Tight focusing of spirally polarized vortex beams

The tight focusing of spirally polarized focused vortex beams is analyzed numerically based on the vectorial Debye theory. The expressions for the electric field and the orbital angular momentum of focused beams are derived. It is shown that the intensity distribution in the focal plane is dependent on the specific spirally polarized state and the coefficient of the spiral polarization function. By presenting the phase contours of the component polarized in the radial direction, it is found that the radii of dislocation lines will increase with the increase of the power of the spirally polarization function. It is reveled that the same orbital angular momentum can be obtained for different spirally polarized state at certain distance along the propagation direction in the focal region. Besides, the orbital angular momentum distributions for different polarized states have fewer crossover points with each other for higher topological charge. The influence of the spirally polarized state on the orbital angular momentum in the focal plane is also studied.     

Comparison of three kinds of polarized Bessel vortex beams propagating through uniaxial anisotropic media

A comparison of differently polarized Bessel vortex beams propagating through a uniaxial anisotropic slab is discussed in terms of the vector wave function expansions.The magnitude profiles of electric field components, the transformation of polarization modes, and the distributions of orbital angular momentum(OAM) states of the reflected and transmitted beams for different incident angles are numerically simulated.The results indicate that the magnitude profiles of electric field components for different polarization modes are distinct from each other and have a great dependence on the incident angle,thus the transformation of polarization modes which reflects the change of energy can be affected largely.As compared to the x and circular polarization incidences, the reflected and transmitted beams for the radial polarization incidence suffer the fewest transformation of polarization modes, showing a better energy invariance.The distributions of OAM states of the reflected and transmitted beams for different polarization modes are diverse as well, and the derived OAM states of the transmitted beam for radial polarization present a focusing effect, concentrating on the state between two predominant OAM states.     

Separation of spin angular momentum in space-variant linearly polarized beam

We show that the spin angular momentum (SAM) flux in a space-variant linearly polarized beam can be separated in the focal plane. Such a beam carries only orbital angular momentum (OAM) and develops a net SAM flux upon focusing. The radial splitting of the SAM flux density is mediated by the phase vortex (or OAM) and can be controlled by the topological charge of the phase vortex. Optical trapping experiments verify the separation of the SAM flux density. The proposed approach enriches the manipulation of the angular momentum of light fields and inspires more designs of focus engineering, which would benefit optical micromanipulation of microscopic particles.     

Tight focusing of partially polarized vortex beams by binary phase Fresnel zone plates

Based on vectorial Debye theory, the focusing properties of partially polarized vortex beam by high numerical aperture Fresnel zone plate are investigated. The effects of the numerical apertures of and the phase difference of binary phase Fresnel zone plates, the topological charge of vortex beam and the degree of polarization of incident beam on the intensity distribution and degree of coherence in the focal plane are investigated in detail. It is shown that elliptical light spots and the flat top beam can be obtained by selecting certain parameters. Studies of degree of coherence reveal that the degree of coherence between x and y components of the electric field, which is zero in the source plane, is improved in the focal plane for vortex beam, but it is hardly changed for the nonvortex beam. It is also proved that any two of the three electric field components E_x, E_y and E_z are completely coherent everywhere in the focal region if the incident light beam is linearly polarized.     

Focusing of elliptically polarized Gaussian beams through an annular high numerical aperture

Based on the vectorial Debye theory,the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically,including the intensity,the phase and the orbital angular momentum properties.Then the influence of certain parameters on the focusing properties is also investigated.It is shown that sub-wavelength elliptical light spots can be obtained.And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam,indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.     

Tight focusing of femtosecond elliptically polarised vortex light pulses

This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards--Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.     

Probing Dual Asymmetric Transverse Spin Angular Momentum in Tightly Focused Vector Beams in Optical Tweezers

The spin-orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum - both spin and orbital - the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first-order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first-order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.     

