Abstract
Plasmonics is an important part of photonics that explores the interaction between electromagnetic radiation and metallic nano-structures. Metallic structures at nanometer scales exhibit many distinct and unexpected phenomena, such as extraordinary optical transmission, near field enhancement, surface enhanced Raman scanttering.Accurate and efficient computational methods are essential for studying the effects of interactions of light with metallic nanostructures. Existing numerical methods include finite element method (FEM), finite-difference time-domain (FDTD) method, discrete dipole approximation, multiple multipole method, the T-matrix method, etc. These methods have been widely used to analyze phenomena in plasmonics, but they often have limitations in accuracy or efficiency.
Many photonic devices are multiply layered, in the sense that the structure consists of a few parts where each part is a layered structure (the material properties in each region depend only on the vertical variable z). In this thesis, we develop a vertical mode expansion method (VMEM) for three-dimensional multiply layered structures. The VMEM is a rigorous computational method for solving the frequency-domain Maxwell's equations. The method relies on expanding the electromagnetic field in one-dimensional modes, where the expansion coefficients are functions satisfying two-dimensional Helmholtz equations. The method efficiently reduce the original 3D problems to 20 problems, it takes advantages of the special geometries of the structures so that the computational cost is greatly reduced. We use the VMEM to study a number of plasmonic structures.
In Chapter 1, basic concepts of plasmonics are introduced. Two fundamental excitation, surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs), are discussed. In Chapter 2, based on Maxwell's equations, we present the basic vertical mode expansion procedure. In the remaining chapters, we develop the VMEM for different kinds of multiply layered structures, including two-dimensional slit-groove structures, circular apertures, rotationally symmetric structures, multiple circular cylinders on a substrate, and biperiodic structures. The accuracy and efficiency of the method are validated by numerical results, and the properties of surface plasmons are explored based on these calculations. In summary, the VMEM is very efficient and relatively simple to implement, and it should be useful in the design and optimization of photonic structures.
| Date of Award | 21 Jun 2016 |
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| Original language | English |
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| Supervisor | Ya Yan LU (Supervisor) |