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.     

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%.     

Sharper focal spot below λ/4 of azimuthally polarized illumination phase-encoded by the binary 0/π phase plate

The intensity distribution in the focal region for the azimuthally polarized beam phase-encoded by the binary 0/π phase plate is calculated on the basis of the vector diffraction theory. With the annular pupil aperture employed, the resolution of the focal spot will be improved remarkably. We demonstrate a sharper focal spot with full width at half maximum (FWHM) of 0.223λ (below λ/4), significantly smaller that of linear, circular and radial polarization beam under the same condition. The focusing phenomena for illumination beam with various polarization status and beam shapes are analyzed explicitly. This analysis could have potential applications in confocal microscopy and two-photo microscopy for polarization difference imaging.     

Keyhole acceleration for magnetic resonance acoustic radiation force imaging (MR ARFI)

MR ARFI measures the displacement induced by the ultrasonic radiation force and provides the location of the focal spot without significant heating effects. Displacements maps obtained with MR ARFI provide an indirect estimation of the acoustic beam intensity at the target. This measure is essential for dose estimation prior to focused ultrasound treatments (FUS) and adaptive focusing procedures of MR-guided transcranial and transribs FUS. In the latter case, the beam correction is achieved by maximizing the displacement at focus. A significant number of serial MR ARFI images are required and thus, a partial k-space updating method, such as keyhole appears as a method of choice. The purpose of this work is to demonstrate via simulations and experiments the efficiency of the keyhole technique combined with a two-dimensional spin-echo MR ARFI pulse sequence. The method was implemented in an ex vivo calf brain taking advantage of the a priori knowledge of the focal spot profile. The coincidence of the phase-encoding axis with the longest axis of the focal spot makes the best use of the technique. Our approach rapidly provides the focal spot localization with accuracy, and with a substantial increase to the signal-to-noise ratio, while reducing ultrasound energy needed during MR-guided adaptive focusing procedures.     

基于紧聚焦方式的阵列光束相干合成特性分析

为获得高功率、波长量级尺寸的聚焦光斑,提出利用紧聚焦方式实现阵列光束相干合成的新方案.通过建立阵列光束经紧聚焦方式相干合成的物理模型,分析了阵列光束的排布方式、偏振态、束宽、间距和紧聚焦系统数值孔径等参数对合成光束特性的影响及规律.结果表明,阵列光束经紧聚焦方式合束时,线偏振及圆偏振阵列光束均能获得较好的合成效果,径向偏振阵列光束次之,而角向偏振阵列光束则不能有效地合成.通过优化阵列光束的排布方式、束宽和间距,以及合理选择紧聚焦系统的数值孔径,能在保持较好光束质量和较高合成效率的前提下获得能量集中度高的焦斑.     

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.     

Focusing of flattened Gaussian beams by an annular lens

Focusing properties of flattened Gaussian beams (FGBs) passing through an annular lens is studied based on the Collins formula. It is found that the on-axis irradiance distributions of focused FGBs are unsymmetrical with respect to the geometrical focal plane even for large values of Fresnel number F_w associated with the beam, so that there exist focal shifts in general. Detailed numerical results show the dependence of focal shifts on the beam and system parameters. Focal shifts of FGBs by a lens without central obscuration and focal shifts of Gaussian beams by an annular lens can be treated as special cases of the obscure ratio =0 and beam order N=0, respectively. Furthermore, focal shifts of plane waves by an annular lens can also be treated as a special case of N=0 and F_w→∞.     

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.     

Cylindrical vector axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) in high numerical aperture system is investigated theoretically by vector diffraction theory. Results show that intensity distribution in focal region can be altered considerably by beam parameter μ and polarization angle. Polarization angle may adjust transverse intensity distribution, for instance from one focal spot to one ring shape. While μ alters axial intensity distribution remarkably, focal splitting may occur with tunable focal shift, and real value μ also may induce local intensity minimum. For certain case, with increasing imaginary value μ, transverse focal spot shrinks accompanied with higher full width half maximum of axial intensity distribution.     

Tight focusing of phase modulated radially polarized hollow Gaussian beam using 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 hollow 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 hollow Gaussian (HGB) beam. Potential applications of this focal shaping technique are also discussed.     

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.     

