現代半導體產業已經使用各式各樣的檢測技術來優化半導體元件的製作過程以及監控終端產品的品質變化。在目前的檢測技術中，已經有許多已被開發的工具可以監控每道製程所需的線寬 (Critical Dimension, CD) 要求，例如: 線寬掃描式電子顯微鏡 (CD-Scanning Electron Microscopy, CD-SEM) 、線寬原子力顯微鏡 (CD-Atomic Force Microscopy, CD-AFM) 以及線寬小角度X-射線散射儀 (CD-Small Angle X-ray Scattering, CD-SAXS) 皆已被廣泛地應用在產線上以監控在每道製程的品質。然而，上述的技術具有量測時間長和容易破壞樣品的缺點。在此論文中，本研究團隊結合了現有的光學散射術和高次諧波產生(High-Harmonic Generation, HHG) 極紫外 (Extreme-Ultraviolet, EUV) 光源來發展一套新型的極紫外線散射儀 (EUV Scatterometer) ，用以量測奈米尺度線寬和高密度週期的一維光柵繞射訊號，可達到快速且非破壞性的量測。首先，我們在研究中使用了高次諧波產生來製造波長介於25奈米至34奈米的極紫外線，用以量測不同週期密度的一維光柵並重建這些樣品的三維表面形貌。實驗中所使用的光柵密度分別為1200條/釐米和7200條/釐米。此外，我們也在研究過程中發展了一套專門用於極紫外線散射儀的嚴格耦合波理論 (Rigorous Coupled-Wave Analysis, RCWA) 資料庫比對方法來克服現有高次諧波產生光源本身的限制。在經過實際電子顯微影像與重建結果的比對後，彼此對光柵結構的上底線寬、下底線寬和高度之差異度皆為5個百分點以下。最後，本篇論文將以不同的觀點來探討極紫外線散射儀的設計要點。

The semiconductor industry has applied different metrologies to optimize the manufacturing process and maintain certain quality of the final products. There are many tools used to control Critical Dimension (CD) of integrated circuits during each manufacturing process such as CD Scanning Electron Microscopy (CD-SEM), CD Atomic Force Microscopy (CD-AFM) and CD Small Angle X-ray Scattering (CD-SAXS). However, those tools are either time-consuming or sample-damaging. In this thesis, we have developed a new type of scatterometer to reconstruct surface structures of one-dimensional gratings by measuring diffraction signals. We applied a High-Harmonic Generation (HHG) Extreme-Ultraviolet (EUV) light source with wavelengths ranging from 25 nm to 34 nm in our research. The current results reveal satisfactory reconstruction of the grating structures which included densities of 1200 lines/mm and 7200 lines/mm. Additionally, we have developed a data-matching technique using Rigorous-Coupled Wave Analysis (RCWA) for our EUV scatterometers. The data matching method has given results of depths, top CDs and bottom CDs with discrepancies all smaller than 5 percent after comparing to SEM images. Finally, an analytical method has been presented in order to evaluate the performance of our scatterometers and guidelines of designing EUV scatterometers are also discussed from different viewpoints at the end.

