Photonic Crystal (PC) devices are the most exciting advancement in the field of photonics. The use of computational techniques has made considerable improvements in photonic crystals design. We present here an ultrahigh quality factor (Q) photonic crystal slab nanocavity formed by the local width modulation of a line defect. We show that only shifting two holes away from a line defect is enough to attain an ultrahigh Q value. We simulated this double heterostructure nano cavity by using Finite Difference Time Domain (FDTD) technique. We observed that photonic crystal cavities are very sensitive to the frequency, size and position of the source. So we must choose the right values for these parameters.

Photonic crystal fibers (PCFs) are divided into two different kinds of fibers. The first one, index-guiding PCF, guides light by total internal reflection between a solid core and a cladding region with multiple air-holes. On the other hand, the second one uses a perfectly periodic structure exhibiting a photonic band-gap (PBG) effect at the operating wavelength to guide light in a low index core-region. A compact 2D-FDTD method based on finite-difference time-domain method is formulated and is effectively applied to analysis PCFs and PBGFs. We study the propagation features of fundamental mode and the fundamental characteristics such as effective index, modal-field diameter and chromatic dispersion in index-guiding PCFs. By optimizing the air-hole diameters and the hole-to-hole spacing of index-guiding PCFs, both the dispersion and the dispersion slope can be controlled in a wide wavelength range. We also investigate the propagation features of fundamental mode and band-gap effect of PBGFs.

The finite-difference time domain(FDTD) method is formulated by discretizing Maxwell¡¦s equation over a finite volume and approximating the derivatives with centered difference approximation. The total-field/scattered-field formulation use for simulating the uniform plane wave and the added -source formulation use for simulating the plane wave,compare the result of the electric field within metallic enclosures through aperture excited by uniform plane wave with plane wave,The larger of the exciting plane of the plane wave the more approximate to the result of the uniform plane wave .It must be very large for the induced electrical field within enclosure with a slot which vertical to interference source polarization . Generally speaking, the aperture on the enclosures not the slot but small holes on the condition of don¡¦t know interference source polarization.

