環型磁極矩(toroidal dipole)由甜甜圈型的表面電流所產生的環型磁場，屬於第三類的多極矩展開元素。由於自然界中環形矩材料訊號微弱難以被測量，因此一般常被忽略。過去有許多研究利用超穎材料的設計以產生環型磁極矩，但這些設計往往需要複雜的奈米結構或特殊的激發光源才能有效激發環型矩共振並同時削弱電磁多極矩。在本論文中，我們透過三維的週期性矽奈米圓柱結構成功得產生環極矩，與以往不同的是，此結構可經由垂直入射的光源來激發平行於基板的環形偶極矩，此外介電材料能降低材料本身的損耗，同時簡單的奈米結構降低了製程上的困難。在本文中，首先我們透過有限元素法來模擬計算矽奈米圓柱的頻譜響應，並利用多極矩展開進行模態分析，並探討各個結構的幾何參數對於多極矩的影響，以最佳化設計出能環型矩超穎材料。接著，利用電子微影術來製作設計好的矽奈米圓柱，其量測光譜與模擬計算結果十分相符，顯示我們成功實現了環型矩超穎材料。由於環形矩共振具強近場與低遠場輻射的特性，未來極具潛力應用於高敏感度的生醫感測器、非線性光學等應用。

Toroidal dipole is determined by static currents flowing on the surface of a torus which induced circular magnetic field and it can be considered as the third family of multipole decomposition elements. Natural toroidal response was masked by stronger electromagnetic effects, so its signal was too weak to be observed. However, recent studies have solved this problem by using metamaterials to enhance the strength of toroidal dipole. The toroidal metamaterials often require complex nanostructures or special light sources to effectively excite toroidal response and simultaneously weaken electromagnetic multipole moments. Here, we have successfully designed three-dimensional periodic silicon cylinders which can generate transverse toroidal dipole moment through normal incident light. Moreover, plasmonic metamaterials suffer from ohmic loss, so we change such a situation with the use of the simple dielectric nanostructure. In this thesis, we first utilized finite element methods to simulate the optical spectra of dielectric metamaterials and used multipole expansion to analysis the modal distribution. Then, we discuss the effect of geometric parameters on toroidal dipole response in order to optimize our design. Next, the designed structure were fabricated through the electron beam lithography process. The measured spectra are consistent with simulation results, which shows we successfully realize the toroidal metamaterials. Due to the sub-radiation property and strong near-field confinement of toroidal mode, toroidal metamaterials are promising to be applied for high sensitivity biosensors and nonlinear optics.

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