Chapter 1 Introduction ---------------------------------------------------------- 11
Chapter 2 Literature Review ------------------------------------------------- 13
2.1 High-Harmonic Generation ---------------------------------------------- 13
2.2 Gratings --------------------------------------------------------------------- 16
2.3 Rigorous Coupled-Wave Analysis -------------------------------------- 17
2.4 Scatterometry -------------------------------------------------------------- 19
Chapter 3 Principles -------------------------------------------------------------- 23
3.1 High-Harmonic Generation ---------------------------------------------- 23
3.1.1 Three-Step Model ------------------------------------------------- 23
3.1.2 Cut-Off Energy in the Three-Step Model ------------------------ 27
3.1.3 Ionization Model -------------------------------------------------- 30
3.1.4 Saturation Intensity ----------------------------------------------- 33
3.1.5 Cut-Off Energy Considering Depletion of the Ground State --- 37
3.1.6 Phase-Matching Condition in High-Harmonic Generation ----- 38
3.1.7 Phase-Matched Cut-Off Photon Frequency --------------------- 44
3.1.8 High-Harmonic Spectrums --------------------------------------- 45
3.2 Rigorous Coupled-Wave Analysis -------------------------------------- 47
3.2.1 Definition of the Grating Problem ------------------------------- 47
3.2.2 The Grating Structure -------------------------------------------- 49
3.2.3 Fields in the Reflection Region ---------------------------------- 49
3.2.4 Fields in the Transmission Region ------------------------------- 50
3.2.5 Fields in the Grating Region ------------------------------------- 50
3.2.6 The Grating Equation --------------------------------------------- 50
3.2.7 Eigenvalue Problems --------------------------------------------- 53
3.2.8 Fast Fourier Factorization ---------------------------------------- 55
3.2.9 Boundary Conditions --------------------------------------------- 58
3.2.10 Diffraction Efficiency ------------------------------------------- 61
Chapter 4 Methodology --------------------------------------------------------- 63
4.1 Experimental Configurations -------------------------------------------- 63
4.1.1 Long-Working Distance Mode ----------------------------------- 65
4.1.2 Short-Working Distance Mode ----------------------------------- 65
4.2 Wavelength Fitting -------------------------------------------------------- 67
4.3 Building a Database ------------------------------------------------------- 68
4.4 Ratios of Diffraction Efficiencies --------------------------------------- 69
4.5 Intensity Correction ------------------------------------------------------- 69
4.6 A Criterion of Evaluation ------------------------------------------------ 72
4.7 Reconstruction of Grating Structures ----------------------------------- 73
Chapter 5 Results and Discussion ------------------------------------------- 75
5.1 Experimental Results ----------------------------------------------------- 75
5.1.1 Diffraction Signals in the Long-Working Distance Mode ------- 75
5.1.2 Diffraction Signals in the Short-Working Distance Mode ------- 78
5.1.3 Reconstruction in the Long-Working Distance Mode ----------- 81
5.1.4 Reconstruction in the Short-working Distance Mode ------------ 83
5.2 Discussion ------------------------------------------------------------------ 84
5.2.1 Reconstruction from the Two Configurations ------------------- 84
5.2.2 A Perspective of Imaging System -------------------------------- 85
5.2.3 Reconstruction by a Self-Made Program ------------------------ 90
5.2.4 A Perspective of Data Processing -------------------------------- 91
5.2.5 Tolerance Towards Deviation ------------------------------------ 93
5.2.6 Diffraction Efficiency of a Reflection Grating in EUV regions 94
5.2.7 Convergence of Diffraction Efficiency in TE Polarization ----- 96
5.2.8 Guidelines of Designing an EUV Scatterometer ---------------- 98
Chapter 6 Conclusions ---------------------------------------------------------- 101
Appendix ----------------------------------------------------------------------------- 103
A. Fundamentals -------------------------------------------------------------- 103
A.1 Maxwell’s Equations in Free Space ------------------------------- 103
A.2 Polarization --------------------------------------------------------- 104
A.3 Magnetization ------------------------------------------------------ 105
A.4 Maxwell’s Equations in Matter ------------------------------------ 106
A.5 Poynting’s Theorem ------------------------------------------------ 106
A.6 Electromagnetic Wave Equations --------------------------------- 107
A.7 Intensity ------------------------------------------------------------ 109
A.8 Refractive Index ---------------------------------------------------- 110
A.9 Absorption ---------------------------------------------------------- 110
A.10 Energy Flux Density in Dielectrics ------------------------------ 112
A.11 Direction of Energy Flux Density in Centrosymmetric Media - 113
A.12 Odd Harmonics in Centrosymmetric Media --------------------- 114
A.13 Keldysh Parameter ---------------------------------------------------- 117
Bibliography ------------------------------------------------------------------------- 121

