四瓣高斯光束的Gyrator变换性质和矩形空心光束的产生

基于Gyrator变换,推导了四瓣高斯光束场分布的解析表达式,研究了四瓣高斯光束通过Gyrator变换后的光强分布和相位分布.结果表明:在Gyrator变换过程中,四瓣高斯光束能够转换为具有光涡旋的矩形空心光束,在获得矩形空心光束时其四顶角处光束强度最强,而四条边上的光束强度分布几乎是均匀的.对影响矩形空心光束强度和相位分布的光束参数和变换角进行了详细的分析,发现光束阶数不同,产生不同类型的空心光束;Gyrator变换的变换角则影响空心光束能量分布;空心光束亮环的大小由四瓣高斯光束的束腰宽度决定,束腰宽度越大,矩形空心光束的宽度越小.     

广义双曲正弦-高斯光束的Gyrator变换性质和暗空心光束产生

基于Gyrator变换,推导了广义双曲正弦-高斯光束场分布的解析表达式,研究了广义双曲正弦-高斯光束在Gyrator变换平面上的光强分布和相位特性.结果表明,在Gyrator变换过程中,具有边缘位错相位特性的双曲正弦-高斯光束能转换为具有涡旋的暗空心光束,并确定产生的暗空心光束的拓扑荷指数为一,而不具有边缘位错相位特性的双曲余弦-高斯光束则不可能出现空心结构.对影响变换场强度和相位分布的束结构参数及系统参数进行了分析讨论.     

Fractional Fourier transform for a hollow Gaussian beam

The fractional Fourier transform (FRT) for a hollow Gaussian beam (HGB) is investigated. Based on the definition of FRT in the cylindrical coordinate system, analytical formulae are derived for the FRT for a HGB. By using the derived formulae, the properties of a HGB in the FRT plane are illustrated numerically. The derived formulae provide a convenient way for analyzing and calculating the FRT of a HGB.     

基于柱坐标系下的空心高斯光束的分数傅里叶变换

推导出分数傅里叶变换基于柱坐标系下的解析表达式,应用此解析表达式对空心高斯光束进行分析,得到其分数傅里叶变换的解析表达式。讨论其在分数傅里叶变换平面的光强分布与各种光束参数之间的变换关系,并进行数值计算,从而得出基于柱坐标系下的空心高斯光束的分数傅里叶变换的传输性质。所得结果为分析和计算这种光束的分数傅里叶变换提供了方便,同时对此类光束的传输控制提供了基础理论支持。     

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular ?-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.     

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.     

Effect of binary phase plate on incident radially polarized hollow Gaussian beam

Effect of a pure binary phase filter on the three-dimensional light intensity distributions in focal region is theoretically investigated in this paper. The results show that the proposed binary phase filter may induce flat top profile with large depth of focus and reduced focal spot by properly adjusting the geometrical parameters of the binary phase filter of incident radially polarized hollow Gaussian beam (HGB) beam. On the other hand, the HGB beam benefits the most from the use of an annulus. Such kind of system is potentially useful for lithography, imaging, optical data storage, optical trapping, optical excitation of molecules, or coupling to optical fibers.     

Generation of hollow Gaussian beams by spatial filtering

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.     

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.     

Propagation properties of a non-paraxial hollow Gaussian beam

Based on the non-paraxial vectorial moment theory of beam propagation, the analytical expressions of the M² factors for a non-paraxial hollow Gaussian beam (HGB) have been derived. The analytical formulae are further simplified for paraxial and highly non-paraxial cases. The beam waists, the divergence angles and the beam propagation factors are also depicted as functions of the parameter w₀. The divergence angles will not exceed the maximum value of 90°. When w₀ is within the scale of one time of light wavelength, the TE polarization results in the different beam propagation factors in the two transverse directions and the beam propagation factors first increase and then decrease. When w₀ is large enough, the beam propagation factors are determined only by the beam order.     

Focusing properties of spirally polarized hollow Gaussian beam

Focusing properties of spirally polarized hollow Gaussian beam (HGB) are investigated theoretically by vector diffraction theory in this article. Results show that the optical intensity in focal region of spirally polarized HGB can be altered considerably by the beam order, numerical aperture of the focusing system, and spiral parameter that indicates the polarization spiral degree of the spirally polarized HGB. Spiral parameter can induce focal pattern change in axial direction remarkably, while beam order and numerical aperture affect radial foal pattern more obviously. The tunable principle of the focal pattern by spiral parameter differs very considerably under condition of different numerical aperture and beam order. Many novel focal patterns may occur in focal pattern evolution. It was also found that focal shift and focal depth can be altered significantly by spiral parameter and beam order.     

Fractional Fourier transform for off-axis elliptical Gaussian beams

The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.     

Optical implement of Hartley transform on elliptical Gaussian beams

The optical Hartley transform (HT) is expressed in matrix form. The analytical formula of an off-axial elliptical Gaussian beam passing through the HT system is obtained. Numerical examples show that the information about the displacement magnitude and direction of the source can be represented in the form of fringes at the output plane of the HT system.     

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.     

Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of hollow Gaussian beams (HGBs) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident HGBs propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of incident HGBs do not remain during propagating in crystals.     

空心高斯涡旋光束的远场特性

基于角谱法和稳相法,推导出了空心高斯涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式,研究了其相位奇点和能流密度分布。结果表明,空心高斯涡旋光束的远场特性主要跟控制参数有关。改变光束中的涡旋离轴量,光涡旋和能流密度黑核会发生移动。圆刃型位错线的半径和能流密度暗环位置跟束腰宽度有关,而能流密度的对称性主要受涡旋离轴量的影响。     

1维线阵离轴高斯光束的分数傅里叶变换

为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明：非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。     

Generation of a hollow Gaussian beam and its anomalous behavior

I attempted to produce a laser beam with no light in the central line of the beam, by Fresnel diffraction of the Gaussian beam by a spiral zone plate (SZP). The study imparts an arbitrary-order phase singularity on the light field. The experimental results show that the optical vortex radius depends on the singularity’s integer order n (also termed topological charge, or order of the dislocation). Also, the radius of maximum intensity is shown to depend on the singularity number. Anomalous behavior of the spectra at phase singularity produced by various zone plates near the focus of a converging Gaussian beam is also studied using a simple experimental technique. It is found that the spectrum of the beam on the SZP (spiral zone plate) consisting of a single spectral profile shows almost vanishing intensity at all frequencies with a tendency of splitting into two peaks at the on-axis point and shows redshift and blueshift around the phase singularity. A comparative study of the anomalous behavior of the spectra at phase singularity produced by various SZPs, with varying phase singularity order n, near the focus of a converging Gaussian laser beam is studied.