Tighter focusing with a parabolic mirror

We demonstrate experimentally and theoretically that a parabolic mirror (PM) with a high numerical aperture (NA) of 1 focuses a radially polarized laser mode to the smallest diffraction-limited spot at a fixed NA and wavelength, having an area of 0.134 lambda(2). The measurements were performed with a confocal microscope, using the PM as a focusing and collecting element. The results stand in accordance with the theoretical calculations presented by Davidson and Bokor [Opt. Lett. 29, 1318 (2004)], who predicted a reduction in the total focal spot size of 43% as compared with an aplanatic lens.     

Tight Focusing of Radially and Azimuthally Polarized Vortex Beams through a Dielectric Interface

Based on vectorial Debye theory, tight focusing of radially and azimuthally polarized vortex beams passing through a dielectric interface are studied. The intensity distribution in the focal region is illustrated by numerical calculations. We show the influence of numerical-aperture （NA） on the full-width at half maximum （FWHM） of the focal spot or the focal hole. It has been found that compared with the azimuthally polarized Besse~Gaussian （BG） beams, the longitudinal component in the z direction of the radially polarized BG beams has no influence on the FWHM of the focal spot and hole, but enhances the total light intensity.     

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.     

Generation of radially polarized beams using spatial light modulator

Radially polarized beams have attracted much attention and found many applications in many optical systems, recently. And generation of radially polarized beams is necessary for experimental research and applications. In this paper, a kind of generation method was proposed. Two beams are obtained by spatial light modulator and pi phase plate, and then interfere to form desirable radially polarized beams. Experimental results show that radially polarized beams are higher property, which shows this kind of interferential generation of radially polarized laser beams work effectively.     

Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

Three-dimensional multiple optical cages formed by focusing double-ring shaped radially and azimuthally polarized beams

We propose and simulate a method for generating a three-dimensional(3D) optical cage in the vicinity of focus by focusing a double-ring shaped radially and azimuthally polarized beam. Our study shows that the combination of an inner ring with an azimuthally polarized field and an outer ring with a radially polarized field and a phase factor can produce an optical cage with a dark region enclosed by higher intensity. The shape of the cage can be tailored by appropriately adjusting the parameters of double-mode beams. Furthermore, multiple 3D optical cages can be realized by applying the shift theorem of the Fourier transform and macro-pixel sampling algorithm to a double-ring shaped radially and azimuthally polarized beam.     

Generation of radially polarized light beams of high quality using a step-index optical fiber

We present an experimental setup to generate radially polarized beams without using high-cost optical elements. In the setup a four-segment polarization converter is used in front of the fiber to produce a pseudo radially polarized beam. A traditional step-index fiber which supports only LP₀₁ and LP₁₁ modes is then used as a mode-cleaning device. A commercial mechanical fiber-squeezer polarization controller is applied to produce adequate pressure and twist onto the fiber. The four-segment polarization converter and the fiber squeezer polarization controller are adjusted by turns for improving the beam quality in intensity and polarization. Additionally, several methods of characterizing the polarization properties of radially polarized beams are reviewed. One of the latest methods is applied for characterizing the polarization properties of the radially polarized beams produced by using our technique. The results show the highquality of the obtained beams.     

显微物镜聚焦光场任意三维偏振方向的控制

线性偏振光在显微物镜焦斑处入射,与径向偏振光相干叠加产生三维偏振光场,通过调节两束光光强比率和入射线偏振光偏振方向实现聚焦光场任意三维偏振方向的控制.基于矢量光场衍射理论建立了仿真计算模型,对所提三维偏振方向控制方法的可行性进行理论验证和实验评估.构建实际控制光路并进行初步测试,实验结果表明了该方法的可行性,且相比于其他三维偏振控制方法,本文所提方法和其控制光路更为简单易实现.     

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.     

