請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/72051完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張宏鈞 | |
| dc.contributor.author | Pi-Kuei Shih | en |
| dc.contributor.author | 石璧魁 | zh_TW |
| dc.date.accessioned | 2021-06-17T06:20:54Z | - |
| dc.date.available | 2023-08-20 | |
| dc.date.copyright | 2018-08-20 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-08-19 | |
| dc.identifier.citation | Ardakani, A. G., M. Naserpour, and C. J. Zapata-Rodr´ıguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl., vol. 20, pp. 1–6, 2016.
Arnoldi,W. E., “The principle of minimized iterations in the solution of the matrix eigenvalue problem,” Quart. Appl. Math., vol. 9, pp. 17–29, 1951. Artigas, D., and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett., vol. 94, 013901, 2005. Averkiev, N. S., and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc., vol. 68, pp. 653–655, 1990. Baken, N. H., M. B. J. Diemeer, J. M. V. Splunter, and H. Blok, “Computational modeling of diffused channel waveguides using a domain integral equation,” J. Lightwave Technol., vol. 8, pp. 576–586, 1990. Berenger, J. P., “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, pp. 185–200, 1994. Bierwirth, K., N. Schulz, and F. Arndt, “Finite-di erence analysis of rectangular dielectric waveguide structures,” IEEE. Trans. Microwave Theory Tech., vol. 34, pp. 1104–1113, 1986. Bj¨orck, Å, “Numerics of Gram-Schmidt orthogonalization,” Linear Algebra Appl., vol. 197, pp. 297–316, 1994 Bloch, F., “Quantum mechanics of electronic crystal,” Zeits. f. Physik, vol. 52, 555, 1928 Bodewig, E., Matrix Calculus. Amsterdam: North Holland Pub. Co., 1956. Bowyer, A., “Computing Dirichlet tessellations,” Comput. J., vol. 24, pp. 162–166, 1981. Chen, B., D. G. Fang, and B. H. Zhou, “Modified Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microw. Guided Wave Lett., vol. 5, pp. 399–401, 1995. Chern, R. L., “Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials,” Opt. Express, vol. 21, pp. 16514–16527, 2013. Chew, W. C., and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Tech. Lett., vol. 12, pp. 599–604, 1994. Cendes, Z. J., and P. Silvster, “Numerical solution of dielectric loaded waveguides: finite element analysis,” IEEE Trans. Microwave Theory Tech., vol. MTT-18, pp. 1124–1131, 1970. Chiang, Y. C., Y. P. Chiou, and H. C. Chang, “Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles,” J. Lightwave Technol., vol. 20, pp. 1609–1618, 2002. Chiang, P. J., C. L. Wu, C. H. Teng, C. S. Yang, and H. C. Chang, “Full-vectorial optical waveguide mode solvers using multidomain pseudospectral frequency-domain (PSFD) formulations,” IEEE J. Quantum Electron., vol. 44, pp. 56–66, 2008. Cojocaru, E., “Comparative analysis of Dyakonov hybrid surface waves at dielectric-elliptic and dielectric-hyperbolic media interfaces,” J. Opt. Soc. Am. B, vol. 31, pp. 2558–2564, 2014. Cojocaru, E., “Dyakonov hybrid surface waves at the isotropic-biaxial media interface,” J. Opt. Soc. Am. A, vol. 32, pp. 782–789, 2015. DeVore, J. R., “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am., vol. 41, pp. 416–419, 1951. Deshmukh, I., and Q. H. Liu, “Pseudospectral beam-propagation method for optical waveguides,” IEEE Photon. Technol. Lett., vol. 15, pp. 60–62, 2003. Duff, I. S., A. M. Erisman, and J. K. Reid, Direct methods for sparse matrices. Oxford, UK: Clarendon Press, 1986. D’yakonov, M. I., “New type of electromagnetic wave propagating at an interface,” Sov. Phys. JETP, vol. 67, pp. 714–716, 1988. Fedyanin, D. Y., A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt., vol. 12, 015002, 2010. Gao, J., A. Lakhtakia, J. A. Polo, Jr., and