發展有限差分時域法數值模型以研究覆液晶金屬繞射光柵的表面電漿共振效應

Abstract

光線在各向異性材料中的折射率是一個張量型式，我們利用有限差分時域法來分析各項異性材料中的光學傳播現象。在本篇論文中，首先利用C程式語言編寫平行化三維有限差分時域法的電磁模擬。這套數值模型可以計算光線在液晶材料中的光學傳播現象。接著利用上述的光學演算法，分析光線在穿透及反射型兩種次波長金屬光柵結構中的光學現象，並分析表面電漿波對此元件的影響。在穿透及反射型兩種光柵中，當光線在金屬光柵的表面激發表面電漿波時，會使穿透及反射的光線能量下降。此外，當光柵的週期長度增加，可以使表面電漿波的共振波長產生紅移。在穿透型光柵中，當入射光光波長略大於表面電漿波的共振波長時，會產生異常穿隧的有趣現象。本研究亦討論次波長金屬光柵在不同液晶配向角度下，穿透及反射頻譜的變化，進一步探討此物理現象在顯示領域的可能應用。

The dielectric permittivity in anisotropic materials is in a tensor form, and we use the finite difference time-domain method (FDTD) to analyze optical propagation in anisotropic materials. In this thesis resarch, we first use the C programming language to estabalish an electromagnetic simulation numerical model based on a parallelized three-dimension (3D) finite-difference time-domain (FDTD) method. This model can treat problems involving anisotropic materials, and the estabalished FDTD algorithm takes case of this property so that the optical-wave propagation in anisotropic materials, such as in liquid crystal, can be analyzed. Then, using this FDTD algorithm, the phenomena of light transmission and reflection in two sub-wavelength metal grating structures are analyzed, and the effect of surface plasmon waves on these devices are investigated. In the transmission and reflection metallic gratings, when the incident light excites a surface plasmon wave on the surface of the grating, the transmitted and reflected energies will be reduced. When the period length of the grating increases, the resonance wavelength of the surface plasmon wave will be red shifted. And in the transmission grating, when the wavelength of the incident light is slightly larger than the resonance wavelength of the surface plasmon wave, an interesting phenomenon of extraordinary optic transmission occurs. This study also discusses the changes of transmission and reflection spectra of sub-wavelength metal gratings at different liquid crystal alignment angles, and further explores the possible applications of this phenomenon in the display field.