Decentered elliptical flattened Gaussian beam

A decentered flattened Gaussian beam (DEFGB), is defined by a tensor method. The propagation formula for a DEFGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a generalized decentered elliptical flattened Gaussian beam under certain condition. As an example application of the derived formula, the propagation characteristics of a DEFGB in free space are calculated and discussed. As another example we have studied the properties of superposition with radial array consisted by DEFGB.     

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.     

Propagation of elliptical cosh-Gaussian beams in a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in spatial domain, an analytical propagation expression for the elliptical cosh-Gaussian beam (EChGB) passing through misaligned optical systems is obtained by using vector integration. Some numerical simulations are illustrated for the propagation properties of an EChGB through a misaligned optical transforming system with a misaligned thin lens. As an application example, the propagation of off-axial EChGBs passing through misaligned optical systems is studied, and further extensions are also pointed out.     

Analytical propagation expression of elliptical Gaussian beams through nonsymmetric systems with an elliptical aperture

A tensor form for describing approximately the elliptical aperture function is defined that can be expanded into a finite sum of complex Gaussian functions. An analytical propagation formula of elliptical Gaussian beams through nonsymmetric and paraxial optical systems with an elliptical aperture is obtained by using tensor method. A simple numerical example is given to illustrate for its applications.     

Fractional Fourier transform of off-axial elliptical cosh-Gaussian beams

Cosh-Gaussian beams are of practical interest because they are more efficient at extracting energy from conventional laser amplifiers, and they have some important applications because their profiles can closely resemble the flat-top field distribution by choosing suitable beam parameters of cosh parts. The fractional Fourier transform (FRFT) is applied to treat the propagation of off-axial elliptical cosh-Gaussian beams (EChGBs). By the use of vector integration, the analytical expression for an off-axial EChGB passing through a FRFT system is derived in terms of tensor method. Our formula provides a convenient way for studying the FRFT of off-axial EChGBs; some numerical simulations are also given.     

Far-field properties of non-paraxial elliptical Gaussian beams

By using the Rayleigh diffraction integral formula, a far-field asymptotic solution of the wave equation is found, which represents non-paraxial elliptical Gaussian beams. The basic properties of such beams are studied, and a comparison with the previous work is also made.     

Focal shift of hollow Gaussian beams through a thin lens

In this paper, the focal shift of hollow Gaussian beams (HGBs) passing through a thin lens is investigated in detail. An analytic expression of the location of the axial maximum intensity for the HGBs is derived. It is found that, both the relative focal shift and the relative location of the axial maximal intensity of the HGBs is strongly affected by the ratio α (where α=s/f, here s is the axial distance from the input plane to the lens plane and f is the focus length of the lens), and it is also greatly affected by the changes of both the effective Fresnel number N_w and the order n of HGBs.     

Far-field properties of electromagnetic elliptical Gaussian vortex beams

The explicit far-field expressions for the TE and TM terms and energy flux distributions of electromagnetic elliptical Gaussian vortex beams are derived and their far-field properties including the phase singularities and energy flux distributions of the TE and TM terms and whole beam are studied in detail. It is shown that there exist two edge dislocations. The number and position of edge dislocations and energy flux distributions are dependent on the amplitude ratio and waist width ratio of electromagnetic elliptical Gaussian vortex beams. The analytical results are illustrated numerically.     

Off-axial elliptical cosine-Gaussian beams and their propagation properties

In this paper, a new kind of light beam called off-axial elliptical cosine-Gaussian beam (ECosGBs) is defined by using the tensor method. An analytical propagation expression for the ECosGBs passing through axially nonsymmetrical optical systems is derived by using vector integration. The intensity distributions of ECosGBs on the input plane, on the output plane with the equivalent Fresnel number being equal to 0.1 and on the focal plane are respectively illustrated for the propagation properties. The results indicate that an ECosGB is eventually transformed into an elliptical cosh-Gaussian beam. In other words, ECosGBs and cosh-Gaussian beams act in a reciprocal manner after propagation.     

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.     

Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) 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 beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals.     

椭圆高斯光束在单轴晶体中垂直于光轴的传输特性

基于光束在各向异性介质中的傍轴矢量传输理论,导出了椭圆高斯光束在各向异性单轴晶体中垂直于光轴的传输公式,并利用此解析式进行数值计算和分析,研究了各向异性介质对x方向偏振的椭圆高斯光束偏振特性的影响. 研究表明,晶体的各向异性对光束的偏振和对称性有较大影响. 关键词： 椭圆高斯光束 单轴晶体 各向异性 传输     

Propagation of hollow Gaussian beam through a misaligned first-order optical system and its propagation properties

Propagation properties of hollow Gaussian beam through a misaligned first-order ABCD system is studied using the generalized Huygens-Fresnel diffraction integral, augmented matrix. It is shown that, as a hollow Gaussian beam passes through the misaligned first-order ABCD system, the beam shape is not preserved, the out-put beams have differences when passing different misaligned optical systems. We can adjust the size of dark region through adjusting the misaligned transverse vector E.     

利用椭圆高斯光束产生266nm紫外连续激光

本文采用商用532 nm激光器作为基频光源,利用偏硼酸钡(β-BBO)晶体进行外腔倍频,实现了266 nm连续激光的高效输出.文中详细模拟了BBO晶体中的束腰形状对倍频效率的影响,仿真和实验结果均表明椭圆高斯光束可以有效改善走离效应,提高倍频转换效率.通过优化蝶形倍频腔,可以使椭圆高斯光束在腔内共振,当1 W基频光输入时可输出约180 mW的266 nm紫外连续激光,倍频转换效率达到18%.     

The elliptical Laguerre–Gaussian beam and its propagation

A new kind of light beam called the elliptical Laguerre–Gaussian beam (ELGB) is proposed in this paper in terms of tensor method. The propagation formula of ELGB through axially asymmetric optical system is derived by the generalized Collins integral. By using this formula, the propagation of ELGB in free space is calculated and discussed. The results show that the propagation behavior of ELGBs is notably different from that of LGBs.     

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.     

Propagation properties of beam generated by Gaussian mirror resonator

Based on scalar diffraction theory, propagation properties of beam generated by Gaussian mirror resonator were investigated. Explicit expressions for the field distribution of the beam that propagate through a paraxial optical ABCD system were derived and numerical examples were given to illustrate our analytical results.     

Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam

Based on the theory of coherence, an analytical propagation formula for partially polarized and partially coherent hollow Gaussian Schell-model beams (HGSMBs) passing through a paraxial optical system is derived. Furthermore, we show that the degree of polarization of source may affect the evolution of HGSMBs and a tunable dark region may exist. For two special cases of fully coherent and partially coherent δ_xx = δ_yy, normalized intensity distributions are independent of the polarization of source.     

Polynomial Gaussian beams and topological charge conservation

We investigate polynomial Gaussian beams with rotationally symmetric Gaussian envelops and complex bivariate polynomial prefactors of finite order. A formalism for the propagation of such beams is developed, which expresses how the coefficients of the polynomial transform during propagation. This formalism is used to proof that global topological charge is conserved for this class of polynomial Gaussian beams.