1. Ian M. Ross. The Invention of the Transistor. Vol. 86, Issue 1, Proceedings of IEEE, 1986.
2. David B Haviland. (2002). The Transistor in a Century of Electronics. Nobelprize.org. Retrieved November 11, 2017, from
https://www.nobelprize.org/educational /physics/transistor/history/
3. Nobelprize.org. (2003). The History of the Integrated Circuit. Nobelprize.org. Retrieved November 11, 2017, from
https://www.nobelprize.org/educational/physics/integrated_circuit/history/
4. Christopher Palmer and Erwin Loewen. Diffraction Grating Handbook. Richardson Grating Laboratory, 1996.
5. Dr. Martin Thum. Joseph Von Frauhofer. Fraunhofer-Gesellschaft Corporate
Communications, 2014.

6. Nicholas C. Thomas. The Early History of Spectroscopy. Vol. 68, No. 8, Journal of Chemical Education, 1991.
7. Alain C. Diebold. Handbook of Silicon Semiconductor Metrology. International SEMATECH Austin, Texas, 2005.
8. Erwin Loewen and Christopher Palmer. Diffraction Grating Handbook, 7th edition. Newport Corporation, 2014.
9. Roland G. Diggers. Encyclopedia of optical engineering. Marcel Dekker Inc., 2003.
10. R. W. Wood. On the remarkable case of uneven distribution of light in a diffraction grating spectrum. Philos. Mag. 4, 396-402, 1902
11. Lord Rayleigh. On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure. Series 5, Vol. 24, Issue 147, Philosophical Magazine, 1887.
12. Geroge William Hill. On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Vol. 8, Issue 1, pp 1–36, Acta Mathematica, 1886.
13. Leon Brillouin. Wave propagation in periodic structures: electric filters and crystal lattices. New York: Dover, 1953.
14. T Tamir and H. C. Wang. Wave Propagation in Sinusoidally Stratified Dielectric Media. IEEE transactions on microwave theory and techniques, 1964.
15. M. G. Moharam and T. K. Gaylord. Coupled wave analysis of reflection gratings. Vol. 20, No. 2, Applied Optics, 1981.
16. M. G. Moharam and T. K. Gaylord. Coupled wave analysis of reflection gratings. Vol. 71, No. 7, J. Opt. Soc. Am., 1981.
17. Herwig Kogelnik. Coupled wave theory for thick hologram gratings. Bell Sys. Tech. J. 48, 2909, 1969. 

18. P. Phariseau. On the diffraction of light by progressive supersonic waves. Proc. Indian Acad. Sci. Sect. A.44,165, 1965. 

19. Charles Elachi. Magnetic Wave Propagation in a Periodic Medium. Lol.mag-11, No. 1, IEEE TRANSACTIONS ON MAGNETICS, 1975.
20. M. G. Moharam and T. K. Gaylord. Diffraction analysis of dielectric surface-relief gratings. Vol. 72, No. 10, J. Opt. Soc. Am., 1982.
21. S. T. PENG. Theory of Periodic Dielectric Waveguides. IEEE Trans. Microwave Theory Tech. MTT-23, 123-133,1975. 

22. M. Neviere, R. Petit, M. Cadilhac. About the theory of optical grating coupler-waveguide systems. Vol.8(2), Optics Communications, 1973
23. K.C. Chang, V. Shah, and T. Tamir. Scattering and guiding of waves by dielectric gratings with arbitrary profiles. Vol. 70, issue 7, J. Opt. Soc. Am., 1980.
24. K. C. Chang and T. Tamir. Simplified approach to surface-wave scattering by blazed dielectric gratings. Vol. 19, No. 2, Applied Optics, 1980.
25. D. Y. K. Ko and J. R. Sambles. Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals. Vol. 5, No. 11, J. Opt. Soc. Am., 1988.
