利用時域有限差分法對奈米銀柱結構的奈米成像性質之研究

FDTD simulation of nano imaging with silver nano rod structure

張鐵明(Tieh-Ming Chang)

指導教授 ： 蔡定平

國立臺灣大學/理學院/物理研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.10109

摘要

在傳統光學微影技術(optical lithography)中，若欲縮小圖形(pattern)線寬時必須利用較短的光源波長，但伴隨而來的卻是成本的增加及製程技術上的困難。在現有光微影技術下，藉由奈米銀柱的結構對於光場的良好侷域性，使得利用可見光波段的光源在近場範圍中產生次波長線寬之圖形成為可能。本文採用三維時域有限差分法(3D-FDTD)的方法，應用至近場光學的領域，有系統的探討奈米銀柱陣列在各種不同參數之下，其對於奈米尺度大小之光源的光場傳輸現象，以及經過此奈米銀柱陣列之後光強(intensity)在近場範圍的分佈特性與光場強的增益作用。並研究表面電漿的局域性與近場光強增強效果之關連性。本文在內容上分為以下四個主題：
一、 建立一套求解電磁散射問題的數學模式，並從數值方法特性的分析，建構出最佳之格式與程式設計之技巧。
二、 研究單一柱狀結構之近場光強分佈，模擬結果顯示：在沿著電場偏振方向上的奈米銀柱截面寬度變化對光場分佈有較顯著的影響。
三、 比較奈米平行銀柱陣列各項參數對近場光強分佈之影響。
四、 研究奈米平行銀柱陣列在不同孔洞大小及孔洞間距下對解析度的影響。

關鍵字

時域有限差分法 ； 奈米銀柱

並列摘要

Silver nanorods have an excellent localization of the transmitted wave; especially the localized spot has a space below the bottom of the nanorods. In this dissertation, the near field distribution of silver nanorods is investigated. The numerical method knows as finite difference time domain (FDTD) is introduced into near field optics. The effects of various radius, lengths, gaps and separations of silver nanorod array are investigated. Results of the calculation provide a direct theoretical basis for the relation between the localization of surface Plasmon and the enhance of near field.
The near field distribution of nano hexagonal rod, and the parallel nanorod array are studies systematically using our FDTD method. It is found that the image is highly dependent on the spacing and radius of nanorods. Results of single nanorod show similar near field distribution to an electrical dipole. Due to the boundary condition at the interface, the polarized incident wave enhance the field at boundary of the nanorod. The influence of nanorods on contrast is studied with FDTD method as well.
Silver nanorods have an excellent effect on localizing the transmitted wave, especially, the enhancements below the bottom of the nanorods. In this dissertation, a systematic apparoach to studying the near-field distributions, from a single nanorod to an array of nanorods, is carried out. The three-dimensional finite difference time domain (3D FDTD) which is a well known and powerful numerical method is used to simulate the interactions of the optical waves with the silver nanorods.
The near-field distribution of a single nanorod is similar to an electrical dipole. The effects of radius variation, lengths of nanorods, gaps and spacings in the silver nanorod array are investigated. It is found that the image formed from the transmitted wave is highly dependent on the spacing and radius of nanorods. According to the relation between the localization of surface plasmon and the enhancement of near field, the optimal criteria can be obtained in constructing optical nanolithographic sturcutures.

並列關鍵字

FDTD ； silver nano rod

參考文獻

[ 1.1] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propagat., AP-14:302-307 (1966).

[ 1.2] H. A. Atwater, Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides, Nature Materials (2003).

[ 1.3] S. Kawata, Subwavelength optical imaging through a metallic nanorod array, PRL 95, 267407 (2005).

[ 2.2] G. R. Fowles, Introduction to Modern Optics 2nd edition, 新智 (1977).

[ 2.3] M. Fox, Optical properties of solids, Oxford (2001).