Orientador: Hugo Enrique Hernandez Figueroa / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-22T14:24:45Z (GMT). No. of bitstreams: 1 Oliveira_LucianoPradode_D.pdf: 36412783 bytes, checksum: 0d0ea68334e1df0ae3e61e59014f3f68 (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta um estudo dos efeitos dos modos espúrios na análise modal e em esquemas de propagação de feixes na modelagem de guias de onda por elementos finitos mistos. A presença dos modos espúrios no espectro das matrizes de elementos finitos é investigada e discutida a partir de uma formulação alternativa para a análise modal em guias de onda bidimensionais, onde a condição de divergente nulo é imposta inicialmente na equação vetorial de onda. Um novo esquema de propagação de feixes é proposto substituindo a componente longitudinal da equação vetorial de onda pela equação de Gauss e uma análise do efeito dos modos espúrios sobre os esquemas de propagação de feixes é realizada. Testes computacionais de convergência e estabilidade dos novos esquemas de propagação de feixes, assim como dos esquemas convencionais, são apresentados / Abstract: This work shows a study of the effects of spurious modes in the modal analysis and in beam propagation schemes based on finite element mixed for modeling bidimensional waveguides structures. The presence of spurious modes in the spectrum of the finite element matrices is investigated and discussed from an alternative formulation for modal analysis of two-dimensional waveguides, where the divergence-free condition is imposed on the vector wave equation. A new beam propagation scheme is proposed by replacing the longitudinal component of the vectorial wave equation with Gauss equation, and analysis of the effect of spurious modes on beam propagations schemes is performed. Computational convergence and stability tests for the new beam propagations schemes as well as the conventional schemes are presented / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

[pt] O objetivo deste trabalho é o estudo das características de propagação de ondas eletromagnéticas em guias de onda dielétricos contendo materiais arbitrariamente não lineares representados por uma distribuição de índice de refração que depende da intensidade local do sinal. Os guias de onda considerados neste trabalho podem ser analisados por meio de uma equação de onda unidimensional. Devido à presença de materiais não lineares, esta equação admite solução analítica apenas para certos tipos de não linearidade. De modo a permitir um estudo mais abrangente, uma solução numérica é desenvolvida para a equação de onda não linear. Esta solução numérica é então utilizada no estudo das características de propagação de guias de onda dielétricos em diversas configurações e diferentes tipos de onda dielétricos em diversas configurações e diferentes tipos de distribuição de índice de refração não linear, tanto em polarização TE como TM. O estudo mostra que estes guias de onda apresentam propriedades de propagação de potencial aplicação em dispositivos para um processador ótico de sinais ou para um computador ótico, como por exemplo histerese e bi-estabilidade óticas. É feito ainda um estudo da estabilidade das soluções da equação de onda não linear, sendo verificado que certas porções das soluções são instáveis, isto é, sofrem alteração à medida em que se deslocam ao longo do guia de onda. Além disso, foi observado a possibilidade de ocorrência, nas soluções instáveis, de rotas para o caos quando a potência do sinal é aumentada gradativamente. Em todos as etapas deste trabalho, os resultados foram comparados com outros métodos existentes na literatura. / [en] In this work, the propagation characteristics of electromagnetics waves in dieletric waveguides with arbitarily non-linear materiais, represented by a distribution of refractive index that depends on the local intensity of the signal, is presented. The waveguides here considered are analysed by means of an unidimensional equation. Due to the non- linearity of the materials this equation has analytical solution only for few types of non-linearities. To permit a more abrangent study, a numerical solution for the non- linear wave equation was developed. This solution is applied to the study of propagation characteristics of dielectric waveguides with different distributions of refractive index, either for TE and TM polarization. It is shown that these waveguides have propagation properties, like hysteresis and optical bi-stability, that fine applications in optical devices and optical computers. It´s also made a study of the stability of the solution of non-linear wave equation, showing that some portions of the solutions are usntable that is, they are a function of the observation point in the waveguide. The possibility of CAOS for unstable solutions, when the power is gradually increased, was also observed. At each step of this work, all results are compared with those of other methods of the literature.