M. Lei, “Dyakonov-Tamm wave guided by a twist defect in a structurally chiral material” J. Opt. Soc. Amer. A, vol. 26, pp. 1615–1621, 2009. Gao, J., A. Lakhtakia, and M. Lei, “Dyakonov-Tamm waves guided by the interface between two structurally chiral materials that differ only in handedness,” Phys. Rev. A, vol. 81, pp. 013801-1–013801-8, 2010. Grama, A., A. Gupta, G. Karypis, and V. Kumar, Introduction to Parallel Computing. Reading, MA: Addison-Wesley, 2003. Gropp, W., E. Lusk, and A. Skjellum, Using MPI: Portable Parallel Programming with the Message Passing Interface. Cambridge, MA: MIT Press, 1994. Hadley, G. R., and R. E. Smith, “Full-vector waveguide modeling using an iterative finite difference method with transparent boundary conditions,” J. Lightwave Technol., vol. 13, pp. 465–469, 1995. Hofer, M., N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, U. Langer, and R. Lerch, “Finite-element simulation of wave propagation in periodic piezoelectric saw structures,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 53, pp. 1192–1201, 2006. Irons, B. M., “A frontal method solution program for finite element analysis,” Int. J. Numer. Meth. Eng., vol. 2, pp. 5–32, 1970. Jin, J., The Finite Element Method in Electromagnetics., 2nd edition. New York, USA: Wiley-IEEE Press, 2002. Kang, X. B., W. Tan, and Z. G. Wang, “Validity of e ffective medium theory for metal-dielectric lamellar gratings,” Opt. Commun., vol. 284, pp. 4237–4242, 2011. Koshiba, M., and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol., vol. 18, pp. 737–743, 2000. Lee, J. F., D. K. Sun, and Z. J. Cendes, “Full-wave analysis of dielectric waveguides using tangential vector finite elements,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1262–1271, 1991. Lehoucq, R. B., D. C. Sorensen, and C. Yang, ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia, PA, 1997. Liu, J. W. H., “The multifrontal method for sparse matrix solution: Theory and practice,” SIAM Rev., vol. 34, pp. 82–109, 1992. Liu, H. H., and H. C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J., vol. 5, 4800806, 2013. L¨usse, P., P. Stuwe, and J. SchAule, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol, vol. 12, pp. 487–493, 1994. Maier, S. A., Plasmonics: Fundamentals and Applications. New York, USA: Springer, 2007. Marowka, A., “Parallel computing on any desktop,” Comm. ACM, vol. 50, pp. 74–78, 2007. Mazancourt, T. D., and D. Gerlic, “The inverse of a block-circulant matrix,” IEEE Trans. Antennas Propagat., vol. 31, pp. 808–810, 1983. Miret, J. J., C. J. Zapata-Rodr´ıguez, Z. Jaksi´c, S. Vukovi´c, and M. R. Beli´c, “Substantial enlargement of angular existence range for Dyakonov-like surface waves at semi-infinite metal-dielectric superlattice,” J. Nanophoton., vol. 6, 063525, 2012. Miret, J. J., J. A. Sorn´ı, M. Naserpour, A. G. Ardakani, and C. J. Zapata-Rodr´ıguez, “Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces,” Photon Nanostruct: Fundam. Appl., vol. 18, pp. 16–22, 2016. Monticone, F., and A. Alu, “Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies,” Proc. IEEE, vol. 103, pp. 793–821, 2015. Nelatury, S. R., J. A. Polo Jr., and A. Lakhtakia, “Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A , vol. 24, pp. 856–865, 2007. Nicolet, A., and C. Geuzaine, “Waveguide propagation modes and quadratic eigenvalue problems,” Proc. 6th International Conference on Computational Electromagnetics, pp. 1–3, 2006. Orlov, A. A., P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B, vol. 84, 045424, 2011. Palik, E. D., Handbook of Optical Constants of Solids. New York, USA: Academic Press, 1998, vol. I, p. 