26. D. Maystre. Electromagnetic study of photonic band gaps. Pur. Appl. Opt. 3. 1994.
27. N. P. K. Cotter, T. W. Preist, and J. R. Sambles. Scattering-matrix approach to multilayer diffraction. Vol. 12, No. 5, J. Opt. Soc. Am. A, 1995.
28. D. M. Pai and K. A. Awada.Analysis of dielectric gratings of arbitrary profiles and thicknesses. Vol. 8, No. 5, J. Opt. Soc. Am, 1991.
29. M. Nevibre and E. Popov. Analysis of dielectric gratings of arbitrary profiles and thicknesses: comment. Vol. 8, No. 5, J. Opt. Soc. Am, 1991.
30. S. Sohail H. Naqvi, Susan Gaspar, Kirt Hickman, Ken Bishop, and John R. McNeil. Linewidth measurement of gratings on photomasks: a simple technique. Vol. 31, No. 10, Applied Optics, 1992.
31. S. S. H. Naqvi, R. H. Krukar,* and J. R. McNeil. Etch depth estimation of large-period silicon gratings with multivariate calibration of
rigorously simulated diffraction profiles. Vol. 11, No. 9. J. Opt. Soc. Am. A, 1994.
32. Ziad R. Hatab, Steven L. Prins, S. Sohail H. Naqvi, John R. McNeil. DRAM trenchdepthcharacterizationusing dome scatterometry. Vol. 86, Applied Surface Science, 1994.
33. Christopher J. Raymond, Michael R. Murnane, S. Sohail, H. Naqvi, and John R. McNeil. Metrology of subwavelength photoresist gratings using optical scatterometry. 13, 1484, Journal of Vacuum Science & Technology B, 1995.
34. Xinhui Niu, Nickhil Jakatdar, Junwei Bao, and Costas J. Spanos. Specular Spectroscopic Scatterometry. VOL. 14, NO. 2, IEEE Transactions On Semiconductor Manufacturing, 2001.
35. Semiconductor Industry Association. International Technology Roadmap For Semiconductors 2007 Edition Executive Summary. Semiconductor Industry Association, 2007.
36. Jan Pomplun, Sven Burger, Frank Schmidt, Frank Scholze, Christian Laubis, Uwe Dersch. Metrology of EUV masks by EUV-scatterometry and finite element analysis. Vol. 7028, Proc. SPIE, 2008.
37. H. Gross, A. Rathsfeld, F. Scholze and M. Bar. Profile reconstruction in extreme ultraviolet (EUV) scatterometry-modeling and uncertainty estimates. Vol. 20, Meas. Sci. Technol., 2009.
38. Bernd Bodermann, Matthias Wurma, Alexander Dienera, Frank Scholze, Hermann GroB. EUV and DUV scatterometry for CD and edge profile metrology on EUV masks. VDE VERLAG GMBH, 2009.
39. F Scholze, A Kato, C Laubis. Improved Diffraction Computation with a Hybrid C RCWA Method. Vol. 311, Journal of Physics, 2011.
40. Masato Nakasuji, Akifumi Tokimasa, Tetsuo Harada, Yutaka Nagata, Takeo Watanabe, Katsumi Midorikawa, and Hiroo Kinoshita. Development of Coherent Extreme-Ultraviolet Scatterometry Microscope with High-Order Harmonic Generation Source for ExtremeUltraviolet Mask Inspection and Metrology. Vol. 50, Jpn. J. Appl. Phys., 2012.
41. Takahiro Fujino, Yusuke Tanaka, Tetsuo Harada, Yutaka Nagata, Takeo Watanabe, and Hiroo Kinoshita. Extreme ultraviolet mask observations using a coherent extreme ultraviolet scatterometry microscope with a high harmonic generation source. Vol. 54, Jpn. J. Appl. Phys., 2015.
42. Yi-Sha ku, Chia-Liang Yeh, Yi-Chang Chen, Chun-Wei lo, Wei-Ting Wang, and Ming-Chang Chen. EUV scatterometer with a high-harmonic- generation EUV source. Vol. 24, No. 24 Optical Express, 2016.
