This paper describes simulation, technology- and process development for the manufacturing of single mode polymeric waveguides by photolithography. Simulations for single mode operation in O- and C-band are carried out. Waveguides are directly patterned with UV-photolithography using Ormocere®-material. Fiber to waveguide coupling and near field are characterized.

the presented work demonstrates the fabrication process of the master for nano-imprint lithography (NIL) stamp for multi-mode waveguide (MM-WG) with μ-mirror using hybrid-lithography, which includes a 2-photon-polymerization direct laser writing process (2PP-DLW) for μ-mirror surface and UV-photo lithography for MM-WGs. For the definition of the mirror surface at either end of waveguides in the master stamp, the 2PP-DLW process was used. It offers a lower surface roughness (< 0.1 λ) with fewer processing steps, alignment accuracy of ± 1 μm, prints fine and sharp contours, and relatively faster scanning for a specific material, which makes it the foremost technology over the traditional micro-mirror processes such as the dicing process, moving mask lithography, laser ablation, wet etching, and dry etching. For the fabrication of the waveguide core with rectangular cross-sections in the master stamp, UV mask exposure with SU-8 was used. It is a mass-production and low-cost technique. It gives a smooth structure with 90-degree sidewalls compared to other processes like dry etching, wet etching, mosquito method, and