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Xiang Lu 《Optics Communications》2007,269(1):39-46
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. 相似文献
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The propagation properties of Bessel beam is a meaningful research. In this paper, based on the expanding the hard-edged circular aperture as a finite sum of complex Gaussian functions and the scalar diffraction theory, an approximate analytical solution for Bessel beam propagating through a fractional Fourier transform system is derived in the cylindrical coordinates. Then, the detailed numerical calculation for Bessel beam is presented. The simulation also shows that the beam parameter and the order of fractional Fourier transform result in the change of field distribution, including location, intensity and width. 相似文献
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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. 相似文献
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Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems 总被引:1,自引:0,他引:1
Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expression for the output field distribution of a rectangular flattened Gaussian beam passing through a circular apertured and misaligned paraxial ABCD system is derived. The result brings more convenient 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 a rectangular flattened Gaussian beam through a circular apertured and misaligned optical system. 相似文献
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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 相似文献
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The main feature of Bessel beams realized in practice is their ability to resist diffractive effects over distances exceeding the usual diffraction length. The theory and experimental demonstration of such waves can be traced back to the seminal work of Durnin and co-workers already in 1987.Despite that fact, to the best of our knowledge, the study of propagation of apertured Bessel beams found no solution in closed analytic form and it often leads to the numerical evaluation of diffraction integrals, which can be very awkward. In the context of paraxial optics, wave propagation in lossless media is described by an equation similar to the non-relativistic Schrödinger equation of quantum mechanics, but replacing the time t in quantum mechanics by the longitudinal coordinate z. Thus, the same mathematical methods can be employed in both cases. Using Bessel functions of the first kind as basis functions in a Hilbert space, here we present a new approach where it is possible to expand the optical wave field in a series, allowing to obtain analytic expressions for the propagation of any given initial field distribution. To demonstrate the robustness of the method two cases were taken into account: Gaussian and zeroth-order Bessel beam propagation. 相似文献
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Based on Collins integral formula and the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of cosh-squared-Gaussian beam passing through ideal and apertured FRFT systems have been studied, and some comparisons between using the methods of analytical formula and diffraction integral formula have been done. Further, the studies indicate that the normalized intensity distributions on FRFT plane depend on the fractional order, truncation parameter and initial beam parameter Ω. Variations of normalized intensity distributions with FRFT order are periodic: when the impact of aperture cannot be ignored, the variation period is 4; and when the impact of aperture can be ignored, the variation period is 2. 相似文献
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《Physics letters. A》2006,360(2):394-399
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. 相似文献
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Based on the method of matrix decomposition and expanding the aperture function into a sum of finite complex Gaussian functions, the analytical propagation equations of Gaussian beams through cat eye optical lens with center shelter are derived. Through numerical calculation, the laws governing the variation of the intensity distribution of the cat eye reflected light with the center shelter ratio and the diameter of the detector at the focal plane are given. The results show that the diffraction series and the intensity of the cat eye reflected light depend strongly on the center shelter ratio. As a further extension, it is found that the eye optical lens can be interpreted as a spatial filter, and different filter effect can be obtained by changing the pinhole size. 相似文献
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Juguan Gu Juguan Gu Daomu Zhao Zhangrong Mei Zhangrong Mei Haidan Mao Haibin Xu 《Optik》2004,115(11-12):529-532
By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture. 相似文献
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By expanding a hard aperture function into a finite sum of complex Gaussian functions, approximate propagation formula is derived in the situation that the beam generated by Gaussian mirror resonator passes through a paraxial ABCD optical system with an annular aperture. The corresponding forms for a circular aperture and a circular black screen are also given. Some numerical simulations are shown to illustrate propagation properties and focusing properties of the beam passing through a paraxial ABCD optical system with the three different kinds of aperture. 相似文献
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Double-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere 下载免费PDF全文
By using the extended Huygens-Fresnel diffraction integral and the method of expanding the aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula of the double-distance propagation for Gaussian beam passing through a tilted cat-eye optical lens and going back along the entrance way in a turbulent atmosphere has been derived. Through numerical calculation, the effects of incidence angle, propagation distance, and structure constant on the propagation properties of a Gaussian beam in a turbulent atmosphere are studied. It is found that the incidence angle creates an unsymmetrical average intensity distribution pattern, while the propagation distance and the structure constant can each create a smooth and symmetrical average intensity distribution pattern. The average intensity peak gradually deviates from the centre, and the central average intensity value decreases quickly with the increase in incidence angle, while a larger structure constant can bring the average intensity peak back to the centre. 相似文献
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Based on the generalized Collins diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of Bessel-Gaussian beams and QBG beams passing through a paraxial ABCD optical system with an annual aperture are derived. As special cases, the corresponding closed-forms for the unaperture or circular aperture or circular black screen cases are also given. The results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Numerical examples are given to illustrate the propagation properties of Bessel-Gaussian and QBG beams. 相似文献
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Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams. 相似文献
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Chieh-Jen Cheng 《Optics Communications》2010,283(24):4892-4898
This study utilizes the focal property of a classical Billet's split lens to create more focal points by splitting the lens. This approach distributes the focal points circularly on the focal plane. This study explores the characteristics of beam propagation and analytically derives the asymptotic characteristics of beam propagation based on the stationary phase approximation and the moment-free Filon-type method. Results show that the unique Billet's N-split lens can generate a quasi Bessel beam if the number of splitting N is large enough, e.g., N ≧ 24. This study also explores the diffraction efficiency of corresponding quasi Bessel beam and the influence of aperture size. The potential advantage of proposed split lens approach is that, unlike the classical means of annular aperture, this simple lens approach allows a much larger throughput in creating the Bessel beam and hence the Bessel beam could have more optical energy. 相似文献