43. Simon Hooker, Colin Webb. Laser Physics. OXFORD University Press. 2010.
44. J. P. Gordon, H. J. Zeiger, and C. H. Townes. Molecular Microwave Oscillator and New Hyper6ne Structure in the Microwave Spectrum of NH. Vol. 95, Iss. 1, Physical Review, 1954.
45. J. P. Gordon, H. J. Zeiger, and C. H. Townes. The Maser—New Type of Microwave Amplifier, Frequency Standard, and Spectrometer. Vol. 9. Iss. 4, 1955.
46. T. H. Maiman. Stimulated optical radiation in Ruby. Vol. 187, No. 4736, Nature., 1960.
47. P. A. Franken, A. E. Hill, C. %. Peters, and G. Weinreich. Generation of Optical Harmonics. Vol. 7, No. 4, Physical Review Letter, 1961.
48. F. J. Mcclung and R. W. Hellwarth. Giant Optical Pulsations from Ruby. Vol. 33, No. 3, Journal of Applied Physics, 1962.
49. H. W. Mocker and R. J. Collins. Mode Competition And Self-Locking Effects In A Q-Switched Ruby Laser. Vol. 7, No. 10, Physical Review Letter, 1985.
50. Donna Strickland and Gerard Mourou. Compression of Amplified Chirped Optical Pulses. Vol. 56, No. 3, Optical Communication, 1985.
51. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K.Boyer, and C. K.Rhodes. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gase. Vol. 4, No. 4, J. Opt. Soc. Am B, 1987.
52. A. McPherson, T. S. Luk, M. H. R. Hutchinson, H. Jara, U. Johann, I. A. McIntyre, A. P. Schwarzenbach, K. Boyer, and C. K. Rhodes. VUV fluorescence and harmonic generation with intense picosecond 248 nm KrF* radiation. Proc. SPIE 0710, Excimer Lasers and Optics, 1987.
53. K. C. Kulander and B. W. Shore. Calculations of Multiple-Harmonic Conversion of 1064-nm Radiation in Xe. Vol. 62, No. 5, Physical Review Letters, 1993.
54. Gunadya Bandarage, Alfred Maquet, and J. Cooper. Harmonic generation by a classical hydrogen atom in the presence of an intense radiation field. Vol. 41, No. 3, Physical Review A, 1990.
55. Bala Sundaram and Peter W. Milonni. High-order harmonic generation: SimpliSed model and relevance of single-atom theories to experiment. Vol. 41, No. 11, Physical Review A, 1990.
56. W. Becker, S. Long, and J. K. McIver. Higher-harmonic production in a model atom with short-range potential. Vol. 41, No. 7, Physical Review A, 1990.
57. R. M. Potvliege and Robin Shakeshaft. Mnltiphoton processes in an intense laser field: Harmonic generation and total ionization rates for atomic hydrogen. Vol. 40, No. 6, Physical Review A, 1989.
58. J. H. Eberly and Q. Su, J. Javanainen. Nonlinear Light Scattering Accompanying Multiphoton Ionization. Vol. 62, No. 8, Physical Review Letters, 1989.
59. P. B.Corkum.. Vol. 71, No. 13, Physical Review Letters, 1993.
60. K. J. Schafer, Baorui Yang, L. I. DiMauro, and K. C. Kulanderc. Above Threshold Ionization Beyond the High Harmonic Cutoff. Vol. 70, No. 11, Physical Review Letters, 1993.
61. X. F. Li, A. L Huillier, M. Ferray, L. A. Lompre, and G. Mainfray. Multiple-harmonic generation in rare gases at high laser intensity. Vol. 39, No. 11, Physical Review A, 1989.
