Aplicação do método de Galerkin descontínuo para a análise de guias fotônicos

Orientador: Hugo Enrique Hernández FigueroaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Um novo método de onda completo para realizar a análise modal em guias de onda é introduzido nesta dissertação. A ideia central por trás do método é baseada na discretização da equação de onda vetorial com o Método de Galerkin Descontínuo com Penalidade Interior (IPDG, do inglês Interior Penalty Discontinuous Galerkin). Com uma função de penalidade apropriada, um método de alta precisão e sem modos espúrios é obtido. A eficiência do método proposto é provada em vários guias de onda, incluindo complicados guias de ondas ópticos com modos vazantes e também em guias de onda plasmônicos. Os resultados foram comparados com os métodos do estado-da-arte descritos na literatura. Também é discutida a importância dessa nova abordagem. Além disso, os resultados indicam que o método é mais preciso do que abordagens anteriores baseadas em Elementos Finitos. As principais contribuições deste trabalho são: foi desenvolvido um novo método robusto e de alta precisão para a análise de guias de ondas arbitrários, uma nova função de penalidade para o IPDG foi proposta e aplicações práticas do método proposto são apresentadas. Adicionalmente, no apêndice é apresentado uma aplicação da análise modal em simulação eletromagnética 3D com um método de Galerkin DescontínuoAbstract: A novel full-wave method to perform mode analysis on waveguides is introduced in this dissertation. The core of the method is based on an Interior Penalty Discontinuous Galerkin (IPDG) discretization of the vector wave equation. With an appropriate penalty function a spurious-free and high accuracy method is achieved. The efficiency of the proposed method was proved in several waveguides, including intricate optical waveguides with leaky modes and also on plasmonic waveguides. The obtained results were compared with the state-of-the-art mode solvers described in the literature. Also, a discussion on the importance of this new approach is presented. Moreover, the results indicate that the proposed method is more accurate than the previous approaches based on Finite Elements Methods. The main contributions of this work are: the development of a novel robust and accurate method for the analysis of arbitrary waveguides, a new penalty function for the IPDG was proposed and practical applications of the methods are discussed. In addition, in the appendix an application of modal analysis on 3D electromagnetic simulations with a Discontinuous Galerkin method is detailedMestradoTelecomunicações e TelemáticaMestre em Engenharia ElétricaCAPE

The finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides

This thesis presents a new variational finite element formulation and its implementation for the analysis of microwave and optical waveguide problem with arbitrarily- shaped cross section, inhomogeneous, transverse-anisotropic, and lossy dielectrics. In this approach, the spurious, nonphysical solutions, which ordinarily appear interspersed with the correct results of earlier vectorial finite element methods and thus have been the most serious problem in finite element analysis of waveguides, are totally eliminated. In this formulation either the propagation constant or the frequency may be treated as eigenvalues of the resulting generalized eigenvalue problem. This formulation also has the capability to find complex modes of lossless waveguides. Furthermore, the numerical efficiency of the solution is maximized since this formulation uses the most economical representation of a problem, in terms of only two vector components. This is achieved without losing the sparsity of the matrices of the resultant eigenvalue equation, which only depends on the topology of mesh used. This property is very important for solving large-size problems by efficient sparse matrix algorithms. In this work, a basic vector wave equation which involves only transverse components of magnetic field is straightforwardly derived from Maxwell equations. This differential equation incorporates the divergence condition V.B = 0 and leads to a canonical form of the resultant eigenvalue equation. The Local Potential Method is used to obtain the variational formulation. When implementing the finite element method, the Rayleigh-Ritz procedure is used to find stationary values of the functional to get the resulting generalized matrix eigenvalue equation. To show the validity and applicability of the method, a series of examples of microwave and optical waveguides including inhomogeneity, anisotropy and loss are studied. These examples show good accuracy and complete absence of spurious modes, demonstrating the effectiveness of the new formulation developed

Mode degeneration in bent photonic crystal fiber study by using the finite element method

The development of highly dispersive lower and higher order cladding modes and their degeneration with respect to the fundamental core mode in a bent photonic crystal fiber is rigorously studied by use of the full-vectorial finite element method. It is shown that changes in the bending radius can modify the modal properties of large-area photonic crystal fibers, important for a number of potential practical applications

