本論文研究X 光曲面共振腔在背向繞射下的聚焦行為以及共振效果，選擇矽原子面(12 4 0) 在14.4388keV 下，當光通過此拋物曲面時，除了折射效應外同時還會發生背向繞射效應。實驗上在繞射下觀察到異常的聚焦行為，相較於無繞射時的結果，兩光繞射下的聚焦點往前縮了5~13%，24 光繞射下往前約23~55%；並且也觀察到了曲面共振腔的共振干涉現象。
理論分析是利用X 光動力繞射理論來模擬通過曲面共振腔繞射光與穿透光的變化，藉由解出純量波場方程式與解邊界條件，可以獲得色散表面以及曲面聚焦鏡內外的波向量和電場資訊。X 光對物質的折射率為n=1-δ+iβ，影響折射的參數來自於實部的修正項δ 。從動力繞射計算結果發現到繞射激發了變形的色散表面導致了折射率的修正項δj 異於沒有繞射下的值δ0，在高於繞射精確能量時，修正項δj > δ0；反之低於繞射能量時，δj < δ0，直到遠離繞射能量δj = δ0。此外，在不平行邊界下，繞射的穿透光會分裂為數個模式，導致在實驗上觀察到種種異於一般光學聚焦的結果。

The thesis investigates the focusing behavior and resonance effect in curved multiplate X-ray cavity using back-diffraction. At the photon energy of 14.4388 keV, the atomic plane (12 4 0) of Silicon was selected as back diffraction. As the beam passes through the device , the transmitted beam-focusing and back diffraction occur at the same time. The measurement on the transmitted x-ray beam size through the crystal cavities shows a reduced focal length and a long beam waist at the focal point. We also observed the resonance effect from this device. According
to the X-ray dynamical diffraction theory, we could obtain information of coordinates of dispersion surface, wavevector and wavefield inside and outside the crystal device. Based on the consideration of the excitation of the dispersion surface for each curved crystal surface involved in the crystal device, beam focusing and beam splitting occur, leading to the observed focusing feature. Detailed
dynamical calculations on the transmitted intensities at different positions near the focal point will be discussed.

[1] W. L. Bond, M. A. Duguay, and P. M. Rentzepis, Appl. Phys. Lett. 10, 216-218 (1967).
[2] R. D. Deslattes, Appl. Phys. Lett. 12, 133-135 (1968).
[3] S.-L. Chang, Y. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, and T. Ishikawa, Phys. Rev. Lett. 94, 174801-1  4 (2005).
[4] A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49-51 (1996).
[5] A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, Applied Optics 37, 653-662 (1998).
[6] A. Authier, Dynamical theory of X-ray diffraction (Oxford, New York, 2001).
[7] B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681-717 (1964).
[8] S.-L. Chang, X-ray multiple-wave diffraction : theory and application (Springer, 2004).
[9] J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, 2001)
[10] J. D. Jackson, Classical Electrodynamics, 3rded (Wiley 1999).
[11] Y. P. Stetsko and S.-L. Chang, Acta Cryst. A53, 28-34 (1997).
[12] 邱茂森, 國立清華大學物理系博士論文(2008).
[13] 陳松裕, 國立清華大學物理系博士論文(2008).
[14] A. Caticha and S. Caticha-Ellis, Phys. Rev. B 25,971-983 (1982).
[15] Yu. V. Shvyd’ko, E. Gerdau, J. Jäschke, O. Leupold, M. Lucht, and H. D. Rüter, Phys. Rev. B 57, 4968-4971 (1998).
[16] S. Kikuta, Y. Imai, T. Iizuka, Y. Yoda, X.-W. Zhang ,and K. Hiranob, J. Synchrotron Rad. 5, 670-672 (1998).
[17] A. Caticha and S. Caticha-Ellis, phys. stat. sol.(a) 119, 47-54 (1990).
[18] V. I. Kushnir and E. V. Suvorov, phys. stat. sol.(a) 122, 391-404 (1990).
[19] J. P. Sutter, E. E. Alp, M. Y. Hu, P. L. Lee, H. Sinn, W. Sturhahn, T. S. Toellner, G. Bortel, and R. Colella, Phys. Rev. B 63, 094111-112(2001).
[20] M. Y. Hu, H. Simn, A. Alatas, W. Sturhahn,E. E. Alp, H.-C. Wille, Yu. Shvyd’ko, J. P. Sutter, J. Bandaru, E. E.Haller, V. I. Ozhogin, S. Rodriguez, R. Colella, E. Kartheuser, and M. A. Villeret, Phys. Rev. B 67, 113306-14
(2003).
[21] C. Giles, C. Adriano, A. F. Lubambo, C. Cusatis, I. Mazzaro, and M. G. Hönnicke, J. Synchrotron Rad. 12, 349-353 (2005).
[22] Yu. V. Shvyd’ko, M. Lerche, U. Kuetgens, H. D. Rüter, A. Alatas, and J. Zhao, Phys. Rev. Lett. 97, 235502-14 (2006).
[23] M.-S. Chiu, Yu. P. Stetsko, and S.-L. Chang, Acta Cryst. A64, 394–403 (2008).
[24] J. M. Vaughan, The Fabry-Perot interferometer: history, theory, practice, and applications (A. Hilger, 1989)
[25] M. Born, E. Wolf , and A. B. Bhatia Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Cambridge University Press, 1999)
[26] Bahaa E. A. Saleh, M. C. Teich Fundamentals of photonics (Wiley-Interscience, 2007).
