復(fù)宗量菲涅耳積分的計算及其性質(zhì)
NUMERICAL COMPUTATIONS AND CHARACTERISTICS OF COMPLEX ARGUMENT FRESNEL INTEGRAL
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摘要: 復(fù)宗量菲涅耳(Fresnel)積分的計算,是有耗介質(zhì)劈電磁散射中遇到的一個難題。本文綜合運用了復(fù)宗量菲涅耳積分的小宗量級數(shù)展開和大宗量漸近展開,并且找到了大宗量展開與小宗量展開的銜接部,圓滿地解決了菲涅耳積分在整個復(fù)平面內(nèi)的計算機(jī)計算問題。本方法計算速度快,精度高。此外,本文還研究了菲涅耳積分在復(fù)平面上的對稱性、零點等性質(zhì),給出了菲涅耳積分在復(fù)平面上的三維立體圖和二維等值線圖。
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關(guān)鍵詞:
- 電磁散射; 菲涅耳積分; 數(shù)值計算; 級數(shù)展開; 漸近展開
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. -
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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