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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳義裕(Yih-Yuh Chen) | |
dc.contributor.author | Yi-Chuan Lu | en |
dc.contributor.author | 盧奕銓 | zh_TW |
dc.date.accessioned | 2021-05-20T20:03:29Z | - |
dc.date.available | 2011-12-22 | |
dc.date.available | 2021-05-20T20:03:29Z | - |
dc.date.copyright | 2011-09-18 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-08-23 | |
dc.identifier.citation | [1] Arnold. Sommerfeld, Lectures on Theoretical Physics Vol.(IV) Optics, Trans-
lated by Otto Laporte & Peter A. Moldauer. (Academic Press Inc., Publishers, New York, 1954), p.311-312 [2] V. A. Rubinowicz, Ann. Phys. 53, 257 (1917). [3] P. 311-318 of [1]. [4] P. 200 of [1]. [5] B. B. Baker & E. T. Copson, The Mathematical Theory of Huygens’Principle, 3rd ed. (Chelsea Publishing Company, New York, 1987), p. 98-101. [6] J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, Inc., New York, 1999), p. 37-40. [7] P. 316 of [1]. [8] J. S. Asvestas, J. Opt. Soc. Am. A2, 891 (1985). [9] P. 249 of [1]. [10] M. Born & E. Wolf, Principles of Optics, 3rd ed. (Cambridge University Press, Cambridge, New York, 1999), p. 657-659. [11] D. L. Clements & E. R. Love, Proc. Cambridge Phil. Sot., 76, 313-325 (1974). [12] E. T. Copson, Proc. Edinburgh Math. Soc., (II) 8, 14-19, (1947) [13] Rudolf Goren‡o, Sergio Vessella, Abel integral equations : Analysis and Applica- tions, (Berlin, New York, Springer-Verlag, 1991) | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8891 | - |
dc.description.abstract | 本篇論文探討以沿著孔洞邊緣的線積分來表示一個純量波經過孔洞之後的繞射行為,並探討不同線積分的形式所能給出的不同物理詮釋。 | zh_TW |
dc.description.abstract | Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to split the solution into two parts: one is the geometrical optics wave that appears only in the geometrical illuminated region, and the other representing the reflected wave is a line integral along the edge of the aperture. Though providing us with an alternative perspective on the diffraction phenomena, this decomposition theory is not entirely satisfactory in the sense that the two separated fields are discontinuous at the boundary of the illuminated region. Also, the functional form of the line integral is not what one would expect an ordinary reflection wave should be due to some confusing factors in the integrand. Finally, the boundary conditions on the screen imposed by Kirchhoff's approximation are mathematically inconsistent, and therefore to be more rigorous this decomposition formulation must be slightly modified by taking into account the correct boundary conditions.
In this thesis, we derive a slightly different decomposition formulation that avoids the discontinuity, and also we deform the functional form of the line integral into another one that mimics the ordinary reflection behavior of waves, and finally, all these works are done based on the mathematically consistent boundary conditions. In the appendix, we digress a little to see how to solve diffraction problems subject to 'physical' boundary conditions, which best describe the diffraction phenomena in the real world. | en |
dc.description.provenance | Made available in DSpace on 2021-05-20T20:03:29Z (GMT). No. of bitstreams: 1 ntu-100-R98222035-1.pdf: 3939837 bytes, checksum: a88f6c30185c0331154685ff1815fbcd (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | Acknowledgement iii
中文摘要 iv Abstract v 1 Introduction 1 2 Maggi-Rubinowicz’ Formulation 5 2.1 Rubinowicz’ Original Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Modified Version of Rubinowicz’ Decomposition . . . . . . . . . . . . . . . . . . 12 3 'Reflective' Representation 17 3.1 Motivations from Geometric Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Reflection at the Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 A More Elegant Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Solid-Angle Representation 29 4.1 Motivation from Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5 Approximations 40 5.1 Approximated Solution for a Point Source . . . . . . . . . . . . . . . . . . . . . . . 41 5.2 Approximated Solution for Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . 45 6 Conclusion 48 Appendices 50 A The Mathematical Foundation of Huygens’ Principle 51 A.1 Kirchhoff’s Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 A.2 Sommerfeld’s Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 B Diffraction Problems with Physical Boundary Conditions 57 B.1 The General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 B.2 Clements and Love’s Method for Circular Aperture . . . . . . . . . . . . . . . . 62 B.3 Normal Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Bibliography 67 | |
dc.language.iso | en | |
dc.title | 繞射之線積分理論 | zh_TW |
dc.title | Line-Integral Representation of Diffraction Theory | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 魏金明,李精益 | |
dc.subject.keyword | 繞射,線積分, | zh_TW |
dc.subject.keyword | diffraction,line integral,Rubinowicz, | en |
dc.relation.page | 68 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2011-08-23 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 物理研究所 | zh_TW |
顯示於系所單位: | 物理學系 |
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