FDTD Numerical Analysis Of Extraordinary Optical Transmission In Nano-Scale Periodic Metallic Structures

In the last decades, with the development of nano-technology and the invention of near-field optical microscopy, an unprecedented transformation is going on in optoelectronics; meanwhile, new interdisciplinary sciences and research orientations are born all the time. Metallic materials draw lots of attentions for their unique physical characteristics, and a new subject named plasmonics is initiated. For the reason that the dielectric constant of metal is negative in the visible and infrared region, when light radiates on the metallic structure, there is a special phenomenon appears in the interface of metal and dielectric, i.e., the electromagnetic fields are confined and enhanced around the metal surface, which is so-called surface plasmon(SP). As the SP is sensitive to materials, incident angle and wavelength, it has been widely used in lots of fields such as biological detection and chemical detection. In the last few years, the SP has been greatly developed from detection to light-guiding. The strong confinement properties of the SP could break through the diffraction limit, reduce the bend scattering and make light propagation in the nano-scale region, so it becomes possible to fabricate sub-wavelength optical devices and realize the integration of optical circuits and electric circuits. Moreover, the light transmission efficiency would be greatly improved for the electromagnetic wave interaction in periodic structures; the transmission efficiency could be higher than one on suitable conditions. The combination of the photonic crystal and the metal structure provides a new way for light control and light guiding.People want to speed up the design process and reduce the development costs by theoretical analysis and numerical simulation, because the fabrication of optical devices is a time-consuming, laborious and expensive process. Both photonic crystal and nano-scale metallic structure have complex geometry, therefore it is hard to solve the Maxwell's Equations exactly through the math analysis method. So solving the Maxwell's Equations by the numerical method is imperative. The Finite-Difference Time-Domain (FDTD) numerical method has been widely employed in microwave and optical simulations. The FDTD method is directly based on the Maxwell's Equations, and the parameters have clear physical meanings. So the FDTD simulation is accurate. Meanwhile, the time-domain iteration feature of the FDTD method could denote the time evolution of the electromagnetic fields and the results could be displayed by pseudo-color in the computer. The visualization of the electromagnetic field evolution shows the physical process clearly and eases the analysis and design. Theoretically, while the parameters of all notes are determined the targets with any shape and material could be constructed. So the FDTD method is a universal technology.In this paper, the FDTD method is employed to analyze the Extraordinary Optical Transmission (EOT) on the periodic nano-scale metallic structure and the waveguide array method is introduced to analyze the electromagnetic wave transmission on metal planes with slit array. The main content is as follows:1. A brief introduction about the research background and the numerical method in Chapter 1.The concepts and research progresses of photonic crystal and surface plasmon are introduced at the beginning of this chapter. Then four mostly used numerical methods in optical simulations, which are the Finite Element Method (FEM), the Plane Wave Expansion Method (PWM), the Beam Propagation Method (BPM) and the FDTD method, are introduced. The advantages and disadvantages of these methods are also discussed. At last the dispersion models of metal are introduced.2. Discussion on several key aspects of the FDTD method in detail. Improvement of the (FD)~2 TD algorithm in Chapter 2.The first section is about the basic FDTD algorithm. The center-difference iterative formulae of ordinary non-dispersive medium are studied firstly. Then the PML absorbing boundary condition, periodic boundary condition, source type, near-far field transform and numerical stability are described. The second section is concerned about two types of FDTD implements of the metal dispersive model. The Lubbers' (FD) ~2TD algorithm for one-dimensional plasma Drude model is improved and applied to the modified Drude model. The algorithm is extended to two-dimensional TM, TE mode and three-dimensional simulation.3. The optical property analysis of the metallic particles and the particle arrays by the FDTD method in Chapter 3.The optical properties of metal, the SPP excitation condition and the implementation are discussed. The Localized Surface Plasmon (LSP) of the nano-scale metallic particles is studied, then the near-field and far-field properties of the particle arrays are analyzed. Simulations on the metallic shell and shell arrays show that the electromagnetic resonance changes in the resonator, which is consisted of the metallic shell array, with the changes of the structure size and the source wavelength. The light could be controlled by changing the electromagnetic field distribution in the metallic shell array. The influence of the defect on the metallic shell on the shell optical properties is also studied. It is shown that the defect changes the charge distribution on the shell, so the optical properties of the structure changes greatly, and more LSP modes are excited. In the last section, the 'fake enhancement' in the FDTD simulation is discussed.4. The waveguide array method is introduced to study the Extraordinary Optical Transmission through the metal plate with slit array, and the FDTD method is employed to verify the results in Chapter 4.The mainstream Extraordinary Optical Transmission (EOT) theories, which are the surface plasmon coupling theory, the Diffracted Evanescent Wave Model (DEWM) and the Fabry-Perot Resonance (FPR) model, are introduced at first. Then the waveguide array method is introduced to study the EOT through the metal plate with slit array. After the analysis of the waveguide resonance enhancement condition and the electromagnetic coupling among waveguides, a formula is derived to calculate the EOT wavelengthes. And the results are verified by the FDTD simulation. The simulation fits well with the waveguide array theory. We find that the EOT excitation mechanism is different in different wavelength regions. When the wavelength is longer than the SPP wavelength, the EOT is mainly caused by the resonance enhancement in the slits; the EOT is excited by the SPP on the metal-dielectric interface when the wavelength is equal to the SPP wavelength; the electromagnetic distributions are hybrid modes on other EOT conditions, which satisfy both resonance enhancement and creeping wave coupling condition. Then the effect of the dielectric substrate is studied. The substrate would improve the light transmission efficiency by affecting the phases and the electromagnetic field distributions. Furthermore, The dielectric substrate with suitable thickness could greatly reduce the light scattering and be 'light transparent' on the resonance enhancement condition.In short, the FDTD method is employed to analyze the EOT in periodic nano-scale metallic structures in this thesis. A new method is introduced to analyze the EOT mechanism after study in the electromagnetic transmission in these structures, and the FDTD method is employed to study the electromagnetic transmission on different EOT excitation conditions.