356. Peterson, A. F., “Vector finite element formulation for scattering from two-dimensional heterogeneous bodies,” IEEE Trans. Antennas Propagat., vol. 43, pp. 357–365, 1994. Pitarke, J. M., V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys., vol. 70, pp. 1–87, 2007. Polo Jr. J. A., S. R. Nelatury, and A. Lakhtakia, “Surface waves at a biaxial bicrystalline interface,” J. Opt. Soc. Am. A, vol. 24, pp. 2974–2979, 2007. Polo Jr., J. A., S. R. Nelatury, and A. Lakhtakia, “Propagation of surface waves at the planar interface of a columnar thin film and an isotropic substrate,” J. Nanophoton., vol. 1, 013501, 2007. Rahman, B. M. A., and J. B. Davies, “Finite-element analysis of optical and microwave waveguides problem,” IEEE Trans. Microwave Theory Tech., vol. 105, pp. 125–138, 1993. Rebay, S., “Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm,” J. Comput. Phys., vol. 105, pp. 125–138, 1993. Rytov, S. M. “Electromagnetic properties of a finely stratified medium,” JETP, vol. 2, pp. 466–475, 1956. Sacks, Z. S., D. M. Kingsland, R. Lee, and J. F. Lee, “Perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propagat., vol. 43, pp. 1460–1463, 1995. Saitoh, K., and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol., vol. 19, pp. 405–413, 2001. Sorn´ı, J. A., M. Naserpour, C. J. Zapata-Rodr´ıguez, and J. J. Miret, “Dyakonov surface waves in lossy metamaterials,” Opt. Commun., vol. 355, pp. 251–255, 2015. Sphicopulos, T., V. Teodoridis, and F. E. Gardiol, “Dyadic Green function for the electromagnetic field in multilayered isotropic media: an operator approach,” Inst. Elec. Eng. Proc.-H, vol. 132, pp. 329–335, 1985. Stern, M. S., P. C. Kendall, and P. W. A. Mcllro, “Analysis of the spectral index method for vector modes of rib waveguides,” Inst. Elec. Eng. Proc.-J., vol. 137, pp. 21–26, 1990. Takayama, O., L. C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, “Dyakonov surface waves: A review,” Electromagnetics, vol. 28, pp. 126–145, 2008. Takayama, O., L. Crasovan, D. Artigas, and L. Torner, “Observation of Dyakonov surface waves,” Phys. Rev. Lett. vol. 102, 043903, 2009. Takayama, O., D. Artigas, and L. Torner, “Practical dyakonons,” Opt. Lett., vol. 37, pp. 4311–4313, 2012. Teixeira, F. L., and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett., vol. 8, pp. 223–225, 1998. Tisseur, F., and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev., vol. 43, pp. 235–286, 2001. Tovallaee, A. A., and J. P. Webb, “Finite-Element Modeling of Evanescent Modes in the Stopband of Periodic Structures,” IEEE Transactions on Magnetics, vol. 44, pp. 1358–1361, 2008. Tsuji, Y., and M. Koshiba, “A finite element beam propagation method for strongly guiding and longitudinal varying optical waveguides,” J. Lightwave Technol., vol. 14, pp. 217–222, 1996. Walker, D. B., E. N. Glytsis, and T. K. Gaylord, “Surface mode at isotropic–uniaxial and isotropic–biaxial interfaces,” J. Opt. Soc. Am. A, vol. 15, pp. 248–260, 1998. Watson, D. F., “Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes,” Comput. J., vol. 24, 167–172, 1981. Xiang, Y., J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express, vol. 22, pp. 3054–3062, 2014. Yan, W., L. Shen, L. Ran, and J. A. Kong, “Surface modes at the interfaces between isotropic media and indefinite media,” J. Opt. Soc. Amer. A, vol. 24, pp. 530–535, 2010. Yariv, A., and P. Yeh, “Electromagnetic propagation in periodic stratified media. II. birefringence, phase matching, and X-ray lasers,” J. Opt. Soc. Am., vol. 67, pp. 438–447, 1977. Zapata-Rodr´ıguez, C. J., J. J. Miret, J. A. Sorni, and S. Vukovi´c, “Propagation of Dyakonon wave-packets at the boundary of metallodielectric lattices,” IEEE J. Sel. Top. Quant. Electron., vol. 19, 4601408, 2013. Zapata-Rodr´ıguez, C. J., J. J. Miret, S. Vukovi´c, and M. R. Beli´c, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express, vol. 21, pp. 19113–19127, 2013. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/72051 | - |