Röntgenmikroskopie ist in den vergangenen Jahren zu einer leistungsfähigen und vielseitigen bildgebenden Methode in vielen Bereiche der Wissenschaft geworden, mit der opake Medien bei hoher räumlicher Auflösung untersucht werden können. Es bleibt jedoch eine Herausforderung, geeignete Röntgenlinsen herzustellen, wie z.B. Frsenlesche Zonenplatten oder refraktive Linsen. In einem alternativen Ansatz linsenloser Abbildung wird die Probe mit kohärenter Röntgenstrahlung beleuchtet. Die Probeninformation wird dann aus dem aufgenommenen Streubild durch numerische, iterative Algorithmen rekonstruiert. In dieser Arbeit wird zunächst die Grundlage von linsenloser holographischer Abbildung mit Röntgenwellenleitern erläutert und zu einem Konzept der Röntgeninterferometrie mit Wellenleitern erweitert. Die spezifische Instrumentierung, die erforderlich war für Demonstrationsexperimente mit Röntgenwellenleitern zur holographischen Abbildung, wird erklärt und die erzielten Ergebnisse präsentiert. Basierend auf diesen Ergebnissen der Demonstrationsexperimente wurde ein Instrument zur holographischen Abbildung mit Röntgenwellenleitern entwickelt und aufgebaut. Die Spezifikationen und Eigenschaften des Kirckpatrick-Beaz Spiegelsystems und anderen mechanischen und optischen Komponenten werden beschrieben und experimentell charakterisiert, zusammen mit dem Steuerungssystem und verschiedenen verfügbaren Detektoren. Erste Ergebnisse belegen die hohe Abbildungsqualität des vorgestellten Instruments.

Optical polymers are a subject of research and industry implementation for many decades. Optical polymers are inexpensive, easy to process and flexible enough to meet a broad range of application-specific requirements. These advantages allow a development of cost-efficient polymer photonic integrated circuits for on-chip optical communications. However, low refractive index contrast between core and cladding limits light confinement in a core and, consequently, integrated polymer device miniaturization. Also, polymers lack active functionality like light emission, amplification, modulation, etc. In this work, we improved a performance of integrated polymer waveguides and demonstrated active waveguide devices. Also, we present novel Si QD/polymer optical materials. In the integrated device part, we demonstrate optical waveguides with enhanced performance. Decreased radiation losses in air-suspended curved waveguides allow low-loss bending with radii of only 15 µm, which is far better than &gt;100 µm for typical polymer waveguides. Another study shows a positive effect of thermal treatment on acrylate waveguides. By heating higher than polymer glass transition temperature, surface roughness is reflown, minimizing scattering losses. This treatment method enhances microring resonator Q factor more than 2 times. We also fabricated and evaluated all-optical intensity modulator based on PMMA waveguides doped with Si QDs. We developed novel hybrid optical materials. Si QDs are encapsulated into PMMA and OSTE polymers. Obtained materials show stable photoluminescence with high quantum yield. We achieved the highest up to date ~65% QY for solid-state Si QD composites. Demonstrated materials are a step towards Si light sources and active devices. Integrated devices and materials presented in this work enhance the performance and expand functionality of polymer PICs. The components described here can also serve as building blocks for on-chip sensing applications, microfluidics, etc. / <p>QC 20171207</p>

Afin de réduire le bruit dans les villes, il est nécessaire d’avoir une bonne compréhension de la propagation acoustique en milieu urbain. Il existe aujourd’hui des logiciels commerciaux qui permettent de modéliser des champs acoustiques urbains à des coûts de calcul raisonnables. Toutefois, ces outils sont basés principalement sur des approches énergétiques qui ne contiennent pas d’informations sur la phase. Pour cette raison, elles ne permettent pas la prise en compte d’effets d’interférence (par exemple, des résonances), nous offrant ainsi une description physique limitée du champacoustique. Inversement, des méthodes ondulatoires classiques (FEM, BEM, FDTD) permettent de prendre en compte ces effets. Or, en raison de la discrétisation et de la grande extension du domaine de propagation, leur utilisation est généralement limitée aux très basses fréquences.L’objectif principal de cette thèse est de développer des méthodes ondulatoires performants, dans le domaine fréquentiel et temporel, nous permettant de modéliser la propagation acoustique dans des zones urbaines étendues. L’approche proposée est basée sur une formulation mixte modale–éléments finis. L’idée