Electromagnetic fields and applications for anisotropic / photonic structures

Abstract

The topic of this doctoral dissertation is oriented in two directions: the first one includes the designing of a novel dual-band implantable antenna for biomedical telemetry applications. The second is in the direction of developing computational techniques for the solution of electromagnetic problems that contain anisotropic materials, such as scattering from anisotropic cylinder, extraction of cutoff wavenumbers for metallic waveguides, with anisotropic infills and the calculation of the whispering gallery mode frequencies (WGM) for the case of a cylindrical resonator. In the first chapter of this dissertation a novel dual-band implantable antenna is designed, for biomedical telemetry purposes. More specifically, the antenna isintended to be implanted inside the human chest, i.e. for pacemaker applications. In order to design the implantable antenna, a 3-layer canonical human chest model was used as an implantation cite. Moreover, the HFSS commercial software was used in order to simulate the antenna’s performance under the aforementioned situation. The designed antenna is able to operate in two different frequency bands, so it permits the use of wake-up and sleep signals in order to extend the battery’s lifetime. Another key fact about the designed antenna is the various degrees of freedomthat it provides, so the ability to be used in other biomedical applications (retinal implants applications, intracranial pressure monitoring, etc), with minimal modification in its design. Furthermore, an extensive comparative study was performed taking into account all the possible combinations of the miniaturization techniques, showing the miniaturization limits of each one of them. In the second chapter, a coupled-field volume integral equation (CFVIE) method for electromagnetic (EM) scattering on electrically large, highly inhomogeneous gyrotropic circular cylinders, under normal incidence, is developed. The CFVIEs are solved by cylindrical Dini series expansion (CDSE) method where the unknown fields are expanded by entire domain orthogonal vectorial basis functions. The main advantage of the present method is that it permits the scatterer to have continuously varying highly inhomogeneous gyrotropic characteristics, i.e., the constitutive parameters of the cylinder can be highly inhomogeneous in both gyroelectric and gyromagnetic tensors. Initially, the two-dimensional (2-D) Green’s function (GF) is expanded in a tensorial form, using the cylindrical vector wavefunctions (CVWFs). Then, by employing the CDSE for the unknown fields, the 2-D volumetric integrals are carried out analytically, reducing the CFVIEs to a set of algebraic equations. The method is validated by comparisons of the exact solution based on the separation of variables method (SVM) for homogeneous isotropic/gyroelectric/gyromagnetic cylinders, with HFSS commercial software for two- and three-layered gyroelectric/gyromagnetic cylinders, as well as with the recently developed hybrid projection method (HPM) for electrically large continuously varying highly inhomogeneous isotropic cylinders. Results for combined gyroelectric-continuously varying highly inhomogeneous isotropic cylinders are presented and discussed.In the third chapter, a coupled-field volume integral equation (CFVIE) method is developed for the calculation of the normalized cutoff wavenumbers of circular metallic walled waveguides, having concentric continuously varying highly inhomogeneous gyrotropic (i.e., gyroelectric and gyromagnetic) infill. The normalized cutoff wavenumbers are obtained as the roots of a determinantal equation, formed by solving the CFVIEs using the cylindrical Dini series expansion (CDSE) method, where the unknown fields inside the waveguide are expanded by entire domain orthogonal Dini-type vectorial basis functions. To account for the electric boundary condition (BC) on waveguide’s circular perfect electric conducting (PEC) surface, two modified two-dimensional (2-D) tensorial Green’s functions (GFs), expanded in cylindrical vector wave functions (CVWFs), are employed in the kernels of theCFVIEs. These modified 2-D tensorial GFs are constructed by enforcing, on their dyadic form, the satisfaction of the electric boundary condition. The CDSE, along with the modified 2-D tensorial GFs, allow for the analytical integration of the volumetric-type integrals and the reduction of the CFVIEs to a set of algebraic equations. We exhaustively demonstrate the validity of the CFVIE-CDSE by a series of comparisons on the normalized cutoff wavenumbers: we firstly construct the solutions for obtaining the normalized cutoff wavenumbers in homogeneous gyrotropic waveguides by the separation of variables method (SVM), and secondly, we employ HFSS commercial software for two-layered isotropic and three-layered gyroelectric loaded waveguides. We characterize the type of modes, i.e., TE/TM or hybrid HE/EH, for each configuration presented, and discuss the efficiency of the CFVIE-CDSE method. In the fourth chapter, asymptotic closed-form expressions for the calculation of the complex TE/TM whispering gallery mode (WGM) frequencies in homogeneous gyroelectric circular cylindrical resonators of infinite length, are derived. In addition, we extend a recently developed volume integral equation-cylindrical Dini series expansion (VIE-CDSE) method, so as to support the prediction of the complex WGMs for continuously varying highly inhomogeneous gyroelectric circular cylindrical resonators. To this end, VIE’s entire domain orthogonal vectorial basisis extended to support, via asymptotic closed-form expressions, very large indices of the involved Dini-type cylindrical vector wave functions (CVWFs). This way, the eigenbasis required for the solution of the VIE becomes free of numerical instabilities, arising when very large orders of the involved Bessel functions are employed. The complex frequencies obtained by the asymptotic closed-form expressions for the case of the homogeneous gyroelectric resonator, as well as those obtained by the VIE, when the multilayered gyroelectric resonator is reduced to one layer, are validatedby comparisons with the complex roots extracted by numerically solving the TE/TM characteristic equations, obtained from the separation of variables method (SVM), using complex root-finding techniques. We demonstrate the calculation of very high order WGM frequencies for cylindrical resonators composed of homogeneous and highly inhomogeneous permittivity profiles. This asymptotic theory constitutes a rigorous tool, which may serve for the verification of method of analytical regularisation (MAR)-based numerical solutions for other non-circular inhomogeneous cylinders, and the interpretation of experimental data for applications such as WGM lasing, refractometric sensing, and magneto-optic coupling.

