Focusing of radially polarized beam with radial cosine phase wavefront

Radially polarized beam has gained much interest recently due to its properties and applications. In this article, the focusing properties of radially polarized beam with radial cosine phase wavefront are investigated theoretically. 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. In the high numerical aperture focusing system, focal shift occurs, and novel focal patterns evolve considerably, for instance, from only one peak to two or multiple overlapping peaks. In addition, peak intensity ratio of radially polarized component to longitudinal polarized component in the focal region fluctuates smoothly for low-frequency parameter, then drops sharply, and comes back remarkably with increasing frequency parameter. Simultaneously focal shift increases slowly, and then decreases, suddenly, focal shift sign changes that results from focal switch phenomenon, and then fluctuates.     

Focal shift of radially polarized axisymmetric Bessel modulated Gaussian beam with radial variance phase plate

Focal shift of the radially polarized axisymmetric QBG beam with radial variance phase plate is investigated theoretically by vector diffraction theory. Axisymmetric Bessel modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. Calculation results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of beam parameter μ of radially polarized axisymmetric QBG beam, there is one focal spot that shifts far away from optical aperture on increasing C. When increases the value of beam parameter, there may occur two focal peaks that also shift remarkably on increasing C.     

Spirally polarized axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the spirally polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) are investigated theoretically by vector diffraction theory. Calculation results show that intensity distribution in focal region can be altered considerably by beam parameter μ and spiral parameter C that indicates polarization spiral degree. For certain real value μ, focal spot can evolve from one focal spot to one focal ring, spherical crust focal shape, then two focal rings on increasing spiral parameter C. It was found that under condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. And some novel focal shapes may appear, including rhombic shape, quadrangular shape, two-spherical crust focus shape, two-peak shape, one dark hollow focus, two dark hollow focuses pattern, triangle dark hollow focus.     

Focusing properties of Gaussian beam by a nonspiral phase plate system

In this article, a nonspiral plate is investigated numerically by vector diffraction theory to observe the focusing properties of Gaussian beams. Both low- and high-numerical-aperture (NA) optical systems are considered in the investigation. It is found that the parameter of NA and the phase vary rate of the phase plate influence the focal intensity distribution considerably. When a nonspiral plate is used to provide linear phase variation on one half of the Gaussian beam, it may adjust the focal spot considerably and conveniently. Changing the vary rate of the phase plate or the parameter of NA can alter optical intensity distribution; some novel focal spots and focal switch may also occur.     

Effect of complex phase plate on tight focusing of azimuthally polarized double ring shaped beam

Based on the vector diffraction theory, the effect of complex phase plate on the intensity distribution of TEM₁₁ mode azimuthally polarized Laguerre–Gaussian beam in the focal region of high NA lens is investigated theoretically. It is observed that a properly designed complex phase plate can generate a subwavelength focal hole having FWHM of 0.332λ with an extended focal depth of 54.4λ. We also observe that by using properly designed complex phase plate generates novel focal patterns including splitting of focal holes and multi focus are obtained. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.     

Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask

We study the focusing properties of a tight focusing of double ring shaped azimuthally polarized beam through complex phase mask (CPM) with high NA objective lens, based on vector diffraction theory. A novel design to generate an azimuthally polarized subwavelength focal hole having FWHM of 0.332λ with long focal depth of about 18.8λ is illustrated numerically. Apart from generating focal hole with long focal depth, it is observed that a properly designed CPM also generates multiple focal hole segments useful for laser cutting, microscopy and the manipulation of optical traps of low refractive index particles.     

Focal shift in radially polarized hollow Gaussian beam

Focal shift in radially polarized hollow Gaussian beam (HGB) with radial wavefront distribution is investigated theoretically. The wavefront phase distribution is cosine function of radial coordinate. Simulation results show that the intensity distribution in focal region of the radially polarized HGB can be adjusted considerably by the beam order of HGB n and cosine parameter C that indicates the phase change degree. 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, threshold value of C for focal shift from one side to the other side of the paraxial focal plane differs for different n.     

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.     

Phase filter design for sharper focus of radially polarized beam

Based on vector diffraction theory, a phase-only filter with cosine function is proposed and a sharper focal spot of radially polarized beam is obtained on the focal plane. The function parameters of the filter are optimized and a series of optimized filters for different Strehl ratio S are given. The optimization results show that there is a significant improvement on obtaining sharper focal spot with this new type of filter. Compared with other results, this type of filters has superior supperresolution effect and higher energy utilization ratio. The numerical calculation results about the phase filter may facilitate new approaches to get superresolution.     

带有相位拓朴数的环形相位板调控高斯光束的梯度力

 用基于德拜近似条件的矢量衍射理论研究了带有相位拓朴数的环形相位板调控高斯光束的光梯度力分布,改变相位板环形区的相对半径或当相位板的相位以一定拓扑数呈现拓扑变化时,可以调节光学系统焦点区域的光梯度力分布,形成各种非常有规则的几何形状的光陷阱,如当拓朴数分别取3,4,5,6时,可形成三角形、四边形、五边形和六边形光陷阱。此种相位板可用来构建可调的光镊系统,且通过调节相位板的各区域半径和拓扑数可以得到所希望的光陷阱。     

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.     