Το παρακάτω κείμενο αποτελεί διπλωματική εργασία που εκπονήθηκε στο Εργαστήριο Ασύρματης Επικοινωνίας του τμήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών του Πανεπιστημίου Πατρών. Σκοπός μας, ήταν η επίλυση των εξισώσεων του Maxwell σε προβλήματα που αφορούν το σφαιρικό και το κυλινδρικό σύστημα συντεταγμένων. Στην προσπάθεια αυτή κάναμε χρήση της μεθόδου επίλυσης των πεπερασμένων διαφορών στο πεδίο του χρόνου (F.D.T.D) σε δύο ειδών εφαρμογές: η πρώτη αφορά έναν κυλινδρικό κυματοδηγό, τον οποίο μοντελοποιήσαμε με τη βοήθεια του κυλινδρικού συστήματος συντεταγμένων και η δεύτερη αφορά μια κωνική κεραία UWB, την οποία μοντελοποιήσαμε με τη βοήθεια του σφαιρικού συστήματος συντεταγμένων. Η προσομοίωση αυτών των δύο εφαρμογών γίνεται με τη βοήθεια του προγραμματιστικού περιβάλλοντος της Matlab. Επειδή η μέθοδος F.D.T.D επιλύει τις εξισώσεις του Maxwell στο χρόνο μας προσφέρει τη δυνατότητα της οπτικής απεικόνισης των πεδίων σε διάφορες χρονικές στιγμές, κάτι που μας επιτρέπει να παρατηρούμε τη χρονική εξέλιξη των φαινομένων. Η μέθοδος γίνεται ιδιαίτερα ελκυστική λόγω του επιπρόσθετου χαρακτηριστικού της απευθείας επίλυσης των εξισώσεων στροβιλισμού του Maxwell, καθιστώντας παράλληλα περιττή την επίλυση της κυματικής εξίσωσης. Στο πρώτο κεφάλαιο γίνεται μια εισαγωγή στις υπολογιστικές τεχνικές στον ηλεκτρομαγνητισμό. Επίσης γίνεται μια πρώτη αναφορά στη μέθοδο των πεπερασμένων διαφορών στο πεδίο του χρόνου (F.D.T.D), στις δυνατότητες της μεθόδου, στο πεδίο εφαρμογής της καθώς και στα πλεονεκτήματά της. Στο κεφάλαιο δύο παρουσιάζονται οι εξισώσεις του Maxwell. Συγκεκριμένα παρουσιάζονται οι εξισώσεις στροβιλισμού και οι βαθμωτές διαφορικές εξισώσεις που προκύπτουν από αυτές στις τρεις και δύο διαστάσεις. Στις δύο διαστάσεις γίνεται διάκριση σε εγκάρσιο ηλεκτρικό ρυθμό (Transverse Electric) και εγκάρσιο μαγνητικό ρυθμό (Transverse Magnetic). Τέλος παρουσιάζονται οι εξισώσεις του Maxwell που ισχύουν για τα σκεδαζόμενα πεδία. Στο κεφάλαιο τρία παρουσιάζονται τα βασικά στοιχεία της μεθόδου F.D.T.D, τα οποία πρέπει να γίνουν κατανοητά προκειμένου να αναδειχθούν τα πλεονεκτήματα και τα μειονεκτήματά της. Συγκεκριμένα παρουσιάζονται οι εξισώσεις πεπερασμένων διαφορών, που προκύπτουν από τις βαθμωτές διαφορικές εξισώσεις, που προκύπτουν από τις εξισώσεις στροβιλισμού του Maxwell. Στη συνέχεια παρουσιάζονται βασικά χαρακτηριστικά της μεθόδου, όπως η επιλογή του χωρικού και χρονικού βήματος και η δημιουργία πηγών. Μετά παρουσιάζεται η σημαντικότερη απορροφητική οριακή συνθήκη PML του Berenger και τέλος οι υπολογιστικές απαιτήσεις του αλγορίθμου F.D.T.D. Στο κεφάλαιο τέσσερα επιλύονται προβλήματα σε δύο διαστάσεις και συγκεκριμένα το πρόβλημα των ρυθμών διάδοσης TM και ΤΕ εντός κυλινδρικού κυματοδηγού με υλικό εντός του τον αέρα. Στο κεφάλαιο πέντε επιλύονται προβλήματα σε δύο διαστάσεις. Συγκεκριμένα παρουσιάζει την ανάπτυξη ενός σετ εργαλείων λογισμικού που είναι χρήσιμα στην ανάλυση κεραιών και δομών εξαιρετικά ευρείας ζώνης (UWB). Αυτά τα εργαλεία χρησιμοποιούνται στην εκτέλεση προσομοίωσης με τη μέθοδο των πεπερασμένων διαφορών στο πεδίο του χρόνου (FDTD) μίας κωνικής κεραίας με συνεχές κύμα (CW) και παλμικές διεγέρσεις UWB. Η κεραία αναλύεται με τη χρήση εξισώσεων σφαιρικών συντεταγμένων FDTD που προέρχονται από τις βασικές αρχές. Τα αποτελέσματα της προσομοίωσης για τη διέγερση τύπου συνεχούς κύματος (CW) συγκρίνονται με τα αποτελέσματα από προσομοιώσεις και μετρήσεις σε δημοσιευμένες πηγές· τα αποτελέσματα της διέγερσης UWB είναι νέα. Τα παραπάνω προβλήματα κάνουν σαφές το πόσο σημαντικό είναι να γνωρίζουμε σε βάθος τα χαρακτηριστικά της μεθόδου προκειμένου να φτάσουμε στην λύση τους. Σε περιπτώσεις όπου γνωρίζουμε τη λύση εκ των προτέρων (είτε ποιοτικά ή ποσοτικά) έχουμε τη δυνατότητα να επαληθεύσουμε την ορθότητα των αποτελεσμάτων της F.D.T.D. Οι λύσεις των προβλημάτων β ασίζονται στην εύρεση των ολικών πεδίων. Ο εναλλακτικός τρόπος της εύρεσης των σκεδαζόμενων πεδίων δεν χρησιμοποιείται. Βέβαια στα προβλήματα ακτινοβολίας κεραιών υποχρεωτικά εφαρμόζεται η διατύπωση των ολικών πεδίων. Μέσω αυτής της εργασίας έγινε σαφής η ικανότητα της F.D.T.D να εφαρμόζεται σε μεγάλη ποικιλία προβλημάτων. Κάτι που δεν έγινε σαφές είναι η δυνατότητα της μεθόδου να συνδυάζεται με άλλες μεθόδους, κάτι που μπορεί να επιφέρει σημαντική καταστολή ή και εξάλειψη των μειονεκτημάτων της. Με αυτό τον τρόπο δημιουργούνται νέες υβριδικές μέθοδοι. Με τις μεθόδους εύρεσης των ηλεκτρομαγνητικών πεδίων (όπως είναι η F.D.T.D) έχουμε τη δυνατότητα να δούμε τον ηλεκτρομαγνητισμό από νέα σκοπιά, κατανοώντας τον καλύτερα και προσαρμόζοντάς τον στις σύγχρονες ανάγκες της εποχής. / -

