Waveguides in Euclidian space are piecewise path connected subsets of R^n that can be written as the union of a compact domain with boundary and their cylindrical ends. The compact and non-compact parts share a common boundary. This boundary is assumed to be Lipschitz, piecewise smooth and piecewise path connected. The ends can be thought of as the cartesian product of the boundary with the positive real half-line. A notable feature of Euclidian waveguides is that the scattering matrix admits a meromorphic continuation to a certain Riemann surface with a countably infinite number of leaves [2], which we will describe in detail and deal with. In order to construct this meromorphic continuation, one usually first constructs a meromorphic continuation of the resolvent for the Laplace operator. In order to do this, we will use a well known glueing construction (see for example [5]), which we adapt to waveguides. The construction makes use of the meromorphic Fredholm theorem and the fact that the resolvent for the Neumann Laplace operator on the ends of the waveguide can be easily computed as an integral kernel. The resolvent can then be used to construct generalised eigenfunctions and, from them, the scattering matrix. Being in possession of the scattering matrix allows us to calculate resonances; poles of the scattering matrix. We are able to do this using a combination of numerical contour integration and Newton s method.

<p>This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes.</p><p>The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations.</p><p>Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications.</p> / Report code: LIU-TEK-LIC 2006:5

The finite-Difference Time Domain method (FDTD) is to derive the discrete form of the Maxwell¡¦s equations by second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space by using leapfrog for time derivatives. This method is also different with the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s impossible to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always occurs error because of the lake of the consideration. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. The purpose of this thesis is to develop the method for simulating microwave circuit, and to verify the credibility between the equivalent source method and the S-parameter method in FDTD by the simulation of active antenna and low-noise amplifier.

The focus of this study is scattering matrices in the framework of quantum graphs,more precisely the matrices which describe equi-transmission. They are unitary andHermitian and are independent of the energies of the associated system. In the firstarticle it is shown that in the case where reflection does not occur, such matrices existonly in even dimensions. A complete description of the matrices in dimensions 2, 4,and 6 is given. In dimension 6, 60 five-parameter families are obtained. The 60 matricesyield a combinatorial bipartite graph K62. In the second article it is shown that whenreflection is allowed, the standard matching conditions matrix is equi-transmitting forany dimension n. All equi-transmitting matrices up to order 6 are described. For oddn (3 and 5), the standard matching conditions matrix is the only equi-transmitting matrix.For even n (2, 4 and 6) there exists other equi-transmitting matrices apart fromthose equivalent to the standard matching conditions. All such additional matriceshave zero trace.

This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes. The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations. Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications. / <p>Report code: LIU-TEK-LIC 2006:5</p>

Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion. A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated. Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods. One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems. In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.

Photonics nowadays is one of the most rapidly developing areas of modern physics. Photonic chips are considered to be promising candidates for a new generation of high-performance systems for informational technology, as the photonic devices provide much higher information capacity in comparison to conventional electronics. They also offer the possibility of integration with electronic components to provide increased functionality. Photonics has also found numerous applications in various fields including signal processing, computing, sensing, printing, and others. Photonics, which traditionally covers lasing cavities, waveguides, and photonic crystals, is now expanding to new research directions such as plasmonics and nanophotonics. Plasmonic structures, namely nanoparticles, metallic and dielectric waveguides and gratings, possess unprecedented potential to guide and manipulate light at nanoscale. This Thesis presents the results of theoretical studies of light propagation in photonic and plasmonic structures, namely lasing disk microcavities, photonic crystals, metallic gratings and nanoparticle arrays. A special emphasis has been made on development of high-performance techniques for studies of photonic devices. The following papers are included: In the first two papers (Paper I and Paper II) we developed a novel scattering matrix technique for calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refraction index. The results demonstrate that the surface imperfections represent the crucial factor determining the $Q$ factor of the cavity. A generalization of the scattering-matrix technique to the quantum-mecha\-nical electron scattering has been made in Paper III. This has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and has provided a new insight and interpretation of the experimental observations. Papers IV and V present a novel effective Green's function technique for studying light propagation in photonic crystals. Using this technique we have analyzed surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications. In Paper VI the propagation of light in nanorod arrays has been studied. We have demonstrated that the simple Maxwell Garnett effective-medium theory cannot properly describe the coupling and clustering effects of nanorods. We have demonstrated the possibility of using nanorod arrays as high-quality polarizers. In Paper VII we modeled the plasmon-enhanced absorption in polymeric solar cells. In order to excite a plasmon we utilized a grated aluminum substrate. The increased absorption has been verified experimentally and good agreement with our theoretical data has been achieved.

