Generation and tight-focusing properties of cylindrical vector circular Airy beams

Tight-focusing properties of cylindrical vector circular Airy beams [i.e., azimuthally polarized (AP) circular Airy beam and radially polarized (RP) circular Airy beam] passing through a high numerical aperture thin lens are investigated in detail. It is found that a super long subwavelength dark channel with full width at half maximum about 0.49λ and depth of focus (DOF) about 52λ can be achieved near the focal region for the case of tight focusing of an AP circular Airy beam, and a super long needle with DOF about 27.5λ of strong longitudinally polarized field can be obtained near the focal region for the case of tight focusing of a RP circular Airy beam. Furthermore, we report experimental generation of an AP circular Airy. Our results will be useful for atom guiding and trapping, particle acceleration and fluorescent imaging.     

Tight Focusing Properties of Phase Modulated Radially Polarized Laguerre Bessel Gaussian Beam

We propose a new approach for generating a multiple focal spot segment of subwavelength size, by tight focusing of a phase modulated radially polarized Laguerre Bessel Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observe that the focal segment with multiple focal structures is separated with different axial distances and a super long dark channel can be generated by properly tuning the phase of the incident radially polarized Laguerre Bessel Gaussian beam. We presume that such multiple focal patterns and high intense beam may find applications in atom optics, optical manipulations and multiple optical trapping.     

Tight focus of a radially polarized and amplitude- modulated annular multi-Gaussian beam

The focusing of a radially polarized beam without annular apodization ora phase filter at the entrance pupil of the objective results in a wide focus and low purity of the longitudinally polarized component. However, the presence of a physical annular apodization or phase filter makes some applications more difficult or even impossible. We propose a radially polarized and amplitude-modulated annular multi-Gaussian beam mode. Numerical simulation shows that it can be focused into a sharper focal spot of 0.125λ² without additional apodizations or filters. The beam quality describing the purity of longitudinally polarized component is up to 86%.     

Radially polarized hyperbolic-cosine-Gaussian beam

Vector beams have attracted much interest recently. In this paper, focusing properties of the radially polarized hyperbolic-cosine-Gaussian beam are investigated. Simulation results show that the focal depth increases with increasing cosine parameter in the cosine term of the beam, while focal spot decreases simultaneously, namely, superresolution occurs. Focal depth increase velocity is quicker for larger cosine parameter, while the transverse focal spot shrinks more quickly for smaller cosine parameter. In addition, for two-portion concentric piecewise radially polarized hyperbolic-cosine-Gaussian beam with π phase shift in center circle portion, focal pattern evolves considerably with increasing cosine parameter, and the evolution principle differs for different radius of the center circle portion. Focal splitting and novel focal spots may appear. This kind of vector beam can be used in optical storage, optical manipulation, and lithography.     

Effect of annular apodization and pupil beam parameter in the focal region of high NA lens

Focusing properties of the radially polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in the focal region of the radially polarized axisymmetric QBG beam can be adjusted considerably by small beam parameter (μ) and annular aperture (δ). When μ increases, the focal spot may change to focal hole and changes focal pattern remarkably. On introducing annular aperture, focus can split or extends along the optical axis for different μ. In this paper, we have shown the generation of the focal spot, dark focal spot, focal split and increase in focal depth in the axial direction of the incident beam propagating through the aligned optical system.     

The focusing property of vector Bessel-Gauss beams by a high numerical aperture objective

The rich available transverse intensity structure of vector Bessel-Gauss beams make it important to probe into the focusing property by high numerical aperture objective. In this paper, we obtain the analytical expressions of azimuthally, radially and longitudinally polarized components in the focal area of the objective after tight focusing. Theoretical analysis and the numerical simulation show that, the transverse intensity distributions of the focused beams still have doughnut-like structure, two separate peak structure and circularly aligned array structure. The focused beam spots obtained by an objective with annular aperture usually have smaller spots than with circular aperture. The focused beam of the vector Bessel-Gauss beam with lowest mode number m = 0 is a radially and azimuthally polarized doughnut-like beam with no longitudinal component. These properties and results are useful in optical trapping and particle alignment.     

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.     