Optical resonators based on Bloch surface waves

A few recent works suggest the possibility of controlling light propagation at the interface of periodic multilayers supporting Bloch surface waves (BSWs), but optical resonators based on BSWs are yet to demonstrate. Here we discuss the feasibility of exploiting guided BSWs in a ring resonator configuration. In particular, we investigate the main issues related to the design of these structures, and we discuss about their limitations in terms of quality factors and dimensions. We believe these results might be useful for the development of a complete BSW-based platform for application ranging from optical sensing to the study of the light-matter interaction in micro and nano structures.Comment: 10 pages, 10 figures. To be published in JOSA

A comparison between different propagative schemes for the simulation of tapered step index slab waveguides

The performance and accuracy of a number of propagative algorithms are compared for the simulation of tapered high contrast step index slab waveguides. The considered methods include paraxial as well as nonparaxial formulations of optical field propagation. In particular attention is paid to the validity of the paraxial approximation. To test the internal consistency of the various methods the property of reciprocity is verified and it is shown that for the paraxial algorithms the reciprocity can only be fulfilled if the paraxial approximation of the power flux expression using the Poynting vector is considered. Finally, modeling results are compared with measured fiber coupling losses for an experimentally realized taper structure

Experimental and theoretical study of an integrated silicon Mach-Zehnder interferometer for chemical sensing applications

This thesis involves the design, fabrication and characterization of an integrated optical waveguide sensor. Prior to fabrication, design parameters of the waveguide need to be determined and optimized. The waveguide parameters such as waveguide dimension and the refractive index of the core and cladding are obtained from the single-mode cutoff frequency calculated using either analytical or numerical methods. In this thesis, details of analytical calculations to determine the cutoff frequency in terms of the waveguide parameters will be presented. The method discussed here is Marcatili\u27s approximation. The purpose is to solve the scalar wave equation derived from Maxwell\u27s equations because it describes the mode properties inside the waveguides. The Finite Element Method is used to simulate the electric and magnetic fields inside the waveguides and to determine the propagation characteristics in optical waveguides. This method is suited for problems involving complicated geometries and variable index of refraction. Fabrication of the Integrated Mach-Zehnder Interferometer sensor involves several important standard processes such as Chemical Vapor Deposition (CVD) for thin film fabrication, photolithography for mask transfer, and etching for ridge waveguide formation. The detailed fabrication procedures of the tested Mach-Zehnder Interferometer sensors are discussed. After completion of the sensor fabrication processes, the characterizations were carried out for the thin film of Si02 and PSG, the waveguides and the Y-junction separately. The waveguides were analyzed to make sure that the sensors are working as expected. The experimental testing on the separated waveguide portions of the first batch Integrated Mach-Zehnder Interferometer (MZI) sensors are described. These testing procedures were also performed for the subsequent fabricated batches of the integrated MZI sensors until optimum performance is achieved. A new concept has been proposed for chemical sensing applications. The novelty of the approach is mainly based on utilizing the multi -wavelength or broadband source instead of single wavelength input to the integrated MZI. The shifting of output spectra resulting from the interference has shown the ability of the MZI to analyze the different concentrations of a chemical analyte. The sensitivity of the sensor is also determined from the plot of intensity versus concentration, which is around 0.013 (%ml)-1 and 0.007 (%ml)-1 for the white light source and the 1.5 ~tm broadband source, respectively, while the lowest detectable concentration of ethanol for the sensor detection is around 8% using a intensity variation method and 0.6% using a peak wavelength variation method

Third-order Optical Nonlinearities for Integrated Microwave Photonics Applications

The field of integrated photonics aims at compressing large and environmentally-sensitive optical systems to micron-sized circuits that can be mass-produced through existing semiconductor fabrication facilities. The integration of optical components on single chips is pivotal to the realization of miniature systems with high degree of complexity. Such novel photonic chips find abundant applications in optical communication, spectroscopy and signal processing. This work concentrates on harnessing nonlinear phenomena to this avail. The first part of this dissertation discusses, both from component and system level, the development of a frequency comb source with a semiconductor mode-locked laser at its heart. New nonlinear devices for supercontinuum and second-harmonic generations are developed and their performance is assessed inside the system. Theoretical analysis of a hybrid approach with synchronously-pumped Kerr cavity is also provided. The second part of the dissertation investigates stimulated Brillouin scattering (SBS) in integrated photonics. A fully-tensorial open-source numerical tool is developed to study SBS in optical waveguides composed of crystalline materials, particularly silicon. SBS is demonstrated in an all-silicon optical platform