理論研究具雙軸負導磁率之平面超穎材料激發磁性表面耦合子

Theoretical Study of Excitation of Magnetic Surface Polariton by Planar Metamaterials with Negative Biaxial Permeability

楊宇航

指導教授 ： 嚴大任

國立清華大學/工學院/材料科學工程學系/博士(2013年)

摘要

表面電漿子是由叢集電子震盪所產生的一種電磁反應,這種電子振盪是來自於電子與光子交互作用而形成.而從馬克思威爾方程式,我們可以合理地預測存在一種類似於表面電漿子的磁性表面耦合子.這種磁性表面耦合子是由磁子和光子交互作用而形成.就我們所知,磁性表面耦合子已被研究超過50年,它的基本理論也都被科學界提出.然而,經由實驗證明磁性表面耦合子的論文確很少看到.這個現象是由於自然界存在磁性材料的本質限制.基本上,磁性材料存在的頻段是在THz以下,導致實驗時所需的樣本必須足夠大,這造成製備樣本的困難.更重要的限制是,大部份磁性材料要能產生足夠大的磁性反應所必須的條件是要極低溫的環境(如antiferromagnet),有時甚至需要加上靜磁場的協助(如ferromagnet).由此可知,這些條件將使觀察磁性表面耦合子變得更不容易.近期學術研究發展了一種全新的人工材料.這種人工材料是由很多次波長大小的單位元件所構成,它允許了原本被自然界排除的電磁學現象,其中著名的實驗有反司乃耳定律,隱形電磁披風和人工材料界面.這種人工材料我們稱為新穎材料.新穎材料著名的特性在於我們可以藉由次波長單位元件的幾何結構來人工定義新穎材料的介電常數和透磁率.換句換說,我們不再受限於天然材料的限制.因此,藉由控制幾何結構我們可以人工地操縱新穎材料的電磁反應.本次論文研究重點將是設計嶄新的新穎材料,藉由此設計我們將宣稱一種人工表面磁性耦合子可存在於常溫,或是存在於無外加靜磁場的環境.我們將此種嶄新的新穎材料稱作平面雙軸新穎材料.此外,本次研究也理論導出表面磁性耦合子的一般性色散公式,此公式將可以幫助指引我們如何設計平面雙軸新穎材料的幾何結構.最後,我們預期人工磁性表面耦合子可以應用於生物感測器,光學天線,無線電力傳輸等等.

關鍵字

磁性表面耦合子 ； 新穎材料 ； 表面電漿子 ； 負透磁率

並列摘要

The surface plasmon polaritons (SPPs) are well-known electromagnetic response that is collective electron oscillations, and are the coupling between electrons and photons. From Maxwell’s equations, it is reasonable to consider a magnetic analog – magnetic surface polaritons (MSPs). The MSPs are the coupling between magnons and photons. To our knowledge, the MSPs have been studying for 50 years, and their theory was well developed. However, only a few experiment of the MSPs were demonstrated. The reason mainly stems from that the magnetic response in naturally occurring medium exists at frequency below THz. Accordingly, we need a big sample that may make measurement of the MSPs difficult. Importantly, the strong magnetic response exists at sufficiently low temperature (i.e. antiferromagnet) or at applied static magnetic field (i.e. ferromagnet). In a consequence, these conditions inevitably make observation of the MSPs difficult. Recently, an artificial medium is rapidly developing. Such artificial medium is composed of subwavelength unit cells and allows a variety of unprecedented electromagnetic responses such as inverse Snell’s law, invisible electromagnetic cloak, and meta-surface. Nowadays, the artificial medium is termed as metamaterials. The magic of the metamaterials is that the constitutive parameters of metamaterials no longer depend on the inherent characteristics of atom or electrons of medium) but on the geometrical structure of unit cell. The property of geometrical structure will make electromagnetic response of metamaterials scalable, and hence the electromagnetic responses can be artificially tailored by designing geometrical structure. In our study, we will demonstrate the artificial MSPs to “live” at room temperature and at no applied static magnetic field, which can be realized by means of our designed metamaterials, and we call our design planar biaxial metamaterials (PBMM). In addition, we derive the general dispersion equation of the MSPs that guides us how to design the PBMM. We expect that the artificial MSPs are applicable to the biosensor, optical antenna, wireless energy transfer, and so on.

並列關鍵字

magnetic surface polariton ； metamaterials ； surface plasmon polariton ； negative permeability

參考文獻

1 Anker, J. N. et al. Biosensing with plasmonic nanosensors. Nat. Mater. 7, 442-453, doi:10.1038/nmat2162 (2008).

2 Lal, S., Link, S. & Halas, N. J. Nano-optics from sensing to waveguiding. Nat. Photonics 1, 641-648, doi:10.1038/nphoton.2007.223 (2007).

3 Pincus, P. Propagation effects on ferromagnetic resonance in dielectric slabs. J. Appl. Phys. 33, 553-&, doi:10.1063/1.1702464 (1962).

4 Damon, R. W. & Eshbach, J. R. Magnetic modes of a ferromagnet slab. J. Phys. Chem. Solids 19, 308-320, doi:10.1016/0022-3697(61)90041-5 (1961).

5 Oliveros, M. C., Almeida, N. S., Tilley, D. R., Thomas, J. & Camley, R. E. Magnetostatice modes and polaritons in antiferromagnetic nonmagnetic superlattices. J. Phys.-Condes. Matter 4, 8497-8510, doi:10.1088/0953-8984/4/44/011 (1992).