4π Focusing with single paraboloid mirror

Creating small bright or dark focal spots with good spherical symmetry requires 4π focusing, usually achieved by using two counter-propagating beams and two high NA lenses that need to be positioned with interferometric accuracy. We investigate a simple alternative way of focusing light to a small and uniform bright or dark focal spot. It only requires a single parabolic mirror illuminated with a single beam from one direction, resulting in a robust and compact setup. The focal spot distribution is tailored by optimizing the polarization, intensity and helicity of the incoming illumination.     

Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex

The focusing properties of the hyperbolic-cosine-Gaussian beam, which contains an optical vortex induced by a non-spiral phase plate, are investigated numerically. The phase plate alters phase distribution linearly in a half-section part of the hyperbolic-cosine-Gaussian beam, which results in one non-spiral optical vortex. Results show that the phase variation rate of the non-spiral phase plate influences focal intensity distribution considerably, and some novel focal patterns, such as line focal spot, “H”-shape focal spot, and intensity peaks array, may occur. Focal shift, focal split, and focal switch appear in focal evolution with increasing phase variation rate. The focal evolution differs for different parameters in cosh parts of the hyperbolic-cosine-Gaussian beam. For big parameters in cosh parts, the value of local intensity peaks is comparable to that of maximum intensity peaks.     

Diffractive phase element for shrinking focal spot diameter: Design, fabrication, and application to laser beam lithography

A diffractive phase element (DPE) capable of shrinking the main-lobe of the focal spot of an incident beam has been developed. The DPE is expected to be used in laser beam lithography to improve the resolution. Special constraints, which force the focal spot to be small while permitting increase of the side-lobes, are introduced in the design of the DPE using an iterative method based on the Gerchberg-Saxton algorithm. Two kinds of DPEs are fabricated by a laser beam lithography system of our own composition and their performances are experimentally measured. The minimum line width obtained by the system is improved from 1.2 μm to 1.0 μm with the fabricated DPE. Focal depth of the focusing system is discussed.     

On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.     

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.     

Laue弯晶聚焦特性的光线追迹研究

由于可有效降低高热负载的影响, Laue弯晶是插入件辐射高通量密度硬X射线(30 keV以上)聚焦、 准直和单色化的最有效的光学元件.研究其聚焦光学特性,对发展高性能、高稳定的Laue弯晶单色器具有重要意义. 采用自行发展的光线追迹软件较为系统地研究了Laue弯晶的聚焦特性, 分析了入射光性质及弯晶参数对聚焦光斑、焦距、发散度等主要光学参数的影响. 结果表明,衍射能量越高,聚焦光斑越小,并趋于稳定值;弯曲半径越小,聚焦光斑越小, 并在其达到一阈值时得到聚焦光斑的极小值,之后随着弯曲半径的变小,由于像差等因素的影响, 聚焦光斑反而变大;晶体越厚,聚焦光斑越大,呈线性正比关系.对于衍射光发散度, 其随着衍射能量的增大而变小,并趋于稳定值;其与晶体曲率呈线性正比关系. 同时通过研究得到弯晶各参数的合理选择范围.     

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.     

Multifocus with small size, uniform intensity, and nearly circular symmetry

We investigate in detail the focusing properties of the composite vector beam (CVB) composed of two orthogonally linearly polarized beams with inhomogeneous polarization modulation. By optimizing the modulation factor, a multifocus with excellent quality is obtained, where the sizes of each focus are fairly smaller than that of the focusing spot of a radially polarized beam, the uniformity in the intensity of the focal spots is as high as 1, and the distributions of each focal spot have nearly circular symmetry. In order to decrease the power loss of the incident beam, the CVB formed by an annular beam is demonstrated as the substitute for the optimized CVB formed by a Gaussian beam. This work is important for high-resolution and high-speed imaging in biology and micro-nanofabrication.     

Imaging and quality assessment of high-harmonic focal spots

We present a direct method of studying the focusability of an intense, short-pulse extreme-ultraviolet (XUV) beam obtained by high-harmonic generation. We perform near-field imaging of the focal spot of five high-harmonic orders strongly focused by a broadband toroidal mirror. To visualize the focal spot directly, we image the fluorescence induced by an XUV beam on a cerium-doped YAG crystal on a visible CCD camera. We can thus measure the harmonic spot size on a single image, together with the Strehl ratio, to evaluate the quality of focusing. Such techniques should become instrumental in optimizing the focusing conditions and reaching intensities required for exploring attosecond nonlinear optics in the XUV range.