Tight focusing of radially polarized Gaussian and Bessel-Gauss beams

We examine the effects of tightly focusing a radially polarized beam with uniform, Gaussian, or Bessel-Gauss pupil functions. The resulting FWHM is smallest for the case of a uniform amplitude profile, while the Bessel-Gauss beam results in the largest FWHM. The uniform amplitude profile also results in an axial field component that increases fastest with increasing NA. The ratio of the axial component to the transverse component is also the greatest for the uniform pupil function. On the other hand, the Bessel-Gauss beam benefits the most from the use of an annulus.     

4Pi focusing of spatially modulated radially polarized vortex beams

We propose a method for generating focal beams with special intensity distributions using radially polarized vortex beams in a 4Pi configuration. A spherical dark-hollow beam and hollow beam array can be obtained by vortex beams with topological charge of m=1. A dark channel can be generated using vortex beams with topological charge of m=2. The length of the well-defined hollow beam array and the dark channel is about 30λ. These interesting beams are useful in optical trapping and manipulation.     

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.     

Generation of a radially polarized doughnut mode of high quality

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.     

Tight focusing of partially coherent radially polarized beam with high NA lens axicon

Tight focusing of radially polarized partially coherent vortex beam over a high numerical aperture lens axicon system is introduced and its propagation properties are studied based on vectorial Debye theory. The effect of propagation parameters on the intensity distribution, the polarization property and the coherent property of the beam is illustrated analytically and numerically. It is shown that the correlation length and maximal NA angle has a significant influence on the intensity profile.     

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.     

Tight focusing of double ring shaped radially polarized beam with high NA lens axicon

A method is presented for generation of a sub wavelength (0.45λ) longitudinally polarized beam, which propagates without divergence over lengths of about 8λ in free space. This is achieved by tight focusing of double ring shaped radially polarized beam with a high NA lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distributions were calculated based on the vector diffraction theory and it was observed that in the case of high numerical aperture (NA) lens axicon, the distribution of the total intensity near the focus had little effect on the degree of truncation of the incident beam by the pupil.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

Anomaly in a high-numerical-aperture diffractive focusing lens

We show an anomalous behavior in a diffractive lens in which the spot size at the focus reaches a minimum at a numerical aperture of ~0.5 and then increases significantly at higher values. Theoretical and experimental results are presented, along with a comparison with refractive aplanatic lenses, in which the anomaly does not appear to exist.     

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.     

4pi聚焦系统中振幅和相位调制的径向偏振涡旋光束聚焦特性的研究

基于Richards-Wolf矢量衍射积分公式, 研究了径向偏振涡旋光束在振幅和相位调制下的4pi聚焦特性.振幅调制是通过振幅滤波实现, 即改变入射光束起始积分值达到调节,相位调制是通过添加相位延迟角δ 的液晶相位延迟器来改变入射光束的偏振态.模拟结果显示,随着振幅的减小, 4pi聚焦系统焦点附近的光轴上呈现出多光球结构; 而相位调制对焦点附近的光强分布产生拉伸作用, 即调节入射光束的拓扑核m和相位延迟器的延迟角δ,可以得到特殊的光强分布. 随着相位δ增大, m=0产生的多光球结构慢慢向光链结构转变,最终变成暗通道;而m=1产生的光链结构慢慢变成光球结构; m=2产生的暗通道变成光球和光链叠加的结构, 这种特殊聚焦光束在光学微操纵领域具有潜在的应用价值. 关键词： 物理光学 偏振 光链 4pi聚焦系统     

Generation of radially polarized beams in a Nd:YAG laser with self-adaptive overcompensation of the thermal lens

Thermal effects such as lensing and birefringence negatively affect the beam quality and limit the power range of solid-state lasers. Self-adaptive overcompensation of the thermal lens is an answer to this problem. It provides a laser system with good beam quality and large stability range. Because the focal length of the thermally induced lens is different for the radial and the tangential polarization, overcompensation can be used to discriminate these two polarizations. Exploiting this method, we demonstrate the generation of radially polarized beams in a self-adaptively overcompensated high-power Nd:YAG laser with an output power of 155 W and an M2 of less than 10.     

Production of radially and azimuthally polarized polychromatic beams

We describe a system that efficiently provides radially or azimuthally polarized radiation from a randomly polarized source. It is constructed from two conical reflectors and a cylindrical sheet of polarizing film. Envisaged applications include a microscope illuminator for high-resolution surface plasmon resonance microscopy, illumination for high-resolution microlithography, and efficient coupling of a laser source to hollow optical fibers. The angular coherence function of light polarized by the device was measured to evaluate its usefulness for these applications.     

Focal properties of cylindrically polarized axisymmetric Bessel-modulated Gaussian beams by a high NA parabolic mirror

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial phase dependence (QBG beam) in high numerical aperture parabolic mirror 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. The tightly focused cylindrically polarized axial symmetric Bessel-modulated Gaussian beams by a high numerical aperture parabolic mirror have possible applications in particle acceleration, optical trapping and manipulating, single molecule imaging and high resolution imaging microscopy.     

Characterizing polarization properties of radially polarized beams

In the present work two methods of characterizing polarization properties of well-known radially polarized beams are discussed in both theoretical aspect and experimental aspect. A rotating linear polarizer used behind the beam is known to be used to qualitatively characterize the polarization properties of a radially polarized beam. In this paper for the first time we give the mathematic model of this characterization process. The proposed model helps to analyze the known experimental results. On the other hand two global parameters have been previously proved to be used to characterize the linear or circular polarization content of the radially polarized beams. In this paper for the first time we propose the theoretical model of determining the two parameters in experiments. Some experimental results on characterizing the polarization properties of the real radially polarized beam produced by using different approaches are shown.     

Analytical vectorial structure of radially polarized light beams

Starting from the vector angular spectrum of the electromagnetic beam, the analytical vectorial structure of the radially polarized beams (RPBs) is presented. The energy flux distributions of the RPBs are demonstrated. The physical pictures of the RPBs are well illustrated from the vectorial structure. This particular electromagnetic field is entirely transverse magnetic, and on axis it only has a longitudinal (z) electric-field component (i.e., no transverse electric field and no magnetic field at all on axis).     

Toward a spherical spot distribution with 4pi focusing of radially polarized light

The properties of the focal spot for 4pi focusing with radially polarized light are presented for various apodization factors. With a focusing system satisfying the Herschel condition, sharp focal spots with almost-perfect spherical symmetry (leading to equal axial and transverse resolution) and extremely low sidelobes are achieved.     

Forces in optical tweezers with radially and azimuthally polarized trapping beams

It has been suggested that radially polarized beams can be used to improve the performance of optical tweezers, with reduced scattering force resulting from both the polarization and the dark center of the beam [Opt. Lett. 32, 1839 (2007)]. We calculate the forces on particles in such traps, using rigorous electromagnetic theory, comparing the results with azimuthally polarized beam, circularly polarized LG 01 beams, and Gaussian beams. Our results agree qualitatively with Opt. Lett. 32, 1839 (2007), but differ quantitatively.     

Efficient extracavity generation of radially and azimuthally polarized beams

We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.