以平行化時域有限差分法分析三維奈米天線與奈米電路元件

Abstract

時域有限差分法被廣泛地運用在電磁模擬上。我們利用C 語言建構了一個平行化三維時域有限差分模擬器，並利用多台電腦透過訊息傳遞介面協定來加速模擬。本論文中，我們利用這個自行建構的平行化時域有限差分模擬器來模擬兩種金屬奈米結構問題。第一部份，我們模擬了四種奈米天線，包含領結天線、偶極天線、環形領結天線以及修正型環形領結天線。我們計算天線間隙之局部場增強，包含其頻譜響應及共振波長。接著，我們討論改變天線結構對共振行為造成的影響，結果顯示共振波長及場增強倍數和這些結構參數有明顯的相關性。為了微小化天線，我們加入新的結構參數到傳統領結天線中，使得傳統領結天線成為環形領結天線或修正型環形領結天線。模擬結果顯示我們可以在不增大天線尺寸的條件下使共振波長紅移，並且透過調變這些新加入的結構參數來操控共振波長。本論文第二部分為光學奈米電路元件。在光波頻段中，我們將金屬與介質用並聯或串聯的方式連接，並利用此複合式結構來實現奈米濾波器。我們把奈米帶通濾波器或帶拒濾波器放置在波導管內，並計算其穿透係數，計算結果顯示時域有限差分法吻合電路理論。接著，我們計算由兩半球所組合成的三維奈米圓球之電位分布，當此兩半球在接近共振條件的情形下被激發，球外會產生相似於完美電導體球或完美磁導體球的電位分布。

The finite-difference time-domain method (FDTD) has been widely used in computational electromagnetics. We construct a parallelized three-dimensional (3D) FDTD simulator in C language where several computers are used to speed-up the simulations by using the message passing interface (MPI) protocol. In this research, we use this self-constructed parallelized FDTD simulator to simulate two kinds of metal nano-particle problems. On the first part, we simulate four types of nano-antennas which are bowtie antenna, dipole antenna, contour bowtie antenna, and modified contour bowtie antenna. The local field enhancement in the antenna gap is calculated, including the broadband response and the resonant wavelength. We explore the behavior of resonances by varying the antenna geometry parameters, and the results show that these parameters will significantly influence the resonant wavelength and its peak value. For miniaturization, we add some new structural parameters into the traditional bowtie antenna, and therefore the bowtie antenna becomes a contour bowtie or modified contour bowtie antenna. The results show that these two contour antennas can red-shift the resonant wavelength without increasing the size of the antenna, and the resonant wavelength is tunable through these new added structure parameters. The second part relates to the nano-elements for optical nano-circuits. The composite nanostructures of metal and dielectric are combined in parallel or series to realize nano-filters at optical frequencies. We put the band-pass or band-stop filters in the waveguide, and the transmission coefficient is calculated. The results show that the FDTD simulations match the circuit theory calculations. Then, we calculate the electric potential distributions around the 3-D nano-spheres which consist of two hemispheres. When two hemispheres are excited near the resonant condition, the potential distributions outside the sphere become similar to the one produced by a homogeneous perfect-electric-conductor (PEC) or a perfect-magnetic-conductor (PMC) sphere.