Microwave radar and radiometer techniques are used to gather crucial information about the earth and its atmosphere. The ERS-1, JERS-1, RadarSAT and NASA’s Mission to Planet Earth projects are designed to study the changing global environment. In all these endeavors, the key instrument is the radar or scatterometer. The advantage of microwave radar is that it is hindered very little by clouds, fog or solar radiation. Polarimetrie sensors like the shuttle-borne SIR-C radar, provides additional information compared to single polarization systems. Correct interpretation of polarimetrie data necessitates proper understanding of the scattering mechanism. Thus theory of polarization synthesis is discussed. Solution to the Kennaugh eigenvalue problem for point targets is derived. Polarimetrie signatures of point targets are shown as surfaces of spherical co-ordinates based on the Poincare sphere. Statistics of the covariance matrix elements for distributed targets are presented. The main topic of this research report is the design and development of a multifrequency, polarimetrie scatterometer for biosphere remote sensing. The system was developed using a standard HP network analyzer, a crossed log-periodic dipole antenna and a reflector. The scatterometer functions in a linear polarization basis between the L- and X-bands and gathers full-polarimetric information. The standard S-parameter measurements using the network analyzer were related to surface and volume scattering coefficients of rough surface, snow cover and vegetation media. The scatterometer measurements were carried out in the frequency domain to make use of narrow band filters in the receiver chain. The fast Fourier transform was used to convert the frequency domain measurements to the time domain. The range resolution of the system was 20 cm; azimuthal and elevation resolutions are determined by the antenna beam widths. Range side lobes were reduced by making use of appropriate weighting (Kaiser-Bessel window) functions. In the process of receiver design, we developed a number of signal processing techniques which are illustrated using appropriate numerical examples. The accuracy of target characterization depends on the quality of scatterometer calibration. A novel technique to estimate the absolute gain and crosstalk of the radar system was developed. Using a distortion matrix approach, the cross-polarization response of the system was improved by 10 to 25 dB. The radar measurements were validated by comparing point target radar observations with the corresponding theoretical values. Also, measurements of fading decorrelation distance and decorrelation bandwidth of rough surfaces were in good agreement with the theory. Backscatter observations of vegetation and snow cover were comparable to earlier published values for a similar environment. Based on initial test results and operations capability, we propose to use the present scatterometer for ground-truthing in support of ERS-1 missions. Direct comparisons of electromagnetic backscatter coefficients are possible between the ERS-1 and the present scatterometer. These joint studies are beneficial for developing inverse scattering techniques, designing new experiments and calibrating ERS-1 radar systems for distributed target environments. / <p>Diss. Umeå : Umeå universitet, 1995</p> / digitalisering@umu

