Investigation of Distinct Magnetic Field in Metamaterials through Effective Medium Theorem

所謂次波長(subwavelength)結構是指單位元小於入射波波長之結構，在此情形下結構會具有特殊性質，不能單純以古典電磁學理論解釋，為現代光電領域中一項重要的議題。自然界存在著許多相對於可見光之次波長結構，諸如蓮花出淤泥而不染、蝴蝶色彩斑斕的翅膀等等。由於可見光波長約在400至700奈米間，因此次波長結構又常被稱作奈米結構。在奈米級製程發達的現代，利用次波長結構的光學特性製作微米層級以下的人工材料，以達到自然界不存在的物理特性，是為超常材料(metamaterials)。目前超常材料被廣泛應用在各領域中，如天線系統、反雷達吸收層、感測器等等，本篇論文則利用其在共振時波異常穿透的現象討論並設計金屬與介電質平板交互堆疊結構型超常材料(Stratified Metal Dielectric Metamaterials, SMDMs)，以達到使外加磁場於結構中產生異常的情形。 一般超常材料皆是由週期性排列的次波長結構組成，這是因為週期性的結構排列使得表面電荷提供額外動量，產生表面電漿共振(Serface Plasma Resonance, SPR)，使得異常光學性質增強，更易觀察。然而單一三明治平板結構經由適當介電係數(permittivity)組成的金屬－介電質－金屬或介電質－金屬－介電質的組合，無須週期排列即可產生明確的反磁(diamagnetism)或高順磁現象。此外兩種材料皆非磁性物質，其相對導磁係數(relative permeability)皆為1，因此控制變因僅剩下材料的介電係數以及平板厚度，即可調整異常磁場的強度和共振頻帶的寬度，在設計上具有高度的自由與便利性。 而在分析上，最常用的方法為等效介質理論(effective medium theorem, EMT)，其為將整個複雜的結構視同一塊簡單的等向性或非等向性塊材，此時結構整體的光學參數可等效為一個值，在共振點時等效光學參數會有特別的變化，透過觀察這些變化可輕易了解結構對入射電磁場的影響。然而等效雖具便利性，其在數學上仍具有無可避免的數值誤差，且這些誤差於特定的奇異點時會被放大。因此除了數學上的反算，必須同時觀察物理現象，並適當地加以修正，此問題亦會在結果中進一步探討。Subwavelength structure, a structure unit which is smaller than wavelength and thus induces some specific properties that can’t be explained by classic electromagnetic theorem, plays a crucial role in the field of photoelectronics nowadays. It can be found easily in nature, and since the wavelength of visible light ranges form 400 to 700 nm, it is also called a nano-structure. Through the nano-level process approaches, an artificial material beyond the micron-level can display distinct features from what they can be seen under a microscope; the features are called metamaterials. Metamaterials is widely used in antenna, stealth, sensor, etc. This thesis focuses on analyze and design the stratified metal dielectric metamaterials (SMDMs) which can lead to enhancement of the magnetic field incident inthe structure. Normally, metamaterials are made of subwavelength structures arranged periodically due to the fact that such arrangements produce extra momentum which cause surface plasma resonance (SPR) and hence enhance the extraordinary phenomenon of electromagnetic wave. However, even an unit cell of the sandwich structure composited of metal and dielectric can reach the unusual magnetic response such as diamagnetism or high quality paramagnetism explicitly without the structure consisting of non-magnetic materials. Therefore, by modifying only two factors—the permittivity and thickness of every slab—the optical properties of the structure can be controlled simply. The effective medium theorem (EMT) is often used to analyze the metamaterial structure, in which the structure can be regarded as an isotropic or anisotropic effective medium and be described by retrieving the effective optical parameters. When resonance occurs, the effect optical parameters also vary abruptly. However, the numerical error may occur upon the retrieval process, and is amplified at some specific singular points. Therefore, the EMT has to be based on physical phenomenon and be modified appropriately. The detail will be discussed in the second and the third chapter