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.     

Focal shift of cylindrical vector axisymmetric Bessel-modulated Gaussian beam with radial variance phase wavefront

Axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. In this paper, the focal shift of the cylindrical vector QBG beam with radial variance phase wavefront is investigated theoretically by vector diffraction theory. Results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of small beam parameter μ of cylindrical vector QBG beam, there is one focal peak that shifts far away from optical aperture on increasing C. When μ increases, there may occur two focal peaks that also shift remarkably on increasing C. And it was found that the dependence of focal shift distance on increasing phase parameter is linear. Phase parameter adjusts the focal shift distance, while, polarization angle does not affect focal shift obviously.     

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.     

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.     

Focal shifting of transversely polarized beam using cosine phase plate

Focal shift of transversely polarized beams induced by cosine phase masks are investigated theoretically by vector diffraction theory. Results show that when the transversely polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift 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 five of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers.     

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.     

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.     

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.     

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.     

Tight focus of an azimuthally polarized and amplitude-modulated annular multi-Gaussian beam

We investigate the focusing properties of an azimuthally polarized and amplitude modulated annular multi Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a subwavelength focal hole of 0.46λ having large uniform focal depth of 36λ without any annular obstruction. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.     

Focusing properties of Gaussian beam with superimposed left-handed and right-handed helical phase fronts

Vector diffraction theory is employed to investigate the focusing properties of the Gaussian beams with superimposed left-handed and right-handed helical phase fronts theoretically. Numerical simulations show that the intensity distribution in focal region can be altered considerably by adjusting topological charge m corresponding to right-handed helix and topological charge n corresponding to left-handed helix. Many novel focal pattern may occur. It was shown that the focal pattern evolves from one intensity peak to multiple intensity peaks with changing the topological charge m and n, and all the intensity peaks form in a circle. As the number of intensity peaks is the sum of m and n, the focal pattern can be controlled through adjusting the topological charge m and n. And in order to show the possible applications of these alterable foci pattern, some optical gradient force distributions were also calculated and illuminated.     

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.     

线偏振高斯光束通过复合型衍射光栅的传输特性

提出一种集合浮雕和折射率周期分布调制的复合型衍射光栅,并利用角谱表示和严格的模式理论研究了线偏振高斯光束通过这种复合型衍射光栅的传输特性.数值计算结果表明,在光栅的同一透射深度处复合型衍射光栅光强的起伏频率要比浮雕型光栅光强的起伏频率小.最后使用复合型衍射光栅模型,研究了亚波长体积相位全息光栅的表面起伏和入射光束的束腰宽度对衍射效率的影响. 关键词： 复合型衍射光栅 亚波长体积相位全息光栅 高斯光束 严格模式理论     

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 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.     

The beam propagation factor and far-field distribution of Bessel-modulated Gaussian beams

The explicit expressions for the beam propagation factor (M ² factor) and far-field distribution of Bessel-Modulated Gaussian beams with quadratic radial dependence are derived. The results are analyzed with numerical example.     

高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布,导出了高斯衍射光束的TE项和TM项远场功率的解析表达式,由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义,给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式,重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大,远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关,当f参数较大时,截取参数对远场发散角的影响不明显;当f参数适中时,随着截取参数的增大,远场发散角先减小后趋向于各自的最小值;但当f参数较小时,高斯衍射光束和TM项二者的远场发散角出现一定的波动性。     

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.     

任意线偏振高斯光束的非傍轴传输

运用非傍轴光束传输的矢量矩理论，对任意线偏振高斯光束的非傍轴传输进行了系统的研究，给出了定量计算偏振对束腰、横向远场发散角和光束传输因子贡献的解析通式. 并对高度非傍轴和傍轴两种极端情形，简化了相应的计算式. 在高斯光源线度趋向于零的极限情形下，两个横向的最大发散角均为90°，与偏振态无关. 在高度非傍轴情形下，可以通过所给出的解析通式设计高斯光源的半宽度与激射光波长之比值以及线偏振态来达到所期望的光束传输特性. 对于傍轴情形，不同偏振对束腰和横向远场发散角稍有影响，但这种影响一般可以忽略不计；而光束传输因子却始终保持不变，与偏振态无关. 若介于这两种极端情形之间，则可以根据高斯光源的半宽度之值和所期望的计算精度，确定解析式中级数的项数进而确定任意线偏振高斯光束的非傍轴传输特性. 关键词： 高斯光束 非傍轴传输 偏振 二阶矩     

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.