Numerical analysis of photonic nano structures in layered geometries
Başlık çevirisi mevcut değil.
- Tez No: 401559
- Danışmanlar: DR. CHRISTIAN HAFNER
- Tez Türü: Doktora
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2013
- Dil: İngilizce
- Üniversite: Eidgenössische Technische Hochschule Zürich (ETH)
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 126
Özet
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Özet (Çeviri)
Layered geometries play a very important role in electromagnetics (EM). Their unique features (guided/surface waves, localization of energy, transmission and reection characteristics, etc) were used in a vast number of applications in the microwave and radio frequency regimes for decades. Recently, following the improvements in the fabrication techniques of structures with dimensions comparable with the wavelength of the visible spectrum, layered geometries have become quite popular in nano photonics. Following this increased interest, it has been highly desirable to analyze nano structures built in layered geometries in an efficient and reliable way. The method of multiple multipoles (MMP), which is a semi-analytic boundary discretization method, is a very strong candidate for such an analysis. But the complexity of classical MMP solutions (that use homogenous medium basis functions) increases dramatically with the number of layers, since special truncation techniques are needed for infinitely long boundaries of the layered media that requires advanced user experience. In order to tackle this problem and to use the advantages of MMP with no additional complexity, layered media Green's functions in 2D and 3D geometries are included in the MMP analysis. In MMP, linear combinations of analytical solutions of Maxwell's equations (called expansions) are used for the general analysis of structures in presence of EM radiation. Therefore, the layered media Green's functions (which require the numerical evaluation of oscillatory and singular integrals, called Sommerfeld integrations) should be obtained with a high accuracy for using them as new expansion sets inMMP. In this thesis, numerical techniques for obtaining layered media Green's functions in 2D and 3D settings with very high accuracy, are introduced. The impact of the Sommerfeld integration path on the efficiency of layered media Green's function calculations is analyzed in detail. As a result of this analysis, several rules for the shape of the Sommerfeld integration path are introduced in order to obtain the layered media Green's functions for all kinds of material parameters and thickness values of layers. Computationally demanding numerical examples are also included, in order to demonstrate the eciency of the technique together with discussions on important aspects. Several unique updates are also introduced in the definition of layered media Green's functions in order to perform new types of analyses or to further decrease the complexity of the problems. One of these updates is the modified 2D layered media Green's functions with a nonzero out-of-plane wave vector component, used in the MMP eigenvalue analysis of 2D photonic waveguides in layered geometries (in commercial software literature this is often called mode analysis). By this new technique it is possible to obtain all the physical eigenvalues (modes) of a waveguide in the range of interest, which is a demanding task for all of the well known numerical methods. The second unique update is the so called complex origin layered media Green's functions that changes the propagation pattern of fields generated by infinitesimal sources in layered geometries. This update uses the concept of complex origin multipole expansions in free space that produce beams. By using the complex origin layered expansions in MMP, it is possible to decrease the total number of expansions and the solution time for the simulations, especially for long structures compared to the wavelength. Finally, all the numerical tools needed and results of the derivations are documented as an appendix for writing a general computer code from scratch, that calculates the layered geometry Green's functions, including the updates mentioned above in 2D and 3D settings. MMP, that is used extensively in the thesis, is described including a detailed analysis of the structure of the corresponding matrix equations. The details of the MMP scattering and eigenvalue analyses for the nano structures built in layered geometries are introduced and important aspects are addressed. Various numerical examples including the comparison of results with commercial software, scattering cross section calculations, implementation of complex origin layered expansions in MMP problems, eigenvalue analysis of plasmonic waveguides and optimization of nano structures are also presented to demonstrate the efficiency of the new method in the different analyses of nano structures in layered geometries. As a result of this work, a robust, reliable and efficient numerical tool for the analysis of nano structures in layered media is presented.
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