62. S. Kazamias, F. Weihe, D. Douillet, C. Valentin, T. Planchon, S. Sebban, G. Grillon, F. Aug ́e, D. Hulin, and Ph. Balcou. High order harmonic generation optimization with an apertured laser beam. Vol. 21, Eur. Phys. J. D., 2002.
63. Steffen Hädrich, Jan Rothhardt, Manuel Krebs, Stefan Demmler, Arno Klenke, Andreas Tünnermann and Jens Limpert. Single-pass high harmonic generation at high repetition rate and photon flux. Vol. 49, J. Phys. B: At. Mol. Opt. Phys., 2016
64. Ariel Paul, Emily A. Gibson, Xiaoshi Zhang, Amy Lytle, Tenio Popmintchev, Xibin Zhou, Margaret M. Murnane. Phase-Matching Techniques for Coherent Soft X-Ray Generation. VOL. 42, NO. 1, IEEE Journal of Quantum Electronics, 2006.
65. Arman Cingo ̈z, Dylan C. Yost, Thomas K. Allison, Axel Ruehl, Martin E. Fermann, Ingmar Hartl and Jun Ye. Direct frequency comb spectroscopy in the extreme ultraviolet. Vol. 482, No. 7383, Nature, 2012.
66. E. Lorek, E. W. Larsen, C. M. Heyl, S. Carlström, D. Palecˇek, D. Zigmantas, and J. Mauritsson. High-order harmonic generation using a high-repetition-rate turnkey laser. Vol. 85, No. 123106, Review of Scientific Instruments, 2014.
67. J. C. Maxwell. Xxv. on physical lines of force: Part i.–the theory of molecular vortices applied to magnetic phenomena. 21. 139., In: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1861. 

68. David J. Griffiths. Introduction To Electrodynamics 3rd edition. Pearson Education, Inc, 2008.
69. B. E. A. Saleh and M. C. Teich. Fundamentals Of Photonics 2nd edition. John Wiley& Sons, Inc. Hoboken, New Jersey, 2007.
70. David Attwood. Soft X-Rays And Extreme Ultraviolet Radiation. Cambridge University Press, 1999.
71. Peter E. Powers. Fundamentals of Nonlinear Optics. CRC Press, 2011.
72. Zeng-Hu Cheng. Fundamentals of Attosecond Optics. CRC Press, 2011.
73. L. V. Keldysh. Ionization in The Field of A Strong Electromagnetic Wave. Vol. 20, No. 5, Soviet Physics JEPT, 1965.
74. A. M. Perelomov, V. S. Popov, And M. V. Terent'ev. Ionization of Atoms In An Alternating Electric Field. Vol. 23, No. 5, Soviet Physics, JEPT, 1966
75. Mark Fox. Quantum Optics: An Introduction. Oxford University Press, 2006.
76. M. V. Ammosov, N. 8. Delone, and V. P. Krainov. Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field. Sov. Phys. JETP 64 (6), 1986.
77. Britton Chang, Paul R. Bolton, and David N. Fittinghoff. Closed-form solutions for the production of ions in the collisionless ionization of gases by intense lasers. Vol. 47, No. 5, Physical Review A, 1993.
78. Zenghu Chang, Andy Rundquist, Haiwen Wang, Margaret M. Murnane, and Henry C. Kapteyn. Generation of Coherent Soft X Rays at 2.7 nm Using High Harmonics. Vol. 79, No. 16, Physical Review Letters, 1997.
79. Ioachim Pupeza, Tino Eidam, Jens Rauschenberger, Birgitta Bernhardt,1 Akira Ozawa, Ernst Fill, Alexander Apolonski, Thomas Udem, Jens Limpert, Zeyad A. Alahmed, Abdallah M. Azzeer, Andreas Tünnermann, Theodor W. Hänsch, and Ferenc Krausz. Power scaling of a high-repetition-rate enhancement cavity. Vol. 35, No. 12, Optics Letters, 2010.