| dc.description.abstract | A full-vectorial finite element method is developed to analyze the surface waves propagating at the interface between two media which could be dissipative particularly. The dissipative wave possessing a complex-valued propagation constant can be determined precisely for any given propagation direction and thus the property of losses could be thoroughly analyzed. Besides, by applying a special characteristic of the implicit circular block matrix, we can greatly reduce the computational consumptions in the analysis.
By utilizing this method, the Dyakonov-like surface wave (DLSW) at the interface between a dielectric and a metal-dielectric multilayered (MDM) structure is discussed. At first, we consider the case when the involved MDM structure serves as an elliptic medium according to the effective medium approximation (EMA). Different from the conventional Dyakonov surface waves, we find that this kind of DLSW possesses an unexpected leaky property due to an additional hyperbolic-like wave in the MDM structure, resulting in a significant increase of propagation loss compared to the results estimated by a simple effective model based on the EMA. Moreover, such leaky property is found to be sensitive to the period of the MDM structure. Thus, to diminish this non-negligible leaky loss, one can suppress the amplitude of the leaky component by designing the MDM structure with a shorter period. As to the case when MDM structure serves as a hyperbolic medium, we find the calculated results for the DLSW with a small period of the MDM structure will show a great inaccuracy if we ignore the metallic absorption. However, for cases of longer periods, the influence of the metallic absorption for the DLSW becomes slight. In addition, for this DLSW, we find a trade-off between its propagation loss and the field confinement. Its propagation loss is smaller for the longer period of the MDM structure but the field becomes less confined to the propagating interface of the DLSW. Furthermore, as this hyperbolic-like MDM structure with serious nonlocal effect sometimes can support an additional elliptic-like isofrequency contour, we also discuss the DLSW based on this contour. For such DLSW, an apparent leaky property is observed similarly to the case when the MDM structure serves as an elliptic medium. This DLSW propagates with a wider range of propagation direction but suffers from a poor field confinement to the interface it is propagating along. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T06:20:54Z (GMT). No. of bitstreams: 1 ntu-107-D98941003-1.pdf: 8499724 bytes, checksum: ddabf1b6f883b29e2e41313889cc8ea1 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 1 Introduction 1
1.1 Dyaknov-like Surface Waves based on the Metal-Dielectric Multilayered structure . . . . . . . . . . . 1 1.1.1 Background . . . . . . . . .. . . . . . . . . . . 1 1.1.2 Numerical Techniques for the Investigation . . . 2 1.2 Organization of the Dissertation . . . . . . . .. . 3 1.3 Contributions of the Present Work . . . . . . . . . 5 2 The Full-Vectorial Three Dimension Finite Element Method and Related Techniques 8 2.1 Overview of the Finite Element Method . . . . . . . 8 2.2 Mathematical Formulation of the General Three Dimension Finite Element Method in Electromagnetics . . 