clé de cette méthode estde considérer la rue comme un guide d’ondes ouvert, dont la base modale est composée de modes de fuite (modes qui rayonnent une partie de leur énergie en se propageant). Cette approche combine une description multimodale du champ acoustique dans la direction longitudinale et un calcul par éléments finis des modes propres transverses.L’approche a été mise en oeuvre précédemment à l’échelle d’une seule rue. Dans cette thèse, nous nous intéressons à l’extension de la méthode à l’échelle du quartier, afin de modéliser la propagation dans des milieux contenant un grand nombre de rues interconnectées. Une version simplifiée dans le domaine temporel, contenant uniquement lemode de propagatif le moins fuyant, est également développée.En nous basant sur ces approches, nous étudions des phénomènes ondulatoires qui peuvent apparaître dans des configurations urbaines particulières. Plus précisément, nous nous intéressons à l’interaction des modes de la rue avec des résonances dans une cour intérieure adjacente, ainsi qu’à la formation de bandes de fréquences interditesdans des réseaux périodiques de rues interconnectées. Le résultat principal de cette étude est que, malgré la forte présence de pertes par radiation dans le milieu, des effets de résonance importants peuvent encore se produire. Les résultats présentés dans ce manuscrit mettent en évidence l’importance d’une approche ondulatoire pour décrirecorrectement des champs acoustiques aux basses fréquences, et ils suggèrent l’usage potentiel de ces phénomènes afin de contrôler la propagation acoustique dans le milieu.Enfin, nous présentons une étude sur l’utilisation de métasurfaces (surfaces contenant un réseau de résonateurs) pour améliorer la performance des murs antibruit. Nous démontrons que, grâce à l’excitation des résonances locales sur la métasurface, il est possible d’obtenir des propriétés non conventionnelles, comme par exemple des angles de réflexion négatifs ou de l’absorption acoustique aux basses fréquences. / The improvement of the urban sound environment requires a good understanding of the acoustic propagation in urban areas. Available commercial softwares give the possibility to simulate urban acoustic fields at relatively low computational costs. However, these tools are mainly based on energy methods that do not contain information on the phase. Therefore, these tools are unable to capture interference effects (e.g., resonances), providing a limited physical description of the acoustic field. Conversely, classical wave methods such as FEM, BEM or FDTD give the possibility to model interference effects, but their use is often restricted to very low frequencies due to discretisation and the huge extension of the propagation domain.The main goal of this thesis is to develop efficient wave methods for the acoustic propagation modelling in extended urban areas, both in the frequency and time domain. The proposed approach is based on a coupled modal–finite elements formulation. The key idea is to consider the urban canyon as an open waveguide with a modal basis composedof leaky modes, i.e., modes that radiate part of their energy into the atmosphere as they propagate. The approach combines a multimodal description of the acoustic field in the longitudinal direction and a finite elements computation of the transverseeigenmodes. This coupled approach, which has been successfully implemented at the scale of a single street, is extended in the present manuscript at a larger scale (the neighbourhood scale), in order to model problems arising in propagation domains containing many interconnected streets. A time domain version of the method, containing only the least damped mode, is also proposed.Using these methods, we investigate wave phenomena arising in specific urban configurations, as forbidden frequency bands in periodic networks of interconnected streets, and resonances in inner yards. It is found that, despite the presence of significant radiative losses in the propagation medium, strong interference effects are still observed. Not only this result highlights the relevance of a wave approach to describe accurately urban acoustic fields at low frequencies, but it suggest the potential use of these phenomena to control the acoustic propagation in urban environments.The last part of this dissertation presents a preliminary study on the use of metasurfaces (surfaces decorated with an array of resonators) to improve the performance of noise barriers. It is shown that, exciting resonances in these structures, it is possible to achieve some unconventional behaviours, including negative angles of reflection and low frequency sound absorption.

