Numerical Study on the Effect of Periodic Metal Structures on Lighting Devices Using Finite-Difference Frequency-Domain Method

本論文以二維頻域有限差分法探討在光波波段，金屬上的電子和入射的TE極化電磁波共振產生表面電漿波，引起高穿透現象以及藉近場能量提高自發放光效應。頻域有限差分法較時域有限差分法容易處理有色散介質(如金屬)的問題，但需要較多的電腦記憶體。在頻域有限差分法使用上，我們用邊界條件去處理金屬和介質之間的邊界，故能精確模擬出金屬表面電漿波在近場的分布情形。 在我們的分析上，先採用週期性單位結構。我們以TE極化的平面波入射到方形的金屬(銀)結構，來觀察表面電漿波的分布和金屬損耗效應，並探討金屬的長寬與模態之間的關係。接著我們把平面波改成用一個磁流線源或電偶極來等效一個發光波源，以模擬表面電漿波和波源之間的耦合現象。得到提升光源的發光效率和光穿透率的結果後，我們擴大金屬結構範圍來接近實際的情況。模擬結果顯示週期性金屬結構上的表面電漿波對於兩種發光波源，均可提高發光效率。 為考慮更真實的情況，我們將八百個磁流線源或電偶極排成一排，每個波源有著隨機產生的不同相位，以代表主動發光層。經一百次的統計分析後，得知在適當的條件下，這兩種波源均可藉由週期性金屬結構提升光源的發光效率和光穿透率。The objective of this thesis is to investigate the surface plasmon polariton (SPP) existing on the metal surface for inducing extraordinary transmission and enhancing the spontaneous emission rate by using the finite-difference frequency domain (FDFD) method. The FDFD method is superior to the finite-difference frequency-domain method in treating the dispersive materials, suck as metal. However, more computer memory is needed for FDFD. We match the boundary conditions to take care of the interface between the metal and the dielectric in the FDFD method. Thus the SP wave distribution on the metal surface can be accurately simulated. In the simulation process, a unit cell of the periodic structure is first adopted as our simulation domain. We use the TE plane wave incidence on the rectangular metal (silver) structure to observe the surface plasmon distribution and the metal loss effect, and to investigate the relationship between the SPP modes and the width and thickness of the metal. Next, we use a magnetic current line source or electric dipole source in place of the plane wave to examine the coupling between the SPP and a point source. When we get the results of increasing spontaneous emission rate and optical transmission, we expand the metal structure domain to fit the real situation. According to the simulation results, the surface plasma waves on the periodic metal structure indeed can enhance the emission rate of these two kinds of sources. For the more realistic situation, we use 800 magnetic current line sources or electric dipole sources with random phases and distribute them along a line. These sources may represent an active layer for lighting. After one hundred statistical realizations, we find that the spontaneous emission rate and optical transmission can be enhanced for both kinds of sources by the periodic metal structure under the suitable conditions.Content 摘要 ii Abstract iii List of Figures v Chapter 1 Introduction 1 1.1 Extraordinary optical transmission in LEDs 1 1.2 Background and Motivations 2 Chapter 2 Theoretical Formulation 4 2.1 Finite-Difference Frequency-Domain Method 4 2.1.1 Transverse electric (TE) and Transverse magnetic (TM) cases 4 2.1.2 Perfectly matched layer 11 2.2 Numerical Verification 17 Chapter 3 Numerical Results 24 3.1 Metal Structure 25 3.2 Plane Wave in the Periodic Metal Structure 26 3.3 Periodic Sources in the Periodic Metal Structure 31 3.3.1 Normalized power flow spectrum and Poynting vector 32 3.3.2 Variation of sources 38 3.4 Multiple Sources with Random Phases 42 3.4.1 Large simulation domain containing several metal structures with the magnetic current line source 43 3.4.2 Large simulation domain containing several metal structures with the electric dipole source 47 Chapter 4 Conclusions 81 References 8