9 2.2.1 The Governing Equation . . . . . . . . . . . . . 9 2.2.2 Finite Element Discretization . . . . . . . . . 11 2.3 Boundary Conditions for the Computational Domain . 14 2.3.1 Perfectly Matched Layers . . . . . . . . . . . . 14 2.3.2 Periodic Boundary Conditions . . . . . . . . . . 17 2.4 Numerical Schemes for Dealing with Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.1 Standard Eigenvalue Problems . . . . . . . . . . 20 2.4.2 Quadratic Eigenvalue Problems . . . . . . . . . 24 2.4.3 The Linear System in the Eigenvalue Problems . . 26 2.4.4 Parallelization . . . . . . . . . . . . . . . . 28 3 An Finite Element Based Eigenvalue Algorithm for Dissipative SurfaceWaves at an Invariant-z Interface 33 3.1 Background . . . . . . . . . . . . . . . . . . . . 33 3.2 Derivation of Eigenvalue Algorithm . . . . . . . . 34 3.3 The Triangular Prism Element . . . . . . . . . . . 38 3.3.1 Domain Discretization . . . . . . . .. . . . . . 38 3.3.2 Elemental Basis Function . . . . . . . . . . . . 39 3.4 Implicit Circular Matrix for the Solution of Linear System . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 Computational Consumptions . . . . . . . . . . . . 45 3.6 Validation of Numerical Schemes . . . . . . . . . 46 4 Investigation of the Dyakonov-like Wave at the Surface of the Semi-infinite Elliptic-like MDM Structure 59 4.1 Brief introduction to the Metal-Dielectric Multilayered structure . . . . . . . . . . . . . . . . 59 4.2 Characteristics of the Elliptic-like MDM Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Analysis of the Dyakonov-like Surface Wave . . . . 63 4.3.1 Based on the Elliptic-like Dispersion . . . . . 63 4.3.2 Effect of Different Periods . . . . . . . . . . 67 5 Investigation of the Dyakonov-like Wave at the Surface of the Semi-infinite Hyperbolic-like MDM Structure 78 5.1 Characteristics of the Hyperbolic-like MDM structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 Analysis of the Dyakonov-like Wave . . . . . . . . 81 5.2.1 Based on the Hyperbolic-like Dispersion . . . . 81 5.2.2 Based on the Elliptic-like Dispersion from the Nonlocal Effect . . . . . . . . . . . . . . . . . . . 83 6 Conclusion 97 List of Abbreviations 100 Bibliography 101 | |
| dc.language.iso | en | |
| dc.subject | 傳播損耗 | zh_TW |
| dc.subject | 洩漏波 | zh_TW |
| dc.subject | Dyakonov表面波 | zh_TW |
| dc.subject | 金屬介電質多層結構 | zh_TW |
| dc.subject | 週期性結構 | zh_TW |
| dc.subject | 全向量式有限元素分析法 | zh_TW |
| dc.subject | Dyakonov surface wave | en |
| dc.subject | propagation loss | en |
| dc.subject | periodic structure | en |
| dc.subject | metal-dielectric multilayered structure | en |
| dc.subject | leaky wave | en |
| dc.subject | full-vectorial finite element method | en |
| dc.title | 發展有限元素特徵模態分析方法以研究存在於介電質與金屬介電質多層結構之表面電磁波 | zh_TW |
| dc.title | Development of Finite-Element Based Eigenvalue Algorithm for Analyzing Electromagnetic Surface Waves at the Interface between a Dielectric and a Metal-Dielectric Multilayered Structure | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 許文翰,楊宗哲,陳宜良,江衍偉 | |
| dc.subject.keyword | 全向量式有限元素分析法,週期性結構,金屬介電質多層結構,Dyakonov表面波,洩漏波,傳播損耗, | zh_TW |
| dc.subject.keyword | full-vectorial finite element method,periodic structure,metal-dielectric multilayered structure,Dyakonov surface wave,leaky wave,propagation loss, | en |
| dc.relation.page | 110 | |
| dc.identifier.doi | 10.6342/NTU201803967 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-08-19 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 光電工程學研究所 | zh_TW |
| 顯示於系所單位： | 光電工程學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-107-1.pdf 未授權公開取用 | 8.3 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。