Effect of spherical aberrations in tight focusing of higher order radially polarized beam

The effect of spherical aberration, in higher order radially polarized beam, is investigated theoretically by vector diffraction theory. It is observed that an increase in aberration results in the spreading of the intensity distribution, positional shift and the size of the generated focal pattern.     

相位板偏振偏转角对径向偏振光的梯度力分布的影响

研究了同心分区偏振偏转相位板对径向偏振光梯度力的调制效应。给出了相位板各部分偏振偏转角不同时,光学梯度力的分布情况。模拟结果表明:随着同心分区相位板各部分的半径和偏振旋转角的改变,光学梯度力方向及大小明显变化,且会产生许多可控的梯度力分布模式,可应用于微粒的收集、分离和合并。结果显示同心分区相位板对径向偏振光的调制可以用来生成可调光镊。     

Focal patterns of sine-azimuthal wavefront-modulated cosh-Gaussian beams by half space phase plate

The pure phase plate was introduced to alter the half-space phase value of the incident linearly polarized hyperolic-cosine-Gaussian (cosh-Gaussian) beams with sine-azimuthal variation wavefront, and focusing properties of the cosh-Gaussian beams by half space phase plate were investigated in detail. Simulation results show that focal pattern can be altered very considerably by the phase plate under condition of different beam parameters, numerical aperture, and phase parameter that indicates the phase change frequency on increasing azimuthal angle. Symmetry of the whole focal pattern can be altered remarkably, polysymmetrical focal patterns evolve into nonsymmetrical focal patterns. And some novel focal shape may appear, including cross-shape, multiple-peak focal pattern, multiple intensity lines, wheel focal pattern, swallowtail focal pattern, and dark hollow focal spots.     

Concentric piecewise azimuthally polarized beam by a pure phase plate

Focusing properties of the azimuthally polarized beam induced by a pure phase plate are investigated theoretically. The pure phase plate consists of two concentric portions, one center circle portion and one outer annular portion, through which the azimuthally polarized beam passed evolves into concentric piecewise azimuthally polarized beam. When the phase shift of the center portion is π, one ring focus may evolve into novel focal patterns with increasing radius of the center circle portion, such as cylindrical crust focus, two-ring focus, and three-ring focus. And if the geometrical parameters are unchanged, focal patterns also changes considerably with tunable phase of the center portion. Ring focus shifts along the optical axis on the increasing phase. Some optical gradient force distributions and dependence of focal shift on phase shift are also illustrated. This kind of concentric piecewise azimuthally polarized beam can be used in optical manipulation technology.     

Focal shift and focusing properties generation by radial cosine phase masks

Focal shift and focusing properties of Gaussian beams induced by radial cosine phase masks are investigated. Results show that focal shift and the energy distribution among intensity peaks are controlled by two different parameters of the radial cosine phase mask. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift and focal switch may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter or phase variation parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to six of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers. In practice, the tunable phase mask can be implemented through liquid crystal spatial light modulator, which can conveniently alter the wavefront phase distribution of the incident laser beam in the control of computer.     

带有相位拓朴数的环形相位板调控高斯光束的梯度力

用基于德拜近似条件的矢量衍射理论研究了带有相位拓朴数的环形相位板调控高斯光束的光梯度力分布,改变相位板环形区的相对半径或当相位板的相位以一定拓扑数呈现拓扑变化时,可以调节光学系统焦点区域的光梯度力分布,形成各种非常有规则的几何形状的光陷阱,如当拓朴数分别取3,4,5,6时,可形成三角形、四边形、五边形和六边形光陷阱。此种相位板可用来构建可调的光镊系统,且通过调节相位板的各区域半径和拓扑数可以得到所希望的光陷阱。     

线偏振相位涡旋光束的像散特性

提出采用像散系数表征涡旋光束的像散特性。利用螺旋相位板产生了线偏振相位涡旋光束,并对其光束质量及像散特性进行了实际测量。数值模拟了不同拓扑荷数的涡旋光束的传输特性及光束质量,分析了像散系数随拓扑荷数变化的规律,结果表明：当拓扑荷数为整数时,光束无像散,像散系数为零;当拓扑荷数为半奇数时,光束的像散特性明显,像散系数达到极大值;随着拓扑荷数整数部分的增加,像散系数的极大值减小。     

相位片角向衍射产生拉盖尔-高斯光束的实验研究

设计了一种角向分布的相位片,利用离子束刻蚀技术加工成0和π二级的相位片.利用角向衍射理论对相位片的衍射场分析表明,衍射场为拓扑指数相反的两束拉盖尔-高斯光束的叠加场.用直径为4 mm的近平行光照射相位片,获得径向指数为零,拓扑荷相反的叠加拉盖尔-高斯光场.采用较大孔径的光束入射时,仍为拓扑荷相反的两束光的叠加,但径向指数会发生变化. 关键词： 信息光学 拉盖尔-高斯光束 相位片 离子束刻蚀     

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.