Orientadores: Hugo Enrique Hernández Figueroa, Gustavo Silva Wiederhecker / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-26T11:40:14Z (GMT). No. of bitstreams: 1 MalheirosSilveira_GilliardNardel_D.pdf: 5160562 bytes, checksum: 33058c0e1fc01da7e9a2ea1ab88b0ad4 (MD5) Previous issue date: 2014 / Resumo: Esta tese aborda o emprego de nano-antenas e antenas ópticas com configurações e materiais diversos, envolvendo atividades de modelagem e simulação. Tais propostas visam viabilizar novas soluções para problemas desafiadores de acoplamento, e também, de comunicação, no sentido da tecnologia de comunicações sem-fio entre dispositivos ópticos integrados, incluindo os do tipo plasmônico. Neste sentido, foram avaliadas novas propostas de nano-antenas; com particular ênfase em estruturas baseadas nas chamadas antenas dielétricas ressonantes / Abstract: This thesis addresses the use of nano-antennas and optical antennas with various configurations and materials, involving modeling and simulation activities. Such proposals are intended to enable new solutions to challenging problems of coupling, and also, communication, in the sense of wireless communications between integrated optical devices, including the plasmonic ones. Accordingly, proposals for new nano-antennas were evaluated; with particular emphasis on structures based on the dielectric resonator antennas / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Le présent travail a été consacré à l'étude des non linéarités de troisième ordre dans des structures intégrées à base de silicium exploitant des configurations de cavités à miroir de Bragg (nanobeam) et guides à cristaux photoniques à modes lents. Tout d'abord, nous avons développé une méthode non destructive à faisceau unique pour caractériser les effets de troisième ordre instantanés, c’est-à-dire la quantification de la susceptibilité complexe effective dans les guides d'ondes. La méthode a été dénommée "Top-hat D-Scan bi-directionnelle" et constitue un analogue temporel de la méthode Top-hat Z-Scan développée précédemment. Nous avons établi un modèle analytique et numérique et nous rendons compte de la première mesure d'un guide d'ondes en silicium utilisant une impulsion mis en forme dans un étireur et complétée par une procédure d’injection bi-directionnelle. L’ensemble instrumental développé constitue une expérience de métrologie des effets non-linéaires dans des guides d’ondes silicium au meilleur niveau de l’état de l’art. La méthode proposée a été validée dans des guides SiGe, chalcogénures et nitrure du silicium. Forts de cet outil métrologique, nos travaux d’exploration des interactions non linéaires lumière-matière ont été consacrés à deux grandes familles de nanostructures photoniques : des microcavités optiques et guides d'ondes en régime de lumière lente. Dans la première des deux situations, les variations d'indice provoquées par les non linéarités sont responsables d’un décalage des fréquences de résonance excluant sa coïncidence avec la fréquence du signal d'excitation et diminuant ainsi l'efficacité de l'injection optique de manière drastique. Afin de maintenir le bénéfice de localisation de la lumière tout au long de l'excitation pulsée, nous avons expérimentalement et numériquement étudié le comportement d'une cavité en silicium conçue, fabriquée, et enfin excitée par une impulsion présentant une puissance crête élevée. En contrôlant temporellement la phase des composantes spectrales injectée, la relation de phase spectrale compensant la dérive de fréquence non linéaire de la résonance de la cavité, nous avons effectué la première démonstration expérimentale de l'excitation cohérente d'une micro-cavité silicium non linéaire. Enfin, nous avons consacré des efforts importants pour concevoir, fabriquer et caractériser des guides d'ondes à cristaux photoniques (SPhCW) en silicium à fente, matrice d’une intégration hybride de matériaux optiques non-linéaires sur silicium. Les résultats rapportés fournissent la première preuve expérimentale d’un contrôle précis des propriétés de dispersion de guides à cristaux photoniques à fente propres à être remplis par des matériaux souples comme des polymères ou des couches minces dopées. La dispersion de groupe des modes lents guidés est contrôlable en signe et en amplitude et correspond à des bandes passantes optiques exploitables (~10nm). Ces résultats démontrent l’intérêt direct pour le traitement des données tout-optique sur puce des guides à modes lents à cœur creux utilisant des effets optiques non linéaires d’ordre trois pour le traitement tout-optique des données sur puce. / All-optical signal processing implemented in silicon photonics is considered as a promising route to solve several bottlenecks for the realization of future dense and mixed integrated electronic and photonic chips including ultrahigh data bit rate issues and power consumption constraints. In the context of the planar silicon photonics technology, a dramatic reduction of the needed power to reach optical nonlinear effects is obtained due to the sub-micrometer size of silicon wires (~450nmX260nm) in the telecommunication wavelength window, although silicon does not exhibit second-order response (χ^((2))) due to the centrosymmetry of its lattice. Moreover, third-order effects (χ^((3))) are partially spoiled in this material due to the strength of the two-photon-absorption (TPA) effect, which in turn generates free-carriers inducing additional absorption and refractive index changes. One way to overcome this limitation is the hybrid integration on silicon of low index soft materials with luminescence or nonlinear optical properties lacking to silicon. In this context, the present work is devoted to the study of third order nonlinearities in silicon-based integrated structures exploiting enhanced electromagnetic field effects (e.g. in Si resonators and slow light waveguides). First, we have developed a dedicated single beam non-destructive method to characterize the instantaneous third order effects though the quantification of complex effective waveguide susceptibility. The method is named “Bi-directional top-hat D-Scan” and consists on a temporal analogous of the top-hat Z-Scan. We have