https://scholars.lib.ntu.edu.tw/handle/123456789/119593
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor | 邱奕鵬 | en |
dc.contributor | 臺灣大學:光電工程學研究所 | zh_TW |
dc.contributor.author | 施乃元 | zh |
dc.contributor.author | Shih, Nai-Yuan | en |
dc.creator | 施乃元 | zh |
dc.creator | Shih, Nai-Yuan | en |
dc.date | 2007 | en |
dc.date.accessioned | 2007-11-25T23:22:38Z | - |
dc.date.accessioned | 2018-07-05T02:34:39Z | - |
dc.date.available | 2007-11-25T23:22:38Z | - |
dc.date.available | 2018-07-05T02:34:39Z | - |
dc.date.issued | 2007 | - |
dc.identifier | en-US | en |
dc.identifier.uri | http://ntur.lib.ntu.edu.tw//handle/246246/50658 | - |
dc.description.abstract | 傳統的頻域演算法或多或少存在有收斂性和效率方面的問題; 為了克服這些困擾, 本篇論文提出一種稱為多區域假譜頻域法的替代方案。 其優越的 "譜準度" 特性大大降低了對於離散化密度的要求, 而多區域法能夠良好地接合不同的材料。透過一些實際範例的實作, 這種方法用於光電結構模擬與設計的實用性及潛力得到了驗證。 | zh_TW |
dc.description.abstract | Conventional frequency-domain algorithms suffer more or less from convergence and efficiency problems; to overcome these headaches, an alternative called the multidomain pseudospectral frequency-domain method is presented in this thesis. The superior "spectral accuracy" greatly reduces the requirement for discretization density for smooth functions, and the multidomain approach patches distinct materials together properly. Via implementation of some practical examples, the utility and potential of the method for modeling and design of photonic structures are verified. | en |
dc.description.tableofcontents | 1 Introduction 7 2 Theory 13 2.1 The Fourier System [5] . . . . . . . . . . . . . . . . . . . . . . ..14 2.1.1 The Continuous Fourier Expansion . . . . . . . . . . . . . . . . . . . . 14 2.1.2 The Discrete Fourier Expansion . . . . . . . . . . . . . . . . . . . . 21 2.1.3 Differentiation . . . . . . . . . . . . . . 25 2.2 Orthogonal Polynomials in (−1, 1) [5] . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 Sturm-Liouville Problems . . . . . . . . . . . . . . . . . . . ..29 2.2.2 Orthogonal Systems of Polynomials . . . . . 30 2.2.3 Gauss-Type Quadratures and Discrete Polynomial Transforms 32 2.3 Chebyshev Polynomials [5] . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.1 Basic Formulas . . . . . . . . . . . . . . . . . . . . .36 2.3.2 Differentiation . . . . . . . . . . . . . . 39 2.4 The Multidomain Pseudospectral Frequency-domain (PSFD) Method 42 2.4.1 Source-free Wave Equations . . . . . . . . . . . . . . . . . . . . 42 2.4.2 The Multidomain Approach . . . . . . . . . . . . . . . . . . . . 44 3 Numerical Examples and Results 49 3.1 Laser Facet . . . . . . . . . . . . .. . . . . . . . . .50 3.2 Convergence for Grating Modeling . . . . . . . . . . . . . . . . . . . . .56 3.3 Metallic Gratings as Color Filters . . . . . . . . . . . . . . . . . . . ... 61 3.4 Rectangular Channel Waveguide End . . . . . . . . . . . . . . . . . .. . .. . . 94 4 Conclusion 99 A Hilbert and Banach Spaces 100 B Functions of Bounded Variation and the Riemann(-Stieltjes) Integral 104 C The Lebesgue Integral and Lp-spaces 107 References 111 | en |
dc.language | en-US | en |
dc.language.iso | en_US | - |
dc.subject | 假譜 | en |
dc.subject | 頻域 | en |
dc.subject | 多區域 | en |
dc.subject | 光柵 | en |
dc.subject | 色光濾波器 | en |
dc.subject | pseudospectral | en |
dc.subject | frequency-domain | en |
dc.subject | multidomain | en |
dc.subject | grating | en |
dc.subject | color filter | en |
dc.title | 多區域假譜頻域法及其在光電結構模擬上之應用 | zh |