[27] S. O. Kasap, Optoelectronics and photonics: principles and practices (Prentice Hall, 2001).
[28] M Hart, Rep. Prog. Phys. 34, 435-490 (1971).
[29] A. Steyerl and K.-A. Steinhauser, Z. Physik B 34, 221-227 (1979).
[30] A. Caticha and S. Caticha-Ellis, phys. stat. sol.(a) 119, 643-654 (1990).
[31] V. G. Kohn, Yu. V. Shvyd’ko, and E. Gerdau, Phys. Stat. Sol.(b) 221, 597-615 (2000).
[32] K.-D. Liss, R. Hock, M. Gomm, B. Waibel, A. Magerl, M. Krisch, and R.Tucoulou, Nature 404 ,371-373 (2000)
[33] Yu. V. Shvyd’ko, M. Lerche, H.-C.Wille, E. Gerdau, M. Lucht, H. D. Rüter, E. E. Alp , and R. Khachatryan, Phys. Rev. Lett. 90, 013904-14 (2003).
[34] S.-L. Chang, Yu. P. Stetsko, M.-T. Tang, Y.-R. Lee, W.-H. Sun, M. Yabashi, T. Ishikawa, H.-H. Wu, B.-Y. Shew, Y.-H. Lin, T.-T. Kuo, K. Tamasaku, D. Miwa, S.-Y. Chen, Y.-Y. Chang, and J.-T. Shy, Phys. Rev. B 74, 134111-1~7 (2006).
[35] S.-Y. Chen, H.-H. Wu, Y.-Y. Chang, Y.-R. Lee, W.-H. Sun, S.-L. Chang, Yu. P. Stetsko, M.-T. Tang, M. Yabashi, and T. Ishikawa, Appl. Phys. Lett. 93, 141105-13 (2008).
[36] F. van der Veen and F. Pfeiffer, J. Phys.: Condens. Matter 16, 5003–5030 (2004).
[37] H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa,H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi1, Nature 6, 122-125 (2010).
[38] A. Snigirev and I. Snigireva, C. R. Physique 9, 507-516 (2008).
[39] H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, and S. Vogt, Phys. Rev. Lett. 96, 127401-1~4 (2006).
[40] C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, Appl. Phys. Lett. 87, 124103-1~3 (2005).
[41] C. G. Schroer and B. Lengeler, Phys. Rev. Lett. 94, 054802-1~4 (2005).
[42] K. Evans-Lutterodt, A. Stein, J. M. Ablett, N. Bozovic, A. Taylor, and D. M. Tennant, Phys. Rev. Lett. 99,134801-1~4 (2007).
[43] C. G. Schroer, J. Meyer, M. Kuhlmann, B. Benner, T. F. Günzler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, Appl. Phys. Lett. 81,1527-1529 (2002).
[44] C. Bergemann, H. Keymeulen, and J. F. van der Veen, Phys. Rev. Lett. 91,204801-1~4 (2003).
[45] B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Günzler1, O. Kurapova, F. Zontone, A. Snigirev, and I. Snigireva, J. Phys. D: Appl. Phys. 38, A218–A222 (2005).
[46] M. Guizar-Sicairos and J. R. Fienup, Optics Express, 17, 2670–2685 (2009).
[47] S. D. Shastri, J. Almer, C. Ribbingb, and B. Cederström, J. Synchrotron Rad. 14, 204–211 (2007).
[48] V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058-4060 (2000).
[49] A. F. Isakovic, A. Stein, J. B. Warren, S. Narayanan, M. Sprung, A. R. Sandy, and K. Evans-Lutterodt, J. Synchrotron Rad. 16, 8-13 (2009).
[50] E. Hecht, Optics (Addison-Wesley, 2002).
[51] W. M. DuMond, Phys. Rev. 52, 872-883 (1937).
[52] G. S. Brown, Ernst-Eckhard Koch, and D. E. Moncton, Handbook on synchrotron radiation Vol.3 (North-Holland, 1991)
[53] Yu. V. Shvyd’ko X-ray optics: high-energy-resolution applications (Springer, 2004).
[54] T. Ishikawaa, K. Tamasakua, and M. Yabashi, Nucl. Instr. and Meth. A 547, 42-49 (2005).
[55] S. Brauer, G. B. Stephenson, and M. Sutton, J. Synchrotron Rad. 2, 163-173 (1995).
[56] A. I. Chumakov, R. Rüffer, O. Leupold, A. Barla, H. Thiess, T. Asthalter,B. P. Doyle, A. Snigirev, and A. Q. R. Baron, Appl. Phys. Lett. 77, 31-33 (2000).
[57] M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, Rev. Sci. Instr. 72, 4080-4083 (2001).
[58] Y.-Y. Chang, S.-Y. Chen, H.-H. Wu, S.-C. Weng, C.-H. Chu, Y.-R. Lee, M.-T. Tang, Yu. Stetsko, B.-Y. Shew, M. Yabashi, and S.-L. Chang1, Optics Express, 18, 7886–7892 (2010).
[59] Y.-Y. Chang, S.-Y. Chen, S.-C. Weng, C.-H. Chu, M.-T. Tang, Yu. Stetsko, B.-Y. Shew, M. Yabashi, and S.-L. Chang, X-Ray Opt. Instrum. 2010, 1-7 (2010).
[60] K.-J. Kim, Yu. Shvyd’ko, and S. Reiche, Phys. Rev. Lett. 100, 244802-1~4 (2008).
[61] A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, Phys. Rev. Lett. 103, 064801-1~4 (2009).