During the design and commissioning of combustion equipment, combustion associated instabilities are commonly encountered. These thermo-acoustic instabilities can cause undesirable noise, vibrations, local thermal and mechanical stresses in the combustor and are prominent in lean combustion. An often used mathematical tool to predict the instability in combustors is the so called network model where the system under study is subdivided in several subsystems and the acoustic state variables are regarded as the input/output of these subsystems. Solving this system of equations gives rise to the complex Eigen-frequencies of the system which tell if the complete system will have an unstable/stable response for specific operating conditions. In such a model it is critical to know what the influence of each subpart is on the acoustic wave propagation to correctly predict the unstable frequencies of the system. The area expansion is a common element found in combustors and the acoustic properties of the area expansion under quiescent conditions are well known, however in the presence of flow, acoustic flow interactions may occur. These interactions change the acoustic properties and are challenging to model and accurate experimental data is needed to validate the modelling. In this study, measurements of the aero-acoustic properties of an area expansion are presented, however the focus is on the experimental techniques and methods used to obtain accurate and precise measurement data in the plane wave frequency regime. The measurement accuracy of the setup used to determine the passive aero-acoustic properties of the area expansion is assessed by measuring a known impedance. Several sources of errors are identified and methods to account for these error sources are given. It is shown that the microphone impedance affects the measurement results and the upper limit of the measurement accuracy for quiescent measurements is governed by this error. The measurement precision of the setup is assessed using a multi-variate analysis and compared with results obtained from a Monte-Carlo simulation. Also the problem to determine the uncertainty of the measured complex pressures receives attention. Using a framework based on the Hilbert-transform, expressions are derived which estimate the uncertainty on the measured complex value from the background signal spectrum. The obtained knowledge is used to determine the scattering matrix of the area expansion. For the quiescent case, the measured results agree within 1.5% of the absolute values and within 1 degree in comparison with the analytical models. In the case with flow, the errors are slightly larger due to the increased flow-noise but a good correspondence with analytical models is found. Also a sudden sound absorption at high flow speeds and low frequencies is observed. / Vid konstruktion och användning av förbränningsutrustning observeras ofta instabiliteter i förbränningsprocessen. Dessa så kallade termo-akustiska instabiliteter kan orsaka buller och vibrationer samt lokala termiska och mekaniska belastningar i förbränningskammaren och de uppstår ofta vid mager förbränningen. Nätverksmodeller används ofta att förutsäga när instabiliteter uppträder och i dessa modeller är hela systemet indelat i olika delsystem och de akustiska ljudfältsstorheterna används som ingående och utgående parametrar. Löser man hela modellen, så får man de komplexa egenfrekvenser som ger information om när systemet är instabilt för vissa operativa förhållanden. I de här modellerna är det kritiskt att veta hur varje delsystem påverkar det akustiska ljudfältet om man vill få korrekta förutsägelser av de frekvenser där systemet kommer att vara instabilt. Ett areasprång är ett element som man ofta hittar i förbrännings-utrustning. Dess akustiska egenskaper är välkända utan strömning, men med strömning kan växelverkan mellan strömning och akustisk tillkomma och påverka de akustiska egenskaperna. Denna inverkan är komplex att modellera och det finns behov av noggranna mätdata för att validera sådana modeller. Denna avhandling presenterar experimentellt bestämda akustiska egenskaper för ett areasprång, men fokus är på förbättringar av de experimentella tekniker och metoder som används för att få precisa och noggranna mätdata för akustiska delelement i planvågsområdet. Den experimentella noggrannheten hos mätuppställningen bedöms genom att mäta upp en bekant impedans. Flera felkällor identifieras och metoder att utvärdera felen presenteras. Dessutom visar det sig att mikrofonimpedansen påverkar mätresultaten och impedansen begränsar mätnoggrannheten i fallet med mätningar utan strömning. Precisionen av mätuppställningen bestäms med hjälp av en multivariat analys som jämförs med en Monte-Carlo analys. Det visar sig att det är lämpligt att använda en multivariat analys för att bestämma noggrannhets-intervaller för de uppmätta spridningskoefficienterna för areasprånget. Problemet att bestämma noggrannhet för det uppmätta komplexa ljud trycket behandlas också. Med hjälp av ett ramverk baserat på Hilbert-transformen, härleds uttryck för uppskattning av noggrannheten i det uppmätta ljud trycket baserat på bakgrundsljudets spektrum. De erhållna kunskaperna används sedan för att bestämma de akustiska egenskaperna för ett areasprång. De uppmäta resultaten är inom 1.5% för absolutvärdet och 1 grad för fasen, jämfört med analytiska modeller i fallet utan strömning. Med strömning är noggrannheten något sämre, beroende på strömningsgenererat brus, men resultaten stämmer fortfarande bra överens med modellen. Dessutom observeras en plötslig ljudsabsorption för högre strömhastigheter och låga frekvenser. / <p>QC 20150522</p>

La propagation acoustique guidée est étudiée dans ce travail. La propagation des ondes acoustiques dans une direction principale est privilégiée. La méthode des éléments finis ondulatoires est donc exploitée pour extraire les nombres d'ondes. Les déformées des différents modes de conduit rigide sont aussi obtenues. Pour des conduits avec des discontinuités d'impédance, la matrice de diffusion peut être calculée à l'aide d'une modélisation par éléments finis de la partie traitée acoustiquement. Une modélisation tridimensionnelle des conduits traités acoustiquement permet une étude de la propagation pour tous les ordres des modes, de leur diffusion et du comportement acoustique des matériaux absorbants. Les réponses forcées de diverses configurations de guides d'ondes aux conditions aux limites imposées sont également calculées. L'étude est finalement étendue à la propagation acoustique dans les guides d'ondes avec un écoulement moyen uniforme. / The guided acoustical propagation is investigated in this work. The propagation of the acoustic waves in a main direction is privileged. A Wave Finite Element method is therefore exploited to extract the wavenumbers. Rigid duct's mode shapes are moreover obtained. For ducts with impedance discontinuities, the scattering matrix can be then calculated through a Finite Element modelling of the lined part. A three dimensional modelling of the lined ducts allows a study of the propagation for the full modes orders, their scattering and the acoustic behaviour of the absorbing materials. The forced responses of various configurations of waveguides with imposed boundary conditions are also calculated. The study is finally extended to the acoustical propagation within waveguides with a uniform mean flow.