Το πρώτο μέρος αφορά τoν σχεδιασμό κεραίας με σκοπό την εμφύτευση της σε περιβάλλον ανθρώπινου ιστού. Πιο συγκεκριμένα, η κεραία προορίζεται για την ενσωμάτωση της σε εφαρμογές τύπου βηματοδότη, δηλαδή σε εφαρμογές που έχουν ως περιβάλλον την μορφολογία του ανθρώπινου στήθους. Επιπλέον πραγματοποιείται εκτενής συγκριτική μελέτη όλων των συνδυασμών των τεχνικών σμίκρυνσης που αναφέρονται στην βιβλιογραφία, προκειμένου να εξαχθεί ένας οδηγός για τους σχεδιαστές εμφυτεύσιμων κεραιών, όσον αφορά τις δυνατότητες σμίκρυνσης που προσφέρει ο κάθε συνδυασμός και επομένως να διευκολύνει την διαδικασία σχεδίασης.Το δεύτερο, και κύριο μέρος, της διδακτορικής διατριβής πραγματεύεται την επίλυση ηλεκτρομαγνητικών (ΗΜ) προβλημάτων διαφόρων τύπων. Αρχικά, αναπτύχθηκε μια μέθοδος με σκοπό τον υπολογισμό του σκεδαζόμενου ηλεκτρομαγνητικού πεδίου από κυλινδρικούς σκεδαστές, με άπειρο μήκος κατά μήκος του άξονα του κυλίνδρου. Κύριος πυλώνας της μεθόδου αυτής αποτέλεσε η χρήση των Coupled Fields Volume Integral Equations (CFVIEs), καθώς και η ανάπτυξη των άγνωστων πεδίων σε αναπτύγματα τύπου Dini. Η μέθοδος αυτή μπορεί να χειριστεί με ευκολία ηλεκτρικά μεγάλες διατάξεις, οι οποίες αποτελούνται από ισοτροπικά/ανισοτροπικά υλικά, ακόμη και με υψηλή ανομοιογένεια. Στην συνέχεια, αναπτύχθηκε υπολογιστική μέθοδος για την εξαγωγή των κυματαριθμών αποκοπής για την περίπτωση του κυλινδρικού κυματοδηγού κυκλικής διατομής, με μεταλλικά τοιχώματα. Η μέθοδος αυτή, επίσης, στηρίχθηκε στις CFVIEs καθώς και στα αναπτύγματα τύπου Dini. Τέλος, αναπτύχθηκε ασυμπτωτική μέθοδος για τον υπολογισμό των μιγαδικών συντονισμών των Whispering Gallery Modes (WGM) για την περίπτωση κυλινδρικού συντονιστή. Για την εξαγωγή των ασυμπτωτικών εκφράσεων χρησιμοποιήθηκε η συνάρτηση Airy.