Tight Focusing Properties of Radially Polarized Gaussian Beams with Pair of Vortices

The tight focusing properties of a radially polarized Gaussian beam with a nested pair of vortices having a radial wave front distribution are investigated theoretically by the vector diffraction theory.The results show that the optical intensity in the focal region can be altered considerably by changing the location of the vortices nested in a radially polarized Gaussian beam.It is noted that focal evolution from one annular focal pattern to a highly confined focal spot in the transverse direction is observed corresponding to the change in the location of the optical vortices in the input plane.It is also observed that the generated focal hole or spot lead to a focal shift along the optical axis remarkably under proper radial phase modulation.Hence the proposed system may be applied to construct tunable optical traps for both high and low refractive index particles.     

Natural shaping of the cylindrically polarized beams

We have experimentally and theoretically shown that the circularly polarized beam bearing a singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in the vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs.     

Tight focusing properties of radially polarized Lorentz–Gaussian beam

Focusing properties of radially polarized Lorentz–Gauss beam with one on-axis optical vortex was investigated by vector diffraction theory. Results show that intensity distribution in the focal region can be altered considerably by charge number of the optical vortex and the beam parameters. Many novel focal patterns may occur, Such as Peak-centered, donut focal shapes which is potentially useful in optical tweezers, material processing and laser printing.     

Effect of polarization on focal depth in high numerical apertures optical systems

The generalized cylindrical vector beam is just a linear combination of radial and azimuthal polarization. For radially polarized light in the focal plane, there are two electric field components, the radial component and z-component whose magnitude increase with the increase of numerical aperture. By contrast, for azimuthally polarized light in the focal plane, there is only one electrical field component in the azimuthal polarization, it is easy to understand the difference between the two polarization effects. In this paper, we demonstrate how this phenomenon can be harnessed to make a properly selected polarization component to achieve high focal depth in high numerical aperture systems. Numerical simulations show that the evolution of the focal shape is very considerable by changing polarization rotation angle of the generalized cylindrical vector beam. And some interesting focal spots and focal split may occur. And if the ratio of radial and azimuthal polarization is set properly by changing the polarization rotation angle, a largest focal depth is achieved. The tunable range of the focal depth is very considerable. The ratio of radial and azimuthal polarization is different in different NA optical system for obtaining the largest focal depth. We will denote a technique of polarization-assisted high focal depth in high numerical aperture systems.     

Propagating a partially coherent radially polarized beam through aligned and misaligned ABCD optical systems

In the present work the propagation of a partially coherent radially polarized beam through aligned and misaligned ABCD optical systems is discussed. The elements of the beam coherence-polarization matrix for a partially coherent radially polarized beam propagating through these systems are derived for the first time. Using the derived analytical results the intensity distribution of the focused partially coherent radially polarized beam after a low-NA lens is investigated. It is shown that the coherence of the light source affects the beam intensity profile at the focal plane significantly, while for the given coherence of the light source the focal length of the used lens does not affect the beam intensity profile at the focal plane. This is consistent with the case of a partially coherent Hermite-Gaussian beam, as expected.     

Effect of binary phase plate on incident radially polarized hollow Gaussian beam

Effect of a pure binary phase filter on the three-dimensional light intensity distributions in focal region is theoretically investigated in this paper. The results show that the proposed binary phase filter may induce flat top profile with large depth of focus and reduced focal spot by properly adjusting the geometrical parameters of the binary phase filter of incident radially polarized hollow Gaussian beam (HGB) beam. On the other hand, the HGB beam benefits the most from the use of an annulus. Such kind of system is potentially useful for lithography, imaging, optical data storage, optical trapping, optical excitation of molecules, or coupling to optical fibers.     

Focal shift in radially polarized beam with high NA lens axicon by using radial cosine phase wavefront

Focal shift in radially polarized beam with radial cosine phase wavefront are investigated theoretically by vector diffraction theory. The wavefront phase distribution is cosine function of radial coordinate. Simulation results show that when the radially polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. On increasing C, focus can shift along optical axis and focal pattern changes remarkably. Focus may move in different direction under different condition. Focal shift distance fluctuates on increasing C, and fluctuation amplitude also increases simultaneously. In addition, focal shift direction can also be adjusted by changing frequency parameter in cosine function.     

Radially polarized hollow Gaussian beam with on-axis spiral optical vortex

The focusing properties of radially polarized hollow Gaussian beam (HGB) with on-axis spiral optical vortex are investigated theoretically by vector diffraction theory. The phase wavefront of HGB is the function of radial coordinate. Calculation results show that the focusing properties can be altered considerably by beam order of HGB, topological charge of the on-axis optical vortex, and phase parameter that characterizes the radial phase wavefront distribution. Higher topological charge induces focal evolution from one focal spot to annular focal pattern in transverse direction, while phase parameter can lead to focal shift along optical axis remarkably. In addition, focal shift direction can also be adjusted by changing varying direction of phase parameter.     