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O método de Ibrahim no Domínio do Tempo (ITD) é considerado um dos métodos clássicos de identificação de parâmetros modais de estruturas. As maiores vantagens da sua aplicação residem na identificação de modos muito próximos com boa precisão, em uma faixa relativamente larga de freqüências, além do número reduzido de equipamentos requeridos para a realização de ensaios experimentais. Neste trabalho foi realizada uma aplicação do método ITD no processo de identificação das freqüências naturais, dos fatores de amortecimento e dos modos de vibrar de uma placa quadrada de alumínio, engastada em um dos lados e livre nos demais. Este modelo experimental apresenta alta densidade modal e a análise foi realizada em uma faixa de freqüências de 0 a 1600 Hz através de um ensaio de impacto. Para produzir um conjunto consistente de resultados é necessário utilizar um modelo sobredeterminado para o sistema em estudo. O resultado desta análise, porém, apresenta modos computacionais que devem ser eliminados. Para tanto, foram utilizados dois índices de confiança para qualificar os resultados, sendo estes o Fator de Confiança Modal (MCF) e a Colinearidade de Fase Modal Ponderada (MPCW). Os modos que apresentaram melhores índices de confiança são considerados o resultado final do processo de identificação. / The Ibrahim Time Domain (ITD) method is considered one of the classical modal parameter identification techniques. The greatest advantages of the ITD application consist of the precise identification of closely spaced modes within a wide range of frequencies and the small amount of equipment required to accomplish experimental testing. In this work, the ITD method was applied in the process of identification of natural frequencies, damping factors and mode shapes of a cantilever aluminium plate. High modal density was detected on the experimental model and the analysis was performed on a frequency range from 0 to 1600 Hz by means of impulse testing. However, an oversized model of the test structure must be used, so that a consistent set of results can be achieved. The results, nevertheless, present computational modes that must be removed from the model. Two confidence factors were used to qualify the results, namely the Modal Confidence Factor (MCF) and the Modal Phase Collinearity - Weighted (MPCW). The modes that presented higher confidence factor values were considered as the final result of the identification process.

The Finite Difference Time Domain (FDTD) Method has been a powerful tool in numerical simulation of electromagnetic (EM) problems for decades. In recent years, it has also been applied to biomedical research to investigate the interaction between EM waves and biological tissues. In Wireless Body Area Networks (WBANs) studies, to better understand the localization problem within the body, an accurate source/receiver model must be investigated. However, the traditional source models in FDTD involve effective volume and may cause error in near field arbitrary direction. This thesis reviews the basic mathematical and numerical foundation of the Finite Difference Time Domain method and the material properties needed when modeling a human body in FDTD. Then Coincident Phase Centers (CPCs) point sources models have been introduced which provide nearly the same accuracy at the distances as small as 3 unit cells from the phase center. Simultaneously, this model outperforms the usual sources in the near field when an arbitrary direction of the electric or magnetic dipole moment is required.

Simulating wave propagation in microstrip lines with Gyrotropic magnetic substrate is considered in this thesis. Since the static internal field distribution has an important effect on the device behavior, accurate determination of the internal fields are considered as well. To avoid the losses at microwave frequencies it is assumed that the magnetic substrate is saturated in the direction of local internal field. An iterative method to obtain the magnetization distribution has been developed. It is applied to a variety of nonlinear nonuniform magnetic material configurations that one may encounter in the design stage, subject to a nonuniform applied field. One of the main characteristics of the proposed iterative method to obtain the static internal field is that the results are supported by a uniqueness theorem in magnetostatics. The series of solutions Mn,Hn, where n is the iteration number, minimize the free Gibbs energy G(M) in sequence. They also satisfy the constitutive equation M = χH at the end of each iteration better than the previous one. Therefore based on the given uniqueness theorem, the unique stable equilibrium state M is determined. To simulate wave propagation in the Gyrotropic magnetic media a new FDTD formulation is proposed. The proposed formulation considers the static part of the electromagnetic field, obtained by using the iterative approach, as parameters and updates the dynamic parts in time. It solves the Landau-Lifshitz-Gilbert equation in consistency with Maxwell’s equations in time domain. The stability of the initial static field distribution ensures that the superposition of the time varying parts due to the propagating wave will not destabilize the code. Resonances in a cavity filled with YIG are obtained. Wave propagation through a microstrip line with YIG substrate is simulated. Magnetization oscillations around local internal field are visualized. It is proved that the excitation of magnetization precession which is accompanied by the excitation of magnetostatic waves is responsible for the gap in the scattering parameter S12. Key characteristics of the wide microstrip lines are verified in a full wave FDTD simulation. These characteristics are utilized in a variety of nonreciprocal devices like edgemode isolators and phase shifters.