超短脉冲径向偏振光束的解析解及时空耦合效应

从超短脉冲光束的傍轴传输方程出发, 运用傅里叶变换和相关数学算符的对易性, 得到了超短脉冲径向偏振光束的解析表达式.该解可适用于任意脉冲驱动的径向偏振光束. 基于该解析表达式并结合具体例子,讨论了超短脉冲径向偏振光束在自由空间中的传输性质. 结果表明, 在传输过程中时空耦合主要体现在光束边沿的脉冲延迟. 这一效应导致了脉冲不同时间位置处横向光强分布随传输的变化, 以及脉冲前后沿关于束腰的不对称性. 本文的方法同样适用于得到超短脉冲方位角偏振光束的解析解和传输性质.     

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.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam

Based on vectorial Debye theory, the effect of annular apodization of tightly focused partially coherent radially polarized vortex beams in the focal field of high NA lens is studied. The intensity distribution in the focal region is illustrated by numerical calculations. It is found that the focal depth of the generated focal segment strongly dependent on the source coherence length for unobstructed case and the presence of annular aperture reduces the variation of focal depth with source coherence length.     

Propagation and parametric characterization of the polarization structure of paraxial radially and azimuthally polarized beams

Analytical expressions are provided for describing the free-space evolution of the polarization structure of paraxial beams whose electric-field vector at some transverse plane exhibits either a radially or an azimuthally polarized behavior. At each transverse plane, the polarization distribution across the beam profile is characterized by means of two sets of parameters, namely, the so-called (local) radial Stokes representation, and the (overall) percentage of the irradiance associated with the radial and azimuthal field components. The propagation laws for these sets of parameters are also shown. As an illustrative example, a radially polarized beam is analized whose wavefront contains a spiral phase factor.     

Study on propagation properties of a radially polarized partially coherent dark hollow beam through a high numerical aperture lens

In recent years the partially coherent beams have attracted very much due to novel properties and its applications. In this paper the tight focusing properties of radially polarized partially coherent dark hollow beam (DHB) through a high numerical aperture lens are investigated numerically based on vectorial Debye theory in detail. The result shows that the optical intensity distribution in the focal region directly fluctuates due to small change in coherence length and high numerical aperture angle of the focused radially polarized partially coherent DHB.     

Focusing of high polarization order axially-symmetric polarized beams

We study the high numerical aperture focusing properties and typical applications of axially-symmetric polarized beams （ASPBs） with high polarization orders. We calculate the field distribution near focus of an aplanatic system for incident ASPBs with different polarization orders and initial azimuthal angles, and based on the simulation results, we find some unique focusing properties of the beams, such as ever on-axis energy null, strong longitudinal field, and flowerlike intensity distribution at focus. In addition, we can manipulate the three-dimensional （3D） focused field distribution flexibly by use of diffractive optical elements （DOEs）, which will give rise to some interesting applications, and we also discuss possible applications and present an example of a 3D optical chain at last.     

Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate

Simultaneous generation of helical beams with linear and radial polarization is demonstrated by use of a segmented half-wave plate in a Ti:sapphire laser cavity. A linearly polarized Laguerre-Gaussian beam is converted to a radially polarized beam with a spiral phase shift and vice versa. In addition, these two beams coexist in the cavity, and the cavity emits one of these two beams from an output coupler.     

Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEM(n1)) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM(01)). Simulation results show that the accuracy of the fifth-order correction for R-TEM(n1) depends not only on the diffraction angle of the beam as R-TEM(01) does, but also on the order of the beam.     

Spatial correlation properties of apertured partially coherent radially polarized beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, the analytical formulae for the cross-spectral density matrix of the partially coherent radially polarized beams diffracted at a circular aperture in turbulent atmosphere are derived. The unapertured and free-space cases can be viewed as the special cases of our general result. By using the degree of coherence formula, the spatial correlation properties of the apertured partially coherent radially polarized beams in turbulent atmosphere are studied. The analyses indicate that the spatial correlation of the apertured partially coherent radially polarized beams are more affected by the atmospheric turbulence with the larger structure constant, the smaller truncation parameter, the larger coherence length, and the farther propagation distance.     

The nucleon facility at PSI

The new nucleon area (NA) at PSI is designed as a multi-purpose facility with nucleon beams. The area can be used for experiments with polarized or unpolarized protons or neutrons. For both kinds of nucleons the available energy ranges from about 100 MeV up to a maximum of about 590 MeV.