The Effect of the Spin Angular Momentum on the Tight-Focusing Vortex Hollow Gaussian Beams

The propagation properties of a hollow Gaussian beam (HGB) carrying on-axis and off-axis vortices through a high numerical aperture lens are investigated. The intensity of the focused beam in the focal plane can be controlled by choosing the different topological charges, the beam order, and the semi-aperture angle. As intrinsic properties, vortex beams possess both spin and orbital angular momenta. The spin angular momenta (SAM) density can be treated as a vector in 3D since it exists in arbitrary orientation during the beam propagation. The vectors of SAM density orientation of the focused beam in 3D rotate around the central axis whose locations mainly rely on the vortices. The magnitude of the SAM density near the focus plane abruptly varies by altering the focal length of the lens. Under tightly focusing condition, two new pairs of vortices generate alternately on x and y axes in the vectorial electric fields, while the topological charges increase by one.     

Twisted optical communications using orbital angular momentum

Angular momentum, a fundamental physical quantity, can be divided into spin angular momentum(SAM) and orbital angular momentum(OAM) in electromagnetic waves. Helically-phased or twisted light beams carrying OAM that exploit the spatial structure physical dimension of electromagnetic waves have benefited wide applications ranging from optical manipulation to quantum information processing. Using the two distinct properties of OAM, i.e., inherent orthogonality and unbounded states in principle, one can develop OAM modulation and OAM multiplexing techniques for twisted optical communications. OAM multiplexing is an alternative space-division multiplexing approach employing an orthogonal mode basis related to the spatial phase structure. In this paper, we review the recent progress in twisted optical communications using OAM in free space and fiber. The basic concept of momentum, angular momentum, SAM, OAM and OAM-carrying twisted optical communications,key techniques and devices of OAM generation/(de)multiplexing/detection, high-capacity spectrally-efficient free-space OAM links, fiber-based OAM links, and OAM processing functions are presented. Ultra-high spectral efficiency and petabit-scale freespace data links are achieved benefiting from OAM multiplexing. The key techniques and challenges of twisted optical communications are also discussed. Twisted optical communications using OAM are compatible with other existing physical dimensions such as frequency/wavelength, amplitude, phase, polarization and time, opening a possible way to facilitate continuous increase of the aggregate transmission capacity and spectral efficiency through N-dimensional multiplexing.     

Tight focusing of linearly and circularly polarized vortex beams; effect of third-order spherical aberration

Tight focusing of linearly and circularly polarized vortex beams is studied in the presence of third-order spherical aberration, using vectorial Debye–Wolf integral. Results for total intensity distribution are presented for both polarizations. In addition, results for x-, y-, and z-polarization components are presented for the circularly polarized beam. Generation of longitudinal optical vortex in the tightly focused left circularly polarized beam has also been demonstrated by plotting its phase distribution. Compensation for the effect of spherical aberration has been studied in the presence of defocusing. Effect of aberration on the dark core of a tightly focused azimuthally polarized beam is also investigated.     

Beam moments and angular momentum in non-uniformly polarized beams

The angular momentum of non-uniformly totally polarized beams is investigated using methods from the beam characterization approach. The relationship between the elements of the beam matrix for the two components of the field and the angular momentum is given. The unconventional distribution of the polarization across the beam profile could result in contributions to both the spin and orbital terms of the angular momentum. To illustrate this, a particular example with a vortex beam is considered.     

The effect of electron initial longitudinal velocity on non-sequential double ionization process in elliptically polarized laser field

The effect of initial longitudinal velocity of the tunnelled electron on the non-sequential double ionization (NSDI) process in elliptically polarized laser field is studied by a semiclassical model. We find that the non-zero initial longitudinal velocity has a suppressing effect on single-return collision (SRC) events in double ionization process, more specifically, it results in an obvious reduction in the center part of the correlation momentum distributions in the direction of the major polarization axis (z axis) and makes the distribution of single-return collision in the minor polarization axis (x axis) become narrow.     

A simple analytical model of the angular momentum transformation in strongly focused light beams

A ray-optics model is proposed to describe the vector beam transformation in a strongly focusing optical system. In contrast to usual approaches based on the focused field distribution near the focal plane, we use the beam pattern formed immediately after the exit aperture. In this cross section, details of the output field distribution are of minor physical interest but proper allowance is made for transformation of the beam polarization state. This enables the spin and orbital angular momentum representations to be obtained, which are valid for any cross section of the transformed beam. Simple analytical results are available for a transversely homogeneous, circularly polarized incident beam confined by a circular aperture. Variations of the spin and orbital angular momenta of the output beam with change of the focusing strength are analyzed. The analytical results are in good qualitative and reasonable quantitative agreement with the results of numerical calculations performed for the Gaussian and Laguerre-Gaussian beams. The model supplies an efficient and physically transparent means for qualitative analysis of the spin-to-orbital angular momentum conversion. It can be generalized to incident beams with complex spatial and polarization structure.     

