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.     

Propagation of high-order Bessel–Gaussian beam through a misaligned first-order optical system

The generalized diffraction integralis used to derive a generalized formula for high-order Bessel–Gaussian beams (HBGBs) through a misaligned first-order ABCD optical system. It is found that, when a HBGB propagates through a misaligned optical system, the beam shape of the output beam is unchanged. However, the center of the output beam is deviated from the optical axis, forming a decentered HBGB. The position of the output beam may be controlled by adjusting the misaligned parameters. Based on the derived formula, the diffraction patterns of HBGBs propagating through a simple misaligned lens system have been calculated numerically. These results may be useful in the application of laser beams for trapping and manipulating a wide variety of particles.     

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.     

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.     

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.     

Propagation of anomalous hollow beam through a misaligned first-order optical system

In this paper, we consider the propagation of an anomalous hollow beam passing through the first-order ABCD optical system. Based on the generalized diffraction integrals, a general propagating formula of anomalous hollow beam is derived. Based on the derived formula, the propagation properties of anomalous hollow beam through the misaligned optical system are numerically illustrated. From the numerical results we can get that when an anomalous hollow beam propagates through a misaligned optical system, the shape of the output beam changes as the propagation distance increases, and the center of the output beam is deviated from the optical axis. The position of the output beam is effected by the misaligned parameters, and can be controlled by adjusting them. This method provides a convenient tool for studying the propagation and transformation of an anomalous hollow beam through the misaligned optical system.     

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 of a Lorentz-Gauss beam through a misaligned optical system

Based on the generalized integral formula and the convolution theorem of the Fourier transform, an analytical propagation formula of a Lorentz-Gauss beam passing through a misaligned paraxial optical system is derived. As numerical examples, the propagation properties of a Lorentz-Gauss beam through a misaligned thin lens with the lateral displacement and the angle displacement are graphically illustrated, respectively. The influences of the lateral displacement and the angle displacement of the misaligned thin lens on the normalized light intensity and the phase distributions are also examined, respectively.     

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 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.     

Transmitted characteristics for a Gaussian beam passing through a misaligned Fabry-Perot interferometer

After deriving the expression of the intensity of the transmitted beam for a Gaussian beam passing through a misaligned FPI, the influence of the nonparallelism in FPI mirrors alignment on the transmission of a Gaussian beam has been investigated numerically. The results show that the energy profile of the total transmitted beam appears multiple sub-peaks structure; with the increase of the nonparallelism in FPI mirrors alignment, the number of the sub-peaks raises, the peak intensity of the transmitted beam has a declining tendency, and the peak intensity position of the total transmitted beam is shifted.     

Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with a misaligned circular aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel formula. From the study and numerical calculation, the effects of aperture parameters on the propagation properties of flattened Gaussian beams in turbulent atmosphere have been illuminated. The results show that angle misalignments and lateral displacements of aperture create unsymmetrical average intensity distribution at any cross section. The intensity distributions are much more sensitive to the lateral displacement than to the angle misalignments. And the propagation properties of different flattened Gaussian beams in turbulent atmosphere are also compared.     

Propagation characteristics of the two-dimensional off-axial Hermite-cosh-Gaussian beams through rectangular apertured and misaligned optical systems

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for the two-dimensional off-axial Hermite-cosh-Gaussian beams passing through a rectangular apertured and misaligned paraxially ABCD optical system has been derived. The results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral directly. Some numerical simulations are also illustrated for the propagation characteristics of a two-dimensional off-axial Hermite-cosh-Gaussian beam through a rectangular apertured ABCD optical system.     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

高斯光束通过含失调窄缝光阑的失调光学系统的传输特性

 利用硬边窄缝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,得出了高斯光束经含失调窄缝光阑的失调光学系统传输的近似解析式。模拟结果表明输出光束场分布与光束参量、光阑尺寸、ABCD矩阵元、光阑失调量和光学系统失调量有关。针对给定的光学系统和高斯光束定量分析了各失调量对输出光束场分布的影响,结果表明:光阑横向位移、光学系统横向位移和角位移均引起垂直于z轴截面内明显的光强非轴对称分布。当光阑半宽度为1 mm时,光阑的衍射作用使腰斑半径为0.5 mm的高斯光束产生-1.586π～1.465π范围的相对相移,且光阑横向位移、光学系统横向位移和角位移均引起焦平面前后相对相移的迅速变化。随光阑宽度变小,各失调量对输出光束特性的影响越明显。     

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。     

Wigner distribution function of Gaussian beam through an apertured and misaligned ABCD optical system

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical expressions of Wigner distribution function for fundamental mode Gaussian beam through an apertured and misaligned ABCD optical system are derived. Compared with the aligned case, results show that the misaligned optical system will introduce in the output Wigner distribution function a coordinate shift in space-frequency plane. To examine the analytical results, some numerical simulations are carried out and the absolute errors between analytical results and numerical integral ones are presented. It is shown that the approximate analytical results are proper and ascendant.