Propagation of nonparaxial vector hollow Gaussian beams through a circular aperture

Based on the vectorial Rayleith-Sommerfeld formulae, the nonparaxial propagation properties of the vector hollow Gaussian beams (HGBs) through a circular aperture are studied in detail. We describe the derivation of the integral expressions of the propagation of nonparaxial vector HGBs through a circular aperture. The derived expression is independent the approximation of paraxial and far field, which are valid for either far and near field and for the systems in which aperture radius is comparable to or even smaller than wavelength. And it is also strict integral formula for the light field on the axis. Numerical calculation results indicate that there is no difference between derived formulae and the Collins formulae in the situation of paraxial approximation. Using the formula deduced, we calculate the propagation properties of HGBs. The calculated results indicate that the propagation field of vector hollow Gaussian beams is asymmetric in near field, while the propagation field is symmetric in far field. These research results could well shed light on the further understanding of the vectorial property of HGBs through a circular aperture, and would play a guiding role in the practical application of HGBs.     

Propagation of vectorial nonparaxial Gaussian beams through an annular aperture

Starting from the vectorial Rayleigh diffraction integrals, the nonparaxial propagation of vectorial Gaussian beams through an annular aperture is studied. The analytical propagation expressions are derived, which permit us to treat the on-axis field and far field of vectorial nonparaxial Gaussian beams diffracted at the annular aperture, the nonparaxial diffraction at a circular aperture and a circular disc as our special cases in a unified way. The validity of our treatment is confirmed by direct numerical integration of the Rayleigh formulae. It is shown that the f-parameter and annular obscuration affect the beam nonparaxiality in the case of diffraction at the annular aperture.     

Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated.     

Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture

As known, it is important for the propagation of Gaussian beams in optics. In this paper, based on the expanding a hard-edge circular aperture function as a finite sum of complex Gaussian functions and the scalar Rayleigh-Sommerfeld diffraction formula, an approximation analytical solution for Gaussian beams propagating through the anamorphic fractional Fourier transform system with an eccentric circular aperture is performed. Then, the detailed numerical calculation for the two-dimensional Gaussian beams in the above-mentioned optical system is presented. The simulation also shows that different location and size of aperture result in the change of diffracted field, including location, intensity and width. All these characteristics help us understand Gaussian beams propagation better.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

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.     

矢量非傍轴离轴高斯光束的传输

基于矢量瑞利-索末菲衍射积分公式，得出了波动方程的一个解，它代表矢量非傍轴离轴高斯光束，其在自由空间的传输方程表示为解析的结果.矢量非傍轴离轴高斯光束的轴上和远场公式，矢量非傍轴高斯光束的传输方程，以及傍轴的结果都可作为一般表达式的特例而得出.研究表明，f参数对光束的非傍轴特性有重要影响，而离心参数也影响非傍轴行为.与共轴情况不同的是，对离轴情况，在y方向存在场的纵向分量. 关键词： 激光光学 矢量非傍轴离轴高斯光束 瑞利-索末菲衍射积分 f参数 离轴参数     

非傍轴矢量高斯光束单缝衍射的严格理论

提出非傍轴矢量光束衍射严格的电磁场理论,并以非傍轴矢量高斯光束的单缝衍射为例加以说明.与基于矢量瑞利-索末菲衍射积分推出的解析结果做了数值计算比较,表明了二者的一致性.对理论的进一步推广做了简要讨论. 关键词： 严格的电磁场衍射理论 矢量瑞利-索末菲衍射积分 非傍轴矢量高斯光束的单缝衍射     

非傍轴矢量高斯光束的圆屏衍射

利用矢量瑞利衍射积分公式，推导出非傍轴矢量高斯光束圆屏衍射的解析表示式.非傍轴矢量高斯光束圆屏衍射的轴上场分布、远场表示式、自由空间中的传输公式，以及傍轴近似下高斯光束圆屏衍射的菲涅耳和夫琅禾费衍射公式可以作为一般公式的特例统一处理.数 值计算和比较实例说明了非傍轴矢量高斯光束的光强分布和远场特性.分析表明，在圆屏衍 射中，f参数和截断参数决定光束的非傍轴行为. 关键词： 传输光学 非傍轴矢量高斯光束 圆屏衍射 矢量瑞利衍射积分公式     

平顶高斯光束在梯度折射率介质中的传输特性

利用广义惠更斯-菲涅耳衍射积分法,推导出平顶高斯光束在梯度折射率介质中传输时的解析表达式,对平顶高斯光束在梯度折射率介质中的传输特性进行了分析,讨论了介质梯度折射率系数和光束阶数对传输特性的影响。研究表明,平顶高斯光束在梯度折射率介质中传输时轴上光强分布呈现周期性变化,其周期决定于介质梯度折射率系数,而与光束的阶数无关;轴上峰值处的横向光强分布受梯度折射率系数和光束阶数的影响较大,横向光强的最大值随着梯度折射率系数的增大而增大。     

矢量空心高斯光束横纵向光场传输特性

基于矢量瑞利-索末菲衍射积分,研究了矢量空心高斯光束横向光场和纵向光场在自由空间中的传输特性.研究结果表明,空心高斯光束的横向光场与纵向光场在传输过程中光强分布情况并不相同,横向光场的光强分布具有旋转对称性,并且保持空心特性的距离受光束阶数的影响,而纵向光场不再具有旋转对称性,并且在理想状态下纵向光场可以一直保持空心特...     

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.     

Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture

Based on the vectorial Rayleigh diffraction integral, the nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture is studied. The far-field and paraxial cases are treated as special cases of our general result. It is shown that for the apertured case the f parameter still plays an important role in determining the nonparaxiality of vectorial diffracted Gaussian beams, but both the f parameter and truncation affect the beam evolution behavior.     

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.     

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

The spectrum change of a Gaussian pulse in the far field is studied with the Fresnel diffraction integral when it is incident on an aperture with Gaussian form transmittance. It is found that the side-lobes of the diffracted spectral intensity, which exist in a normal circular aperture with unit transmittance, can be eliminated completely under such a condition. Also, the red shift and blue shift of the spectral intensity maximum of the incident pulse are presented.     

Nonparaxial diffraction of vectorial plane waves at a small aperture

By using the vectorial Rayleigh diffraction integrals, a nonparaxial propagation equation of vectorial plane waves diffracted at a small rectangular aperture is derived analytically and some special cases are discussed. Numerical calculation results are given to illustrate the applicability and validity of our theoretical formulae. It is shown that for the apertured case the ratio of the aperture width and wavelength affects the beam nonparaxiality. The nonparaxial approach presented in this paper has to be used for diffracted plane waves if the aperture width is comparable with or less than the wavelength.     

光阑对高斯谢尔模型光束偏振特性的影响

根据光束的相干-偏振矩阵理论,应用柯林公式对部分相干光经光阑衍射后的轴向、横向偏振特性从近场区到远场区的演化规律进行了详细的数值计算。经研究表明,由于光阑的衍射效应,使得高斯谢尔模型光束的偏振出现非均匀分布,光束偏振度沿轴向、横向分布出现多峰振荡现象,并且随着光阑截断参数的减小、光束空间相干长度的增大和传输距离的增大,多峰振荡逐渐增强。光束在自由空间沿轴向传输时,在近场区偏振度分布均匀,与源平面相同,随着传输距离的增大和空间相干长度的减小,偏振度沿轴向分布逐渐增大,无振荡现象。