Manipulating Spin-Dependent Wavefronts of Vortex Beams via Plasmonic Metasurfaces

Conventional metasurfaces based on geometric phase are constrained to spin-locked phase profile, resulting in mirrored functionalities for different spins. A single flat device that enables independent manipulation of wavefronts in two orthogonal circularly polarized channels is of paramount importance in wireless and optical communications. In this work, by tuning the dimension and rotation angle of H-shaped meta-atoms to synthesize propagating phase and geometric phase, spin-dependent plasmonic metasurfaces are presented to manipulate circularly polarized waves in the visible band. To verify the capability of spin-dependent wavefront manipulation, three metasurfaces are implemented. The first metasurface generates vortex beams with orbital angular momentum (OAM) l = 1 under left-handed circularly polarized (LCP) incidence and l = 2 under right-handed circularly polarized (RCP) incidence. By introducing convolution operation, the second metasurface is capable of producing vortex beams with different OAMs and different directions for two spins. The third metasurface produces dual-beam and quad-beam with different OAMs for different circular polarizations. This scheme can provide a new pathway in ultracompact nanophotonic devices and systems.     

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.     

Focusing properties of the double-vortex beams through a high numerical-aperture objective

We study the focusing properties of the double-vortex beams through a high numerical-aperture objective based on the vectorial Debye theory. We investigate the double-vortex beams composing of two rings, and each ring carries different orbital angular momentum (OAM). It is shown that the total intensity distributions in the focal region are of double-ring structure, and by adjusting certain parameters, the shape of double-ring can be changed. The tight focusing of the double-vortex beams may find applications in micro-particle trapping, manipulation, material processing, etc.     

Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams

Second harmonic generation microscopy was conducted on rat-tail tendons with linearly and radially polarized beams. Transverse and axial field components were generated in the focal region through tight focusing of linearly and radially polarized. It was found that the generated SHG signals could not be qualitatively explained with a scalar approximation to the electric field at the focus. Only by accounting for the interactions of the axial and transverse components of the electric field interacting through the nonlinear susceptibility χ⁽²⁾ tensor could the SHG images be explained. For the case of collagen we find that the SHG signal varies as a function of the analyzer angle with a cos² or sin² dependency for linearly polarized beams. For tightly focused radially polarized beams we find that the output SHG is radially polarized after collimation and is independent of the analyzer angle.     

Nongeneric polarization singularities in combined vortex beams

Nongeneric polarization structures of singular beams formed as a coherent coaxial mixture of weighted orthogonally polarized single-charged Laguerre-Gauss modes with different radial indices are analyzed. A general solution for the superposition of elliptically orthogonally polarized partial vortex beams is obtained; the limiting special cases in which the mixed modes are linearly or circularly polarized are investigated. It is established that unusual spatially stable polarization structures such as closed C contours and L contours with a fixed azimuth of linear polarization arise in such combined beams. The results are experimentally confirmed by using a new diffraction method for testing phase singularities in optical beams.     

离轴矢量光束的紧聚焦特性

基于理查德-沃尔夫矢量衍射积分理论,数值研究了离轴矢量光束经过高数值孔径透镜后的紧聚焦特性.通过对比分析偏振奇点离轴的径向、角向矢量光束紧聚焦后,焦点附近的强度和相位分布规律,提出了一种由广义柱矢量光束设计紧聚焦场的方法.此外,通过分析矢量光束自旋分量的聚焦行为和自旋轨道耦合所诱导的自旋角动量分布变化,讨论了偏振奇点离轴对称破缺对高阶矢量光束紧聚焦场空间结构,特别是其自旋角动量空间分布的影响.该研究结果不仅对矢量光场的紧聚焦特性进行了补充,也为改进和完善焦场分布提供了理论参考.