established an analytical and numerical model and we report the first measurement of a silicon waveguide by using a pulse shaping set-up and a bi-directional procedure. The originality of our methods stands in the capability to measure in two steps : the 3rd order nonlinear Figure-Of-Merit (FOM) independently of the injection losses, and the effective nonlinear waveguide parameters (Kerr and TPA) taking into account measured coupling losses at each facet. Furthermore, we apply the method to other integrated novel materials including Ge-rich GeSi alloys, carbon nanotube doped thin films, and chalcogenide waveguides. Additionally, two further enhancements of light-matter nonlinear interactions have been explored within this work: optical microcavities and slow light waveguides. In the first picture, index variations caused by non-linearities shift the resonance frequencies precluding the coincidence with the excitation signal frequency, thereby decreasing the injection efficiency. In order to maintain the benefit of light localization throughout the pulsed excitation, we have experimentally and numerically studied the behavior of a designed and fabricated silicon nanobeam cavity excited by a high power tailored chirped pulse whose spectral phase relation compensates for the nonlinear frequency drift of the cavity resonance. We report a numerical study of this first experimental demonstration of the coherent excitation of a nonlinear micro-cavity, leading to an enhanced intra-cavity nonlinear interaction. Finally, we have dedicated efforts to engineer, fabricate and characterize silicon slot photonic crystal waveguides (SPhCW) in order to compensate their strong dispersion present in the slow light regime while taking benefit from large group index light propagation. We showed that their frequency dispersion properties can be engineered from anomalous to normal dispersion, along with zero group velocity dispersion (ZGVD) crossing points exhibiting a Normalized Delay Bandwidth Product (NDBP) as high as 0.156. The reported results provide the first experimental evidence for an accurate control of the dispersion properties of fillable periodical slotted structures in silicon photonics, which is of direct interest for on-chip all-optical data treatment using nonlinear optical effects in hybrid-on-silicon technologies.

Le but de cette thèse est de développer des sources d’intrication photonique en vue d'applications en sciences information quantique. Dans ce contexte, nous présentons une source très performante et entièrement guidée permettant, au moyen d'une boucle de Sagnac, la génération d'états hyper-intriqués en polarisation et en énergie-temps. La configuration guidée rend le dispositif versatile, efficace et compatible avec une large bande spectrale, répondant ainsi au besoin des systèmes et réseaux de communication fibrés. À cette fin, nous avons distribué simultanément dans différents canaux télécoms des paires de photons hyper-intriqués au moyen de multiplexeurs en longueur d'onde à 5 canaux (DWDM), augmentant de fait le débit. La qualité de l'intrication est validée par la violation d'une inégalité de Bell étendue à un espace de Hilbert à 16 dimensions. Afin de pouvoir interfacer des photons aux longueurs d'ondes des télécommunications avec les bandes d'absorption des mémoires quantiques situées dans le visible, nous avons également développé une interface cohérente en longueur d'ondes. Un nouveau dispositif de métrologie quantique permettant la mesure avec une précision inégalée des effets de la dispersion chromatique dans les fibres optiques standards est également proposé. Notre approche "quantique" améliore la précision par un facteur 2.6 par rapport aux méthodes de mesures conventionnelles. Dans ce même contexte, nous avons aussi implémenté un nouveau protocole de métrologie de la phase de deux photons en ne détectant uniquement qu'un seul photon. Cette réalisation ouvre la voie à des applications potentielles simples s'appuyant sur peu de ressources au niveau de la détection. Finalement, dans la perspective de la miniaturisation de dispositifs quantiques, nous avons démontré un générateur d'intrication annoncée intégré sur puce qui trouve des applications en calcul et métrologie quantique. / The aim of this thesis was to develop photonic entanglement sources and study their implementation in the general field of quantum information technologies. To this end, a novel fully wave-guided, high performance photonic entanglement source is presented, able to generate hyper-entangled states in the observables of polarization and energy-time by means of a nonlinear Sagnac loop. The waveguide-based design makes it flexible, reliable, and adaptable to a wide spectral range, paving the way towards compact photonic entanglement generators, compatible with fiber-based communication systems and networks. This has been underlined by generating and distributing hyperentanglement in 5x2 dense wavelength division multiplexed channel telecom pairs, simultaneously, towards higher bit rates. The quality of the generated entanglement has been qualified by violating the Bell inequalities in a 16-dimension Hilbert space. Moreover, to adapt the wavelength of the entangled telecom photon pairs to the absorption wavelength of current quantum memory systems, a coherent wavelength converter is demonstrated. Furthermore, within the framework of quantum metrology, a new concept for a high-precision chromatic dispersion (CD) measurement in standard single mode fibers is introduced and demonstrated. In this demonstration, due to conceptual advantages enabled by quantum optics, an unprecedented 2.6 times higher accuracy on CD measurements is shown, compared to state-of-the-art techniques. In the same context, a new protocol for measuring two-photon phase shifts is performed using single photon detection only, promising scalable and potential real device applications with limited resources and simplified detection schemes. Finally, any potential application of quantum optics will be realized using small-scale devices. In this framework, an integrated on-chip heralded path entanglement generator is demonstrated, and shown to be adaptable to logic gate operations.

