复宗量菲涅耳积分的计算及其性质
NUMERICAL COMPUTATIONS AND CHARACTERISTICS OF COMPLEX ARGUMENT FRESNEL INTEGRAL
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摘要: 复宗量菲涅耳(Fresnel)积分的计算,是有耗介质劈电磁散射中遇到的一个难题。本文综合运用了复宗量菲涅耳积分的小宗量级数展开和大宗量渐近展开,并且找到了大宗量展开与小宗量展开的衔接部,圆满地解决了菲涅耳积分在整个复平面内的计算机计算问题。本方法计算速度快,精度高。此外,本文还研究了菲涅耳积分在复平面上的对称性、零点等性质,给出了菲涅耳积分在复平面上的三维立体图和二维等值线图。Abstract: Computing complex argument Fresnel integral is a difficult problem meeting in electromagnetic scattering of lossy dielectric wedges. This paper makes use synthetically of series expansion and asymptotic expansion of complex argument Fresnel integral and the connections of the two expansions are found and analyzed. The computing of Fresnel integral in whole complex plane is so solved perfectly. With this method the computing speed is rapid and its precision is high. In addition, the symmetrical relations and complex zeros of Fresnel integral are studied also. Three-dimensional figure and two-dimension contour lines of Fresnel intergral in the complex plane are given.
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Sommerfelu A. Optics. New York: Academic Press Inc., 1954, Chapter 5.[2]Jones D S. The Theory of Electromagnetism. Oxford, London, New York, Paris: Pergamon Press, 1964, Chapter 9.[ [3] Rojas R G. IEEE Trans. on AP, 1988, AP-36(7): 956-970.[3]Clemmow P C. The Plane Wave Spectrum Representation of Electromagnetic Fields. Orford, London, New York, Paris: Pergamon Press, 1966, Chapter 3.[4]Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55. Washington: U. S. Goverm ent Printing Office, 1965, Chapter 7.[5]Muhammad T A. IEEE Trans. on AP, 1989, AP-37(7): 946-947. -
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