非等向週期層狀結構之等效介質理論

近年來，非局部效應的研究再度受到重視，不同於以往的研究如雨後春筍般不斷地推陳出新。非局部效應就是等效介電參數與波向量呈相依關係，更簡單來說，就是材料特性隨入射方向改變而不同。非局部效應產生的原因在於空間色散，強烈的空間色散使等效參數對波向量變化劇烈，甚至是產生共振現象，許多特殊電磁現象往往發生於共振情形之下。以往經常以等效介質理論(effective medium theory,EMT)所得到的色散關係為基礎，往後發展理論並研究現象，的確有許多現象從中探討出來，但近年來發現，若是透過EMT的觀點，有些現象會因此被忽略掉。　　本論文探討非等向週期層狀結構之等效介質理論。將介電金屬層狀週期結構進行推廣，以非等向材料取代金屬，形成二維週期結構。首先我們先利用基礎電磁理論推導非等向的場，並且利用此場透過週期邊界條件求得特徵場，最後求其平均，推導平均電位移與平均電場的關係，藉此方式求得等效介電參數。我們發現到，非等向性提高了材料參數對等效參數的靈活度，增加了一個維度，使得調配參數時多了一種排列組合改變等效參數的趨勢，如此一來，我們求得等向性的結果後，還可以對其結果進行調整，觀察各種調整後所求得的趨勢並加以整理。

關鍵字

非局部效應；空間色散；等效介質理論；介電金屬層狀週期；二維週期結構

並列摘要

Recently, nonlocal effects become to spotlight again,and there are so many kind of this researchs published. The meaning about nonlocal effects is the effective parameters and wave vectors are correlation. Easily to say, nonlocal effects mean that the property of a material changes with the varied incident direction. Nonlocality resulted from spacial dispersion. The stronger spacial dispersion appears, the acute variation for effective parameters with wave vectors happens, even, electromagnetic resonance, and hundred phenomenans occur because of resonance. In the past, plenty researchs are based on effective medium theory(EMT) to get dispersion relation. On the basis of EMT, some special phenomenans can be indeed found, but there are also some anomalous phenomenans ignored by this view. This thesis investigates Nonlocal effective medium model for multilayered isotropic-anisotropic metamaterials. We spread the nonlocal effective medium model for multilayered metal-dielectric metamaterials. We substitute the metal by a anisotropic medium to constuct a two-dimensional periodic structure. Foremost, we deduce the anisotropic electric field based on the Maxwell equation, and utilize this electric field to get eigenmode electric field. In course of time, averaging these two electric field and get the association between averaged displacement field and averaged electric field to find the effective parameters. We discover that anisotropy enhances the agility for material parameters to effective parameters. There is a new parameter to modify after we add the anisotropy to this structure. When we get a isotropic consequence, we can apply the anisotropy to rectify the trend of effective parameters.

並列關鍵字

nonlocal effects ； spacial dispersion ； effective medium theory ； multilayered isotropic-anisotropic metamaterials ； two-dimensional periodic structure

參考文獻

[2] "Frontmatter," in Metamaterials, ed: John Wiley & Sons, Inc., 2006, pp. i-xxi.

[3] B. A. Munk, "Why Periodic Structures Cannot Synthesize Negative Indices of Refraction," in Metamaterials, ed: John Wiley & Sons, Inc., 2008, pp. 1-46.

[5] N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," Antennas and Wireless Propagation Letters, IEEE, vol. 1, pp. 10-13, 2002.

[6] P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Physical Review B, vol. 73, p. 113110, 2006.

[7] Z. Ruan and M. Qiu, "Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances," Physical review letters, vol. 96, p. 233901, 2006.

國際替代計量

非等向週期層狀結構之等效介質理論

全文下載

主題瀏覽