Propagation of elliptical flat-topped beam in spatial-frequency domain

Based on a tensor method, the propagation formulae of elliptical flat-topped beam through aligned and misaligned optical systems in spatial-frequency domain are derived analytically. The derived formulae provide a powerful tool for treating the propagation and transformation of elliptical flat-topped beam through complex optical systems in spatial-frequency domain. As a numerical example, the propagation properties of elliptical flat-topped Gaussian beam in free space are studied in spatial-frequency domain.     

部分偏振高斯－谢尔模光束在准直和失调光学系统中的传输

利用张量方法导出了部分偏振高斯－谢尔模光束在准直和失调光学系统中的相干－偏振矩阵的传输公式，并以经过失调薄透镜为例，详细讨论了部分偏振GSM光束的传输特性。导出的公式提供了一个研究部分偏振GSM光束在准直和失调光学系统中传输的简便方法。     

Propagation of a general-type beam through apertured aligned and misaligned ABCD optical systems

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, analytical formulae for the electric field of a general-type beam propagating through apertured aligned and misaligned ABCD optical systems are derived using the generalized Collins formulae, which provide a convenient way of studying the propagation of a variety of laser beams, such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams, through such optical systems. As numerical examples, the propagation properties of a cos-Gaussian beam through an apertured aligned or misaligned thin lens are studied.     

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.     

The elliptical elegant Laguerre–Gaussian beam and its propagation through aligned and misaligned paraxial optical systems

A new kind of laser beam called the elliptical elegant Laguerre–Gaussian beam (EELGB) is defined by using tensor method. By using the generalized diffraction integral formulas for light beam passing through paraxial optical system, the analytical propagation formulas for EELGB passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, the propagation properties of EELGBs in free space propagation and through a misaligned thin lens are studied.     

An off-axis elliptical flat-topped beam and it’s propagation

A new kind of laser beam named off-axis elliptical flat-topped beam is proposed. This beam is expressed as a finite series of off-axis elliptical Gaussian beams with different beam parameters. Analytical propagation formulas for the off-axis elliptical flat-topped beam through aligned and misaligned optical systems are derived. As a numerical example, the propagation properties of the off-axis elliptical flat-topped beam in free space are calculated and discussed.     

Propagation of elliptical Gaussian beam passing through apertured paraxial optical systems

The propagation of elliptical Gaussian beam passing through paraxial optical systems with aperture is investigated analytically by using tensor method. The approximate formula for propagation of elliptical Gaussian beam through hard apertured optical systems is derived based on the fact that the circ function can be expanded into a finite sum of complex Gaussian functions. The derived formula provides a convenient tool for treating the propagation and transformation of elliptical Gaussian beam through apertured optical systems. As an application example, the propagation properties of elliptical Gaussian beam through apertured fractional Fourier systems are discussed.     

Off-axis flat-topped multi-Gaussian beam and its propagation through paraxial optical system

Off-axis flat-topped multi-Gaussian beam is proposed as an extension of flat-topped multi-Gaussian beam. The electric field of off-axis flat-topped multi-Gaussian beam is expressed as a superposition of a series of off-axis Gaussian beams. Propagation formulae for off-axis flat-topped multi-Gaussian beam through aligned and misaligned optical system are derived. As a numerical example, propagation properties of off-axis flat-topped multi-Gaussian beam in free space and through a misaligned thin lens are discussed.     

Propagation Effect of Hollow Gaussian Beams Passing through a Misaligned Optical System

A generalized formula of hollow Gaussian beams through the first-order misaligned ABCD systems is derived by using the generalized diffraction integral formula. It is shown that the hollow Gaussian beam passing through the misaligned system becomes a decentred hollow Gaussian beam. The propagation properties of the output beam are investigated when it propagates through a simple misaligned lens system. These results provide a powerful theoretical tool for applications of optical traps.     

Propagation of a hollow Gaussian beam through a paraxial misaligned optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a paraxial misaligned optical system in the cylindrical coordinate system, we obtain an analytical formula for a hollow Gaussian beam passing through a paraxial misaligned optical system. Furthermore, we also obtain the approximate analytical formula for a hollow Gaussian beam passing through a paraxial circularly apertured misaligned optical system by expanding the hard aperture function into a finite sum of complex Gaussian functions. As a numerical example, the propagation properties a hollow Gaussian beam through a misaligned thin lens are studied numerically.     

Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system

Propagation of a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry through an apertured optical system is investigated. By expanding the hard aperture function as a finite sum of complex Gaussian functions, some approximate analytical propagation formulas are derived for a flat-topped beam of circular or non-circular (rectangular or elliptical) symmetry propagating through an apertured paraxial general astigmatic (GA) optical system or an apertured paraxial misaligned stigmatic (ST) optical system. The derived formulas are very fast to compute. The results obtained by using the approximate analytical expressions are in a good agreement with those obtained by direct numerical integration. The present analytical formulas provide a convenient and effective way for studying the propagation and transformation of a circular or non-circular flat-topped beam through an apertured general optical system.     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian－Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.     

HfO2/SiO2高反射膜的缺陷及其激光损伤

用原子力、Normaski和扫描电子显微镜等分析仪器,对高损伤阈值薄膜常采用的HfO2光损伤所形成的孔洞,与镀制过程中形成的孔洞形貌相似,激光再损伤能力也相似。低能量密度的激光把节瘤缺陷变为孔洞缺陷是激光预处理提高薄膜损伤阈值的原因之一。     

扩束准直光学系统中光学元件失调对高斯光束传输变换的影响分析

基于广义惠更斯-菲涅尔衍射积分公式, 以高斯光束为激光束模型,推导了激光光束通过失调扩束准直光学系统的传输公式,分析了光学元件失调对扩束准直光学系统输出光束传输特性的影响,并在此基础上进行了仿真。实验结果表明,高斯光束通过失调扩束准直光学系统时,出射光束变为偏心高斯光束,光学元件失调程度越大,输出光束越偏离光轴,光束质量越差。在同样的失调下,长焦距光学元件对输出光束影响更大,因此在激光扩束准直光学系统中,调整长焦距光学元件更为重要。     

Analytical formula for a circular flattened Gaussian beam propagating through a misaligned paraxial ABCD optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial ABCD optical system in the cylindrical coordinate system, analytical formula for a circular flattened Gaussian beam propagating through such optical system is derived. Furthermore, an approximate analytical formula is derived for a circular flattened Gaussian beam propagating through an apertured misaligned ABCD optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Numerical examples are given.     

Paraxial propagation of a partially coherent flattened Gaussian beam through apertured ABCD optical systems

By expanding the hard aperture function into a finite sum of complex Gaussian functions, some approximate analytical formulae for the cross-spectral density of a partially coherent flattened Gaussian beam (FGB) propagating through apertured aligned and misaligned ABCD optical systems are derived based on the generalized Collins formula. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. As a numerical example, the focusing properties (including average irradiance distribution and focal shift) of a partially coherent FGB focused by an apertured thin lens are studied, and it is found that the focusing properties of a partially coherent FGB are closely related to its initial coherence and the aperture width. Our results provide an effective and fast way for studying the paraxial propagation of a partially coherent FGB through apertured ABCD optical systems.     

An alternative model for a partially coherent elliptical dark hollow beam

An alternative theoretical model named partially coherent hollow elliptical Gaussian beam (HEGB) is proposed to describe a partially coherent beam with an elliptical dark hollow profile. Explicit expression for the propagation factors of a partially coherent HEGB is derived. Based on the generalized Collins formula, analytical formulae for the cross-spectral density and mean-squared beam width of a partially coherent HEGB, propagating through a paraxial ABCD optical system, are derived. Propagation properties of a partially coherent HEGB in free space are studied as a numerical example.     

Elliptical cosh-Gaussian beams

Using tensor method, a new kind of light beams named elliptical cosh-Gaussian beam (EChGB) is introduced in this paper. An analytical propagation expression for the EChGB passing through axially nonsymmetrical ABCD optical systems is derived by using vector integration. The derived formula is easily reduced to the propagation formula of a fundamental Gaussian beam and that of a cosh-Gaussian beam passing through optical systems. Some numerical simulations are illustrated for the propagation properties of EChGBs through the nonsymmetrical optical transforming systems, and further extensions are pointed out.     

Propagation of a Laguerre–Gaussian beam through a slightly misaligned paraxial optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a slightly misaligned optical system in a cylindrical coordinate system, an analytical formula for a Laguerre–Gaussian beam passing through such an optical system is derived. Furthermore, an approximate analytical formula is derived for a Laguerre–Gaussian beam passing through an apertured slightly misaligned optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Some analytical formulas are also given for a flattened Gaussian beam by expanding its field as a superposition of a finite series of Laguerre–Gaussian beams. PACS 42.25.Bs; 41.85.Ew; 41.85.Ct