80. Akira Ozawa, Zhigang Zhao, Makoto Kuwata-Gonokami, and Yohei Kobayashi. High average power coherent vuv generation at 10 MHz repetition frequency by intracavity high harmonic generation. Vol. 23, No. 12, Optics Letters, 2010.
81. I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. RusBbuldt, J. Rauschenberger, J. Limpert, Th. Udem, A. Tunnermann, T. W. Hansch, A. Apolonski, F. Krausz and E. Fill. Compact high-repetition-rate source of coherent 100 eV radiation. Vol. 7, Nature Photonics, 2013.
82. Anne L'Huillier and Philippe Balcou. Calculations of high-order harmonic-generation processes in xenon at 1064 nm. Vol. 46, No. 5, Physical Review A, 1992.
83. E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini. Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment. Vol. 82, No. 8, Physical Review Letter, 1999.
84. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L'Huillier, and P. B. Corkum. Theory of high-harmonic generation by low-frequency laser fields. Vol. 49, No. 3, Physical Review A, 1994.
85. A. L'Huillier, X. F.Li, and L.A. Lompr. Propagation effects in high-order harmonic generation in rare gases. Vol. 7, No. 4, J. Opt. Soc. Am. B, 1990.
86. Mihai Garvrila. Atoms in intense laser fields. Academic Press Inc., 1992.
87. Ariel Paul, Emily A. Gibson, Xiaoshi Zhang, Amy Lytle, Tenio Popmintchev, Xibin Zhou, Margaret M. Murnane, Ivan P. Christov, and Henry C. Kapteyn. Phase matching techniques for coherent soft X-ray generation. Vol. 42, No. 1, Ieee Journal Of Quantum Electronics, 2006.
88. Frank L. Pedrotti, Leon M. Pedrotti and Leno S. Pedrotti. Introduction to Optics third edition. Pearson Education Inc., 2007.
89. George B. Arfken and Hans J. Weber. Mathematical Methods for Physicists 6th edition. Elsevier Academic Press, 2005.
90. John J. Hench And Zdenek Strakos. The RCWA Method - A Case Study with Open Questions And Perspectives Of Algebraic Computations. Vol. 31, pp. 331-357, Electronic Transactions on Numerical Analysis, 2008.
91. Lifeng Li and Charles W Haggans. Convergence of the coupled-wave method for metallic lamellar diffraction gratings. Vol. 10, No. 6, J. Opt. Soc. Am. A, 1993.
92. Philippe Lalanne and G. Michael Morris. Highly improved convergence of the
coupled-wave method for TM polarization. Vol. 13, No. 4, J. Opt. Soc. Am. A, 1996.
93. G. Granet and B. Guizal. Efficient implementation of the coupled-wave method
for metallic lamellar gratings in TM polarization. Vol. 13, No. 5, J. Opt. Soc. Am. A, 1996.
94. Lifeng Li. Use of Fourier series in the analysis of discontinuous periodic structures. Vol. 13, No. 9, J. Opt. Soc. Am. A, 1996.
95. Spectra-Physics. Femtopower: Ultrashort Pulse Multipass Amplifier With Optional Cep Stabilization. A Newport Company, 2015.
96. Light Conversion. Pharos: High-Power Femtosecond lasers. Light Conversion, 2016.
97. KlausGiewekemeyer. A study on new approaches in coherentx-ray microscopy of biological specimens. Published by Universitätsverlag Göttingen, 2011.
98. John M. Cowley. Diffraction Physics Third Edition. Elsevier Science B.V., 1995.
99. Tenio Popmintchev, Ming-Chang Chen, Alon Bahabad, Michael Gerrity, Pavel Sidorenko, Oren Cohen, Ivan P. Christov, Margaret M. Murnane, and Henry C. Kapteyn. Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum. Vol. 106, No. 26, PNAS, 2009.
100. M. C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn. Bright, Coherent, Ultrafast Soft X-Ray Harmonics Spanning the Water Window from a Tabletop Light Source. Vol. 105, 173901, Physical Review Letter, 2010.