Simulating wave propagation in microstrip lines with Gyrotropic magnetic substrate is considered in this thesis. Since the static internal field distribution has an important effect on the device behavior, accurate determination of the internal fields are considered as well. To avoid the losses at microwave frequencies it is assumed that the magnetic substrate is saturated in the direction of local internal field. An iterative method to obtain the magnetization distribution has been developed. It is applied to a variety of nonlinear nonuniform magnetic material configurations that one may encounter in the design stage, subject to a nonuniform applied field. One of the main characteristics of the proposed iterative method to obtain the static internal field is that the results are supported by a uniqueness theorem in magnetostatics. The series of solutions Mn,Hn, where n is the iteration number, minimize the free Gibbs energy G(M) in sequence. They also satisfy the constitutive equation M = χH at the end of each iteration better than the previous one. Therefore based on the given uniqueness theorem, the unique stable equilibrium state M is determined. To simulate wave propagation in the Gyrotropic magnetic media a new FDTD formulation is proposed. The proposed formulation considers the static part of the electromagnetic field, obtained by using the iterative approach, as parameters and updates the dynamic parts in time. It solves the Landau-Lifshitz-Gilbert equation in consistency with Maxwell’s equations in time domain. The stability of the initial static field distribution ensures that the superposition of the time varying parts due to the propagating wave will not destabilize the code. Resonances in a cavity filled with YIG are obtained. Wave propagation through a microstrip line with YIG substrate is simulated. Magnetization oscillations around local internal field are visualized. It is proved that the excitation of magnetization precession which is accompanied by the excitation of magnetostatic waves is responsible for the gap in the scattering parameter S12. Key characteristics of the wide microstrip lines are verified in a full wave FDTD simulation. These characteristics are utilized in a variety of nonreciprocal devices like edgemode isolators and phase shifters.

O método de Ibrahim no Domínio do Tempo (ITD) é considerado um dos métodos clássicos de identificação de parâmetros modais de estruturas. As maiores vantagens da sua aplicação residem na identificação de modos muito próximos com boa precisão, em uma faixa relativamente larga de freqüências, além do número reduzido de equipamentos requeridos para a realização de ensaios experimentais. Neste trabalho foi realizada uma aplicação do método ITD no processo de identificação das freqüências naturais, dos fatores de amortecimento e dos modos de vibrar de uma placa quadrada de alumínio, engastada em um dos lados e livre nos demais. Este modelo experimental apresenta alta densidade modal e a análise foi realizada em uma faixa de freqüências de 0 a 1600 Hz através de um ensaio de impacto. Para produzir um conjunto consistente de resultados é necessário utilizar um modelo sobredeterminado para o sistema em estudo. O resultado desta análise, porém, apresenta modos computacionais que devem ser eliminados. Para tanto, foram utilizados dois índices de confiança para qualificar os resultados, sendo estes o Fator de Confiança Modal (MCF) e a Colinearidade de Fase Modal Ponderada (MPCW). Os modos que apresentaram melhores índices de confiança são considerados o resultado final do processo de identificação. / The Ibrahim Time Domain (ITD) method is considered one of the classical modal parameter identification techniques. The greatest advantages of the ITD application consist of the precise identification of closely spaced modes within a wide range of frequencies and the small amount of equipment required to accomplish experimental testing. In this work, the ITD method was applied in the process of identification of natural frequencies, damping factors and mode shapes of a cantilever aluminium plate. High modal density was detected on the experimental model and the analysis was performed on a frequency range from 0 to 1600 Hz by means of impulse testing. However, an oversized model of the test structure must be used, so that a consistent set of results can be achieved. The results, nevertheless, present computational modes that must be removed from the model. Two confidence factors were used to qualify the results, namely the Modal Confidence Factor (MCF) and the Modal Phase Collinearity - Weighted (MPCW). The modes that presented higher confidence factor values were considered as the final result of the identification process.