臺灣博碩士論文加值系統

本篇論文中，我們以曲線混合型元素為基底的全向量有限元素虛軸波束傳遞法來分析表面電漿波導上的波導傳播模態，分析的表面電漿結構分別有雙軸奈米柱鑲嵌在均勻介質的以及將雙軸奈米柱放在介質基板上兩種不同結構。在操作波長500到2000奈米波長的範圍下，我們計算了等效折射率、傳播距離、模態場型以及等效模態面積。首先，我們先探討雙軸奈米柱包含在均勻的二氧化矽以及空氣的情況，藉由比較其單軸構造的特性可以發現兩軸相鄰的奈米柱會發生耦合的現象，並且分裂出多個不同的模態。對於不同的奈米柱半徑在本文中也被調查。接著我們研究加上基座之後的影響，由事先研究的結果可以知道單軸奈米柱在基座上會有一個傳播模態以及一個洩漏模態，藉此我們發現因為耦合的效應，在雙軸在基座上的結構可以分別得到兩種傳播模態以及洩漏模態。最後，我們也調查不同半徑的影響。

In this research, we adopt the full-vectorial finite-element imaginary-distance beam propagation method (FV-FE-ID-BPM) based on the hybrid edge/nodal elements and incorporated with perfectly matched layers (PMLs) to analyze waveguide modes propagating on plasmonic waveguides composed of two parallel circular-cylinders named the double-nanowire, including that immersed in a uniform dielectric matrix and that supported by dielectric substrate. The effective refractive indices, propagation lengths, mode-field profiles, and effective mode areas are calculated for different parameters and structures over the wavelength range from 500 nm to 2000 nm. The double-nanowires immersed in uniform silica and in air are first investigated. The splitting into multiple modes due to the coupling between the two adjacent nanowires is examined by comparing with modal characteristics of the single nanowire. Different nanowire radii are also considered. The effect of including a supporting substrate is studied. Previous studies have given the fact that a single silver nanowire with a silica substrate possesses a silver/substrate guided mode and an air/silver leaky mode. The coupling phenomena of the double-nanowire case are demonstrated in this study, showing the resultant two silver/substrate guided modes and two air/silver leaky modes. Finally, the effect of using different substrate materials is discussed.

1. Introduction 1
1.1 Motivations 1
1.2 Numerical Methods for Waveguide Analysis 2
1.3 Chapter Outline 4
2. The Finite Element Method and Related Mathematical Formulations 5
2.1 The Perfectly Matched Layers 5
2.2 The Finite Element Method and Mode Solver 8
2.3 The Finite Element Beam Propagation Method 12
2.4 The Finite-Element Imaginary-Distance Beam Propagation Method 16
3. Analysis of Surface Plasmon Polaritons in Silver Double-Nanowire System 25
3.1 An Overview 25
3.2 Silver Double-Nanowires Immersed in SiO2 27
3.3 Silver Double-Nanowires with Different Gap Widths 31
3.4 Silver Double-Nanowires Immersed in Air 32
4. Analysis of Silver Double-Nanowires on Silica Substrate 56
4.1 Guiding and Leaky Modes of Silver Nanowires on a SiO2 Substrate 56
4.2 Silver Double-Nanowires on a SiO2 Substrate with Different Gap Widths 58
4.3 Effects of Different Substrate Materials 59
5. Conclusion 76
Bibliography 78

Ademgil, H., and S. Haxha. ``Bending insensitive large mode area photonic crystal fiber." Optik, vol. 122, pp. 1950--1956, 2011.


Barnes, W. L. Dereux, A. and Ebbesen, T. W. ``Surface plasmon subwavelength optics", Nature, vol. 424, pp. 824-–830, 2003.


Berenger, J. P., ``A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., vol. 114, pp. 185--200, 1994.



Cai W., Wang, L., Zhang, X., Xu, J., and F. Javier García de Abajo, ``Controllable excitation of gap plasmons by electron beams in metallic nanowire pairs." Phys. Rev. B. vol. 82, 125454, 2010.

Chen, H. P., Modal Analysis of Triangle-Shaped and Silver-Nanowire Waveguides Using a Full-Vectorial Imaginary-Distance Finite-Element Beam Propagation Method. M. S. Thesis, Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei, Taiwan, June 2015.


Chen, H. P., Liu, H. H., and H. C. Chang. ``On the Leaky Modes for Silver Nanowires on a Silica Substrate."


Dai, D., Shi, Y., He, S., Wosinski, L., and Thylen, L. ``Gain enhancement in a hybrid plasmonic nano-waveguide with a low-index or high-index gain medium. "Opt. Express, vol. 19, pp. 12925--12936, 2011.

Gramotnev, D. K., Bozhevolnyi, S. I., ``Plasmonics beyond the diffraction limit," Nature Photon., vol. 4, pp. 83--91, 2010.


Guo, X., M. Qiu, J. M. Bao, B. J. Wiley, Q. Yang, X. N. Zhang, Y. G. Ma, H. K. Yu, and L. M. Tong, ``Direct coupling of plasmonic and photonic nanowires for hybrid nanophotonic components and circuits," Nano Lett., vol. 9, pp. 4515--4519, 2009.