dc.title | The Multidomain Pseudospectral Frequency-domain Method and Its Application in Modeling of Photonic Structures | en |
dc.type | thesis | en |
dc.relation.reference | [1] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite- Difference Time-Domain Method, 3rd ed., Norwood, MA: Artech House, 2005. [2] J. Jin, The Finite Element Method in Electromagnetics, 2nd ed., New York: Wiley, 2002. [3] J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, New York: IEEE Press, 1998. [4] R. F. Harrington, Field Computation by Moment Methods, New York: Macmillan, 1968. [5] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, New York: Springer-Verlag, 1988. [6] L. N. Trefethen, Spectral Methods in MATLAB, Philadelphia: SIAM, 2000. [7] B. A. Finlayson and L. E. Scriven, “The method of weighted residuals—a review,” Appl. Mech. Rev., vol. 19, pp. 735–748, 1966. [8] J. C. Slater, “Electronic energy bands in metal,” Phys. Rev., vol. 45, pp. 794– 801, 1934. [9] L. V. Kantorovic, “On a new method of approximate solution of partial differential equations,” Dokl. Akad. Nauk SSSR, vol. 4, pp. 532–536, 1934. [10] R. A. Frazer, W. P. Jones, and S. W. Skan, “Approximation to Functions and to the Solution of Differentia1 Equations,” R&M 1799, Aeronautical Research Council, London, 1937. [11] C. Lanczos, “Trigonometric interpolation of empirical and analytical functions,” J. Math. Phys., vol. 17, pp. 123–199, 1938. [12] C. W. Clenshaw, “The numerical solution of linear differential equations in Chebyshev series,” Proc. Cambridge Philos. Soc., vol. 53, pp. 134–149, 1957. [13] C. W. Clenshaw and H. J. Norton, “The solution of nonlinear ordinary differential equations in Chebyshev series,” Comput. J., vol. 6, pp. 88–92, 1963. [14] K.Wright, “Chebyshev collocation methods for ordinary differential equations,” Comput. J., vol. 6, pp. 358–365, 1964. [15] J. V. Villadsen and W. E. Stewart, “Solution of boundary value problems by orthogonal collocation,” Chem. Eng. Sci., vol. 22, pp. 1483–1501, 1967. [16] H.-O. Kreiss and J. Oliger, “Comparison of accurate methods for the integration of hyperbolic equations,” Tellus, vol. 24, pp. 199–215, 1972. [17] S. A. Orszag, “Comparison of pseudospectral and spectral approximations,” Stud. Appl. Math., vol. 51, pp. 253–259, 1972. [18] G.-X. Fan, Q. H. Liu, and J. S. Hesthaven, “Multidomain pseudospectral timedomain method for simulation of scattering from buried objects,” IEEE Trans. Geosci. Remote Sensing, vol. 40, pp. 1366–1373, 2002. [19] Q. H. Liu, “A pseudospectral frequency-domain (PSFD) method for computational electromagnetics,” IEEE Antennas Wireless Propag. Lett., vol. 1, pp. 131–134, 2002. [20] G. Zhao and Q. H. Liu, “The 3-D multidomain pseudospectral time-domain algorithm for inhomogeneous conductive media,” IEEE Trans. Antennas Propag., vol. 52, pp. 742–749, 2004. [21] Y. Shi, L. Li, and C. H. Liang, “Multidomain pseudospectral time-domain algorithm based on super-time-stepping method,” IEE Proc.