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研究生:劉耀仁
研究生(外文):Yao-Jen Liu
論文名稱:以有限差分時域法分析微共振器與金屬次波長孔隙結構
論文名稱(外文):Finite-Difference Time-Domain Analysis of Microresonators and Metallic Subwavelength Aperture Structures
指導教授:張宏鈞
指導教授(外文):Hung-Chun Chang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:光電工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:94
中文關鍵詞:有限差分時域法微共振器次波長孔隙
外文關鍵詞:FDTDMicroresonatorSubwavelength Aperture
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本篇論文採用有限差分時域法為數值模型模擬研究數種不同的元件,並以數學動機推導之完美匹配層作為吸收邊界的處理。首先分析波導耦合圓形微共振腔以及方形微共振腔。在分析微共振腔的同時我們亦針對格點配置的問題做了探討,期能使模型更接近真實情形。討論中發現,將格點中的電場安置在邊界上並將該格點的折射率取為邊界兩邊的平均值,在我們分析的例子中能得到最好的結果。其次,我們討論了表面電漿和金屬次波長孔隙的電磁波穿透問題,之後便著手分析一些光波段以及微波段的次波長孔隙的元件。其中有限差分數值分析使用了Drude色散模型來模擬金屬,在模擬中可以觀察到當表面電漿被激發時,波穿過孔隙穿透率的增強以及指向性。除了元件的研究,我們也提出了以非線性色散模型修改的完美匹配層。當模擬波在非線性色散介質中的行為時,此修改過的完美匹配層可以安置在計算空間的周圍,以有效地吸收往外擴散的波以模擬無限大的空間。
In this research, the finite-difference time-domain (FDTD) method is employed to simulate several categories of devices with the appearance of the mathematic motivated perfectly matching layer (PML) around the computational
domain. First, the micro-ring and square micro-ring resonators are analyzed. The issue of proper grid arrangement over the modelled structures for efficient numerical convergence is discussed. We discover that putting the electric field grid just at the boundary of dielectric interfaces and taking the index average of the grid provide the best results in the cases we concern.
Two geometries of micro-ring resonator coupled by straight waveguides are simulated with the slab index of 3.2 and the cladding index of 1.0. Second, the surface plasmons (SPs) and the metallic subwavelength apertures are discussed. Several structures are analyzed by imposing the Drude model for material dispersion into the FDTD scheme to model the metal in the optical and microwave ranges. The enhancement of transmittance and the directional property are shown through the simulations. Beside simulation of various devices, we also implement a PML modified by nonlinear and dispersive model. The modified PML can be used to truncate the computational domain of modelling a nonlinear-dispersive medium to properly absorb the outgoing waves.
1 Introduction 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Mathematical Formulation 5
2.1 The Finite-Difference Time-Domain
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 The Yee Algorithm . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Numerical Dispersion, Numerical Stability, and Other
Characteristics . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Modelling of Frequency Dispersive Material . . . . . . . . . . 10
2.2.1 The Auxiliary Differential Equation Method . . . . . . 11
2.3 Absorbing Boundary Conditions . . . . . . . . . . . . . . . . . 13
2.3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Mathematically Motivated Perfectly Matched
Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Mathematically Motivated PMLs for Nonlinear-Dispersive Media
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Nonlinear-Dispersive Formulations . . . . . . . . . . . 16
2.4.3 Nonlinear-Dispersive PML . . . . . . . . . . . . . . . . 18
2.4.4 Numerical Experiments . . . . . . . . . . . . . . . . . . 19
2.4.5 Modelling the Nonlinear-Dispersive Phenomenon . . . 20
2.5 Field Extension Techniques in FDTD simulations . . . . . . . 21
3 Modelling of Microresonators 32
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Grid Arrangement Issue . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Grid Arrangement in a Slab Waveguide . . . . . . . . . 34
3.2.2 Grid Arrangement in a 90-Degree Bend Waveguide . . 36
3.3 Micro-Ring Resonators . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Square Micro-Ring Resonators . . . . . . . . . . . . . . . . . . 38
4 Modelling of Subwavelength Aperture 57
4.1 Surface Plasmons . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Subwavelength Apertures . . . . . . . . . . . . . . . . . . . . . 58
4.3 The Drude Model . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Modelling of Subwavelength Apertures in Microwave Range . . 61
4.4.1 The Reference Sample . . . . . . . . . . . . . . . . . . 61
4.4.2 The Sinusoidal Grating Sample . . . . . . . . . . . . . 62
4.4.3 The Symmetric Rectangular Grating Sample . . . . . . 64
4.4.4 The Asymmetric Rectangular Grating Sample . . . . . 64
4.4.5 The Directivity/Beaming Property . . . . . . . . . . . 65
4.5 Modelling of Subwavelength Apertures in Optical Frequency
Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.6 Highly Directional Emission Properties . . . . . . . . . . . . . 67
5 Conclusion 88
[1] Abarbanel, S., and D. Gottlieb, "On the construction and analysis of absorbing layers in CEM," Appl. Numer. Math., vol. 27, pp. 331--340, 1998.
[2] Absil, P. P., J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol.
Lett., vol. 12, pp. 398--400, 2000.
[3] Adar, R., M. R. Serbin, and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol., vol. 12, pp. 1369--1372, 1994.
[4] Akarca-Biyikli, S. S., I. Bulu, and E. Ozbay, "Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies," J. Opt. A, vol. 7, pp. S159--S164, 2005.
[5] Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., vol. 114, pp. 185--200, 1994.
[6] Boriskina, S. V., T. M. Benson, P. Sewell, and A. I. Nosich, "Spectral shift and Q-change of circular and square-shaped optical microcavity modes due to periodic sidewall surface roughness," J. Opt. Soc. Am. B,
vol. 10, pp. 1792--1796, 2005.
[7] Ebbesen, T. W., H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, vol. 391, pp. 667--669, 1998.
[8] Feng, N. N., W. P. Huang, and G. R. Zhou, "A hybrid time-domain technique for simulation of high-density integrated optical circuits," IEEE J. Quantum Electron., vol. 11, pp. 452--456, 2005.
[9] Grupp, D. E., H. J. Lezec, T. Thio, and T. W. Ebbesen, "Beyond the Bethe limit: tunable enhanced light transmission through a single subwavelength aperture," Adv. Mater. vol. 11, pp. 860--862, 1999.
[10] Hagness, S. C., D. Rafizadeh, S. T. Ho, and A. Ta
ove, "FDTD microcavity simulations: design and experimental realization of waveguidecoupled single-mode ring and whispering-gallery-mode disk resonators,"
J. Lightwave Technol., vol. 15, pp. 2154--2165, 1997.
[11] Hong, C. T., Finite-Di erence Time-Domain Analysis of High-Density Integrated Optic Guided-Wave Devices. M. S. Thesis, Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taiper, Taiwan, June 2003.
[12] Joseph, R. M., and A. Taflove, "FDTD Maxwell''s equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat., vol. 45, pp. 364--374, 1997.
[13] Joseph, R. M., P. M. Gooriian, and A. Taflove, "Direct time integration of Maxwell''s equations in two-dimensional dielectric waveguides for
propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett., vol. 18, pp. 491--493, 1993.
[14] Kashiwa, T., and I. Fukai, "A treatment by the FD-TD method of the dispersive characteristics associated with electronic polarization," Microwave Opt. Technol. Lett., vol. 3, no. 6, pp. 203--205, 1990.
[15] Klunder, D. J. W., M. L. M. Balistreri, F. G. Blom, A. Driessen, H. J. W. M. Hoekstra, L. Kuipers, and N. F. Hulst, "High-resolution photonscanning tunneling microscope measurements of the whispering gallery
modes in a cylindrical microresonator," IEEE Photon. Technol. Lett., vol. 12, pp. 1531--1533, 2000.
[16] Liao, Z. P., H. L. Wong, B. P. Yang, and Y. F. Yuan, "A transmitting boundary for transient wave analyses," Scientia Sinica (series A), vol. 27, pp. 1063--1076, 1984.
[17] Little, B. E., H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, "Wavelength switching and routing using absorption and resonance," IEEE Photon. Technol. Lett., vol 10, pp. 816--818, 1998.
[18] Little, B. E., and S. T. Chu, "Theory of loss and gain trimming of resonator-type filters," IEEE Photon. Technol. Lett., vol. 12, pp. 636--638, 2000.
[19] Lezec, H. J., A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-vidal, and T. W. Ebbesen, "Beaming light from a subwavelength
aperture," Science, vol. 297, pp. 820--822, 2002.
[20] Luebbers, R., F. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider. "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat., vol. 32, no.
3, pp. 222--227, 1990.
[21] Manolatous, C., S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "High-density integrated optics," J. Lightwave Technol., vol. 17 pp. 1682--1692, 1998.
[22] Mur, G., "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations." IEEE Trans. Electromag. Compat., vol. 23, pp. 377--382, 1981.
[23] Powell, C. J., J. B. Swan, "Effect of oxidation on the characteristic loss spectra of aluminum and magnesium," Phys. Rev. vol. 118, pp. 640--643, 1960.
[24] Rabus, D. G., M. Hamacher, U. Troppenz, and H. Heidrich, "High-Q channel dropping filters using ring resonators with integrated SOAs," IEEE Photon. Technol. Lett., vol. 8, pp. 69--71, 1996.
[25] Sullivan, D. M, Electromagnetic simulation using the FDTD method, New York, MA: IEEE Press, 2000.
[26] Taflove, A., and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd edition. Boston, MA: Artech House, 2000.
[27] Thio, T., K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," vol. 11 pp. 1972--1974, 2001.
[28] Wang T. J., Y. H. Huang, and H. L. Chen, "Resonant-wavelength tuning of microring filters by oxygen plasma treatment," IEEE, Photon., Technol. Lett., vol. 17, pp. 582--584, 2005.
[29] Wood, R. W., "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Magm., vol. 4, pp. 396--402, 1902.
[30] Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell''s equations in isotropic media," IEEE Trans. Antennas Propagat., vol. 3, pp. 302--307, 1966.
[31] Zhao, L., and A. C. Cangellaris, "GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids," IEEE. Trans. Microwave Theory Tech., vol. 44, pp. 2555--2563, 1996.
[32] Ziolkowski, R. W., "Time-derivative Lorentz materials and their utilization as electromagnetic absorbers," Phys. Rev. E, vol. 55, pp. 7696--7703, 1997.
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