[pt] Transformadores de guia de onda são amplamente empregados no projeto de componentes em onda guiada e são encontrados em praticamente todas as cadeias alimentadoras de antenas e demais estruturas de onda guiada na faixa de microondas. Embora a teoria de transformadores seja conhecida, os requisitos de ordem sistêmica têm levado os projetos de transformadores de guia de onda ao seu limite. Para tal nível de exigência, e considerando o número de variáveis no projeto de transformadores, técnicas numéricas de análise (tais como FDTD e expansão modal dentre outros), e otimização têm sido obrigatoriamente empregadas. Por outro lado, o número de variáveis de um transformador, acaba sendo um processo de alto consumo de tempo computacional, incoerente com o porte e objetivo de custo desses transformadores. Este trabalho propõe uma possibilidade alternativa para a análise mais rápida para essas estruturas, através do emprego de formulações fechadas derivadas de métodos varacionais. Um modelo heurístico é proposto para o caso de descontinuidades em dois planos, sejam para o caso de descontinuidades homogêneas ou para não-homogêneas. / [en] Waveguide transformers are widely used on antenna’s feeder chains and other microwave devices. Although the theory of quarter wavelength transformers is well known, the current electrical performance of such microwave devices has been pushing the waveguide transformers design to its limit. For attending such level of requirements, and considering the number of existing variables on a waveguide transformer design, very accurate numerical techniques has been applied on its analyses, (such as FDTD, mode matching, etc), and optimization techniques as well. On the other hand, such numerical techniques are very memory and/or CPU/time consuming, which do not match with the cost objective of those simple concept transformers. This work proposes an alternative technique, based on close-form models derived from varational theory. A heuristic model is also proposed for attending the two plane transformer case, which can be easily applied for both homogeneous and inhomogeneous structures. Keywords Waveguide;

This thesis is devoted to numerical simulations of integrated optical isolators and circulators. The results contain: Polarization independent isolators Different magneto-optical configurations are required to produce large nonreciprocal phase shifters for orthogonally polarized modes. The polarization independent isolator can be realized by placing two different nonreciprocal phase shifters into the interferometer arms. The light interferes constructively or destructively at the end of the interferometer depending on the propagation direction. Another possibility is to find a magnetic configuration that yields equal nonreciprocal phase shift for transverse electric (TE) and transversemagnetic (TM) modes. Compared to the concept of polarization independent isolators with two different phase shifters in the interferometer arms, the concept with a polarization independent phase shifter has an advantage: the entire length of the device can be almost halved placing an additional nonreciprocal phase shifter into the second arm. Another advantage is that the power loss inside the nonreciprocal phaseshifter may differ from that in the rest of the structure. For the non-symmetrical setup it can lead to a reduction of the device performance. Utilization of multimode waveguides in magneto-optical devices The principle distinction of a Mach-Zehnder type isolator and an isolator based on multimode imaging is that in the latter case the input power is distributed between modes propagating in the same waveguide, whereas in the first case two separate waveguides are used. Nonreciprocal phaseshifters with different effects on guided modes are needed to produce a magneto-optic multi-mode imaging (MMI) isolator or circulator. Multimode imaging splitters with non zero phase difference between the output modes can be used in integrated optical isolators. If the essential phase difference is utilized by the splitter, the rest of the interferometer should be symmetrical.