Investigation of Near-Field Imaging Characteristics of Radial Polarization for Application to Optical Data Storage

Radially polarized incident light can generate a more confined longitudinal electric field on a focal plane in near-field (NF) optics than focusing circularly polarized light. Using this phenomenon, it is feasible to reduce beam spot size on storage media to increase the areal density of optical data storage. A radially polarized beam generates a beam spot which is 20% more confined on the 1st surface of medium than that of circularly polarized light. However, the peak intensity of total electric field sharply decreases and its transverse component is much more dominant inside the media stack. This confirms that radially polarized optics can be a candidate not for an NF recording system but for an NF read-only memory (ROM) system. Potentially, the results could be useful to understand the effect of radial and circular polarizations inside and outside medium for various applications of NF optics.     

Circular grating coupler for creating focused azimuthally and radially polarized beams

We show a planar optical circuit design that takes light from an input waveguide and creates a focused azimuthally or radially polarized beam emanating from the surface of the substrate. It is implemented in silicon-on-insulator waveguides and does not require any external components to focus the beam. The focal spot size can be subwavelength and is potentially useful for lithography, imaging, optical data storage, optical trapping, optical excitation of molecules, or coupling to optical fibers.     

Double pulse quasi-collinear high harmonic generation scheme as a tool for X-ray laser plasma gain probing

We calculate the field distribution based on the vector diffraction theory for a superposition of spirally phase shifted radially polarized beams. Twisted longitudinally polarized field is found in the focal region. The total intensity as well as the polarization components rotates around the beam axis near the focus. Calculation of the Poynting vector at the focal plane shows that the electromagnetic energy is redistributed between different polarization components. Nonzero value of transverse components of the Poynting vector implies the transverse flow of the energy in the focal region.     

径向偏振光下的长焦、紧聚焦表面等离子体激元透镜

表面等离子体激元透镜(plasmonic lens, PL)是一种通过激发和操控表面等离子体激元 (SPPs), 突破衍射极限, 实现亚波长紧聚焦的纳米光子器件. 如何实现高效率的紧聚焦及调控, 一直是研究PL的重点. 如果选取电矢量沿径向振动的径向偏振光作为PL的入射光, 可从各个方向激发SPPs, 提高紧聚焦的能量效率. 本文提出了一种在径向偏振光激发下的长焦深、长焦距、亚波长紧聚焦的表面等离子体激元透镜, 该透镜由中心T 形微孔、阶梯形同心环和同心环结构组成. 本文首先利用有限元方法数值分析了中心微孔-同心环结构透镜的聚焦特性, 结果显示径向偏振光由底部入射可高效激发SPPs, 并且中心微孔透射光与散射至自由空间的SPPs由于多光束干涉形成了紧聚焦. 为进一步压缩焦斑、增加焦距、加深焦深、改善透镜聚焦特性, 本文引入中心T形微孔-阶梯形同心环结构, 从而对阶梯表面的SPPs同时提供了相位调制和传播方向的控制. 经过参数优化, 该透镜结构实现了光斑焦深、半高宽、焦距分别是入射光波长的2.5倍、0.388 倍、3.22倍的亚波长紧聚焦; 而且该透镜具有结构紧凑、尺寸小、易于集成的优点, 满足了纳米光子学对于器件微型化和高度集成化的要求. 该研究结果在纳米光子集成、近场光学成像与探测、纳米光刻等相关领域具有潜在的应用价值.     

大数值孔径光子筛偏振特性研究

根据角谱理论建立不同偏振照明条件下的光子筛矢量衍射模型。在此基础上,对入射光分别为线偏振光、径向偏振光、切向偏振光三种特殊偏振状态下的光子筛聚焦光强分布进行了模拟分析。研究结果表明,对于大数值孔径光子筛,入射光的偏振特性将对光子筛聚焦光强分布产生巨大影响。线偏振光将使聚焦光斑沿偏振方向拉伸,切向偏振光产生的聚焦光斑具有"中空"结构,而径向偏振光所产生的聚焦光斑呈较为规则的圆形,且其焦深优于线偏照明情况。在激光直写及高分辨成像等光子筛典型应用中采用径向偏振照明将进一步提高系统分辨力。