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 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 of elliptical Gaussian beam through misaligned optical systems in spatial domain and spatial-frequency domain

The propagation formulae of elliptical Gaussian beam through misaligned optical systems in spatial domain and spatial-frequency domain are investigated analytically by using tensor method. The derived formulae provide a powerful tool for treating the propagation and transformation of elliptical Gaussian beam through misaligned optical systems. As an application example, the propagation properties of elliptical Gaussian beam through a misaligned thin lens are illustrated.     

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.     

Study on a Bessel–Gaussian beam laser

A new concept and the method are presented to obtain a laser beam output with high luminance and quality. Instead of using the conventional concept of “obtaining a single transverse mode through compressing the oscillating mode volume using a small aperture diaphragm”, the large multimode volume and the high output power are obtained by studying the physical mechanism of the expansion and coupling between a Bessel beam and a Gaussian beam. A high quality light beam (close to the diffraction limit) with high luminance and large intensity difference between the center and the edge is achieved simultaneously.     

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 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.     

Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams

Based on the truncated second-order moments method on the cylindrical coordinate systems and the incomplete gamma function, an analytical expression of the generalized beam propagation factor (M_G² factor) of hard-edged circular apertured diffracted Bessel–Gaussian beams is derived and illustrated numerically. It is shown that the M_G² factor of hard-edged diffracted BGBs mainly depends on the truncation parameter δ and the beam parameters m and η. The results can be reduced to that for the non-truncated Bessel–Gaussian beams case and that for the truncated fundamental Gaussian beams case under certain conditions, respectively. The power fraction is also discussed analytically and numerically.     

Radiation forces of highly focused Bessel–Gaussian beams on a dielectric sphere

The radiation force of highly focused Bessel–Gaussian beams (BGBs) on a dielectric sphere in the Rayleigh scattering regime is theoretically investigated. Numerical results demonstrate that the focused BGBs can be used to trap and manipulate the particles with the refractive index lower than that of the ambient. The radiation force caused by the low-order focused BGBs has been studied under different input parameters and different focus lengths of thin lens. The stability conditions of trapping the particles are also analyzed.     

Propagation of generalized Mathieu–Gauss beams through paraxial misaligned optical systems

Based on the generalized diffraction integral, we derive an analytical formula for generalized Mathieu–Gauss beams (gMGBs) passing through an apertured misaligned optical system. Furthermore, we use the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions to establish an approximate propagation equation of gMGBs through paraxial circularly apertured optical system. As an example, the propagation of ordinary and modified zeroth order MGBs through a misaligned thin lens is studied numerically.     

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。     

Focal shift and focal switch of Bessel–Gaussian beams passing through a lens system with or without aperture

The focal shift and focal switch of Bessel–Gaussian (B–G) beams passing through a lens system with or without aperture is studied in detail. For the unapertured case, the necessary condition for the focal switch and the expression for the amplitude of the focal switch are derived. It is shown that if the truncation parameter δδ_c or beam parameter ββ_c (δ_c, β_c are the corresponding critical values), there exits only one axial intensity maximum, and the focusing without focal shift can be achieved for u/f=1 (u is the separation between the aperture and lens, f is the focal length of the lens); if δ>δ_c and β>β_c, there exist two axial intensity maxima, and the focal switch can take place at the turning point u/f=1 for both apertured and unapertured cases. The dependence of the amplitude of focal switch and normalized axial intensity minimum on the truncation parameter, beam parameter and Fresnel number is also studied.     

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.     

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.     

偏心厄米--高斯光束通过失调一阶光学系统的传输特性

使用广义惠更斯—菲涅尔衍射积分,增广矩阵和Wigner分布函数方法,研究了偏心厄米--高斯光束通过失调非对称一阶光学系统的传输特性,证明了偏心厄米--高斯光束通过一阶光学系统时保持其封闭性,光束的二阶矩矩阵按通常的规律变换,一阶矩矩阵遵循几何光线的变换规律,光束传输因子保持不变。     

高斯光束通过失调透镜系统的聚焦特性

为分析透镜系统中圆孔光栏和透镜失调对高斯光束聚焦特性的影响,利用椭圆光栏近似展开式和失调光学系统的广义衍射公式,推导高斯光束经含圆孔光栏失调透镜系统传输的近似解析式,得到输出光束光强极大值场分布与光束参量、孔径尺寸、光栏和透镜失调量之间的关系。针对特定透镜系统,定量分析失调量对输出光束聚焦特性的影响。结果表明:各元件的失调对输出光束聚焦特性均产生影响,在失调量较小时透镜横位移对输出光束聚焦特性的影响比透镜角位移对输出光束聚焦特性的影响更明显。     

Propagation properties of controllable dark-hollow beams through an annular apertured, misaligned optical system

Within the framework of the paraxial approximation, the propagation formula of controllable dark-hollow beams through an annular apertured and misaligned optical system is derived by using the generalized diffraction integral and augmented matrix. Based on the formula, the propagation properties under the very condition are studied in detail. Finally, some numerical examples are given to illustrate the analytical results. It is shown that as controllable dark-hollow beams pass through a circularly apertured misaligned optical system, they become decentered but with the same size of the dark region and the moved central position related to the misaligned parameters ε_x, ε_y and ε′_x, ε′_y. The results can be directly used in the case of other dark-hollow beams, and also can be applied to study other properties.     

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。     

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.