- Microw. Antennas Propag., vol. 153, pp. 55–60, 2006. [22] Y. Shi, L. Li, and C. H. Liang, “Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method, ” IEEE Trans. Antennas Propag., vol. 54, pp. 1207–1214, 2006. [23] L. Carleson, “On convergence and growth of partial sums of Fourier series,” Acta Math., vol. 116, pp. 135–157, 1966. [24] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., vol. 19, pp. 297–301, 1965. [25] C. Temperton, “Self-sorting mixed-radix fast Fourier transforms,” J. Comput. Phys., vol. 52, pp. 1–23, 1983. [26] R. Peyret, “Introduction to Spectral Methods,” von Karman Institute Lecture Series, 1986-04, Rhode–Saint Genese, Belgium, 1986. [27] A. Brandt, S. R. Fulton, and G. D. Taylor, “Improved spectral multigrid methods for periodic elliptic problems,” J. Comput. Phys., vol. 58, 96–112, 1985. [28] D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, Philadelphia: SIAM-CBMS, 1977. [29] L. Fox and I. B. Parker, Chebyshev Polynomials in Numerical Analysis, London: Oxford Univ. Press, 1968. [30] T. J. Rivlin, The Chebyshev Polynomials, New York: John Wiley & Sons, 1974. [31] D. Gottlieb, M. Y. Hussaini, and S. A. Orszag, “Theory and Applications of Spectral Methods,” in Spectral Methods for Partial Differential Equations, ed. by R. G. Voigt, D. Gottlieb, M. Y. Hussaini, Philadelphia: SIAM-CBMS, pp. 1–54, 1984. [32] A. Solomonoff and E. Turkel, “Global Collocation Methods for Approximation and the Solution of Partial Differential Equations,” ICASE Rep. No. 86-60, NASA Langley Research Center, Hampton, VA, 1986. [33] T. Ikegami, “Reflectivity of mode at facet and oscillation mode in doubleheterostructure injection laser,” IEEE J. Quantum Electron., vol. 8, pp. 470- 476, 1972. [34] Q. Liu and W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 422-429, 1991. [35] P. C. Kendall, D. A. Roberts, P. N. Robson, M. J. Adams, and M. J. Robertson, “Semiconductor laser facet reflectivities using free-space radiation modes,” IEE Proc.-J, vol. 140, pp. 49-55, 1993. [36] Y.-P. Chiou and H.-C. Chang, “Analysis of optical waveguide discontinuities using the Pad´e approximants,” IEEE Photon. Technol. Lett., vol. 9, pp. 964- 966, 1997. [37] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planargrating diffraction,” J. Opt. Soc. Am., vol. 71, pp. 811–818, 1981. [38] M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am., vol. 73, pp. 451–455, 1983. [39] M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A, vol. 12, pp. 1068–1086, 1995. [40] P. Lalanne and G. M. Morris, “Highly improved convergence of the coupledwave method for TM polarization,” J. Opt. Soc. Am. A, vol. 13, pp. 779–784, 1996. [41] S. Peng and G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface relief gratings,” J. Opt. Soc. Am. A, vol. 12, pp. 1087–1096, 1995. [42] J. Adams, K. Parulski, and K. Spaulding, “Color processing in digital cameras,” IEEE Micro, vol. 18, pp. 20–30, 1998. [43] P. B. Catrysse and B. A. Wandell, “Integrated color pixels in 0.18- μm complementary metal oxide semiconductor technology,” J. Opt. Soc. Am. A, vol. 20, pp. 2293–2306, 2003. [44] C.-H. Lee, “Finite-Difference Time-Domain Modeling of Three-Dimensional Metallic Photonic Crystals and Surface Plasmon Phenomena,” master’s thesis, June 2005. [45] W. K. Pratt, Digital Image Processing, 3rd ed., New York: Wiley, 2001. [46] M. A. Ordal, L. L Long, R. J. Bell, R. R. Bell, R. W.Alexander, Jr., and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt., vol. 22, pp. 1099–1119, 1983. [47] H. L. Royden, Real Analysis, New York: McMillan, 1968. [48] W. Rudin, Real and Complex Analysis, New York: McGraw-Hill, 1966. | en |
item.openairetype | thesis | - |
item.fulltext | no fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
item.grantfulltext | none | - |
item.languageiso639-1 | en_US | - |
item.cerifentitytype | Publications | - |
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