subwavelength focal segment may find wide applications in optical traps, biological applications, atmospheric sciences and optical manipulation technology.

Radially polarized Bessel-Gauss beams: decentered Gaussian beam analysis and experimental verification

We derive solutions for radially polarized Bessel-Gauss beams in free-space by superimposing decentered Gaussian beams with differing polarization states. We numerically show that the analytical result is applicable even for large semi-aperture angles, and we experimentally confirm the analytical expression by employing a fiber-based mode-converter.

Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element

We proposed a method to design a ternary optical element in order to achieve a needle of super-resolution longitudinally polarized beam with ultra-long depth of focus, and obtained a beam with a size of 0.3995λ and depth of focus of 12.83λ after focusing a ternary optical element modulated, radially polarized Bessel–Gaussian beam with an aplanatic lens of numerical aperture 0.95. The algorithm we used to design the ternary optical element is based on axial uniformity in the focal region, which allows rapid searching speeds and excellent performance. The ratio of pupil radius to the beam waist was set as 0.57, making the peak intensity of the incident beam occur at the rim of the lens aperture, which maximized the possible resolution of the focused beam.

The beam quality parameter of spirally polarized beams

Starting from the expression for the quality parameter of a superposition of two general fields, the case of beams that can be written in terms of the polarization basis introduced by Gori is investigated. Different types of this class of beam are studied and compared. In particular, spirally polarized beams are considered. As an example, polarized Bessel-Gauss beams are analyzed in detail.

Vector Helmholtz–Gauss and vector Laplace–Gauss beams

We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.

Focal shift in vector beams

We examine the three-dimensional intensity distribution of vector Bessel-Gauss beams with general polarization near the focus of a nonaperturing thin lens. Recently reported linearly and azimuthally polarized Bessel-Gauss beams are members of this family. We define the width and focal plane of such a vector beam using an encircled-energy criterion and calculate numerically that, as for scalar beams, the true focus occurs not at the geometric focus of the lens but rather somewhat closer to the lens. This focal shift depends on the mode number and system parameters and is largest for a narrow beam, long lens focal length, and large wavelength.