Hsu, S. M., Full-Vectorial Finite Element Beam Propagation Method Based on Curvilinear Hybrid Edge/Nodal Elements for Optical Waveguide Problems. M. S. Thesis, Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei, Taiwan, June 2004.


Hu, J., and Curtis R. Menyuk., ``Understanding leaky modes: slab waveguide revisited." Adv. Opt. Photon., vol. 1, pp. 58--106, 2009.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths." Phys. Rev. B, vol. 62, 15299, 2000.


Johnson, P. B., and R. W. Christy, ``Optical constants of the noble metals,'' Phys. Rev. B, vol. 6, pp. 4370--4379, 1972.


Juntunen, J. S., N. V. Kantartzis, and T. D. Tsiboukis. ``Zero reflection coefficient in discretized PML." IEEE Microw. Wirel. Compon. Lett., vol. 11, pp. 155--157, 2001.


Li, Q., and M. Qiu. ``Plasmonic wave propagation in silver nanowires: guiding modes or not?" Opt. Express, vol. 21, pp. 8587--8595, 2013.


Liu, H. H., and H. C. Chang. ``Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials." IEEE Photon. J., vol. 5, pp. 4800806, 2013.


Ma, Aning, Yuee Li, and Xiaoping Zhang. "Coupled mode theory for surface plasmon polariton waveguides." Plasmonics, vol. 8, pp. 769--777, 2013.


Ma, Y., Farrell, G., Semenova, Y., Chan, H., and Zhang, H., ``Novel dielectric-loaded plasmonic waveguide for tight-confined hybrid plasmon mode." Plasmonics, vol, 8, pp. 1259--1263, 2013.


Manjavacas, A., and F. J. García de Abajo. ``Robust plasmon waveguides in strongly interacting nanowire arrays." Nano lett., vol. 9, pp. 1285--1289, 2008.

Manjavacas, A., and F. J. García de Abajo. ``Coupling of gap plasmons in multi-wire waveguides." Opt. Express, vol. 17, pp. 19401--19413, 2009.


Oulton, R. F., Bartal, G., Pile, D. F. P. and Zhang, X., ``Confinement and propagation characteristics of subwavelength plasmonic modes." New J. Phys., vol. 10, pp. 105018, 2008.

Oulton, R. F., Sorger, V. J., Genov, D. A., Pile, D. F. P., and Zhang, X., ``A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation." Nature Photon., vol. 2, pp. 496--500, 2008.


Pierce, J. R., ``Coupling of modes of propagation." J. Appl. Phys., vol. 25, pp. 179--183, 1954.

Prodan, E., Radloff, C., N. J. Halas, Nordlander, P., `` hybridization model for the plasmon response of complex nanostructures." Science, vol. 302, pp. 419--422, 2003.


Rebay, S., ``Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm,'' J. Comput. Phys., vol. 105, pp. 125--138, 1993.


Saitoh, K., and M. Koshiba, ``Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers," IEEE J. Quantum Electron., vol. 38, pp. 927--933, 2002.


Song, Y., Yana, M., Yangb, Q., Tong, L., M. Qiu, ``Reducing crosstalk between nanowire-based hybrid plasmonic waveguides." Opt. Comm., vol. 284, pp. 480--484, 2011.


Sun, S., Chen, H. T., Zheng, W. J., and Guo, G. Y., ``Dispersion relation, propagation length and mode conversion of surface plasmon polaritons in silver double-nanowire systems." Opt. Express, vol. 12, pp. 14591--14605, 2013.


Takahara, J., Yamaguchi, S., Taki, H., Morimoto, A., and Kobayashi, T., ``Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett., vol. 22, pp. 475–-477, 1997.


Tamir, T., and F. Kou., ``Varieties of leaky waves and their excitation along multilayered structures." IEEE J. Quantum electron., vol. 22, pp. 544--551, 1986.



Tsuji, Y., and M. Koshiba., ``Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme." J. Lightwave Technol., vol. 18, pp. 618, 2000.


Veronis, G., and S. Fan., ``odes of subwavelength plasmonic slot waveguides." J. Lightwave Technol., vol. 25, pp. 2511--2521, 2007.


Wang, Y., Ma, Y., Guo, X., and Limin Tong, ``Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates." Opt. Express., vol. 20, pp. 19006--19015, 2012.


Yariv, Amnon. ``Coupled-mode theory for guided-wave optics." IEEE J. Quantum Electron., vol. 9, pp. 919--933, 1973.


Yan, M., Qiu, M., ``Guided plasmon polariton at 2D metal corners.", J. Opt. Soc. Am. B, vol. 24, pp. 2333--2342, 2007.


Zhang, J., Cai, L., Bai, W., Xu, Y., and Song, G., ``Hybrid plasmonic waveguide with gain medium for lossless propagation with nanoscale confinement." Opt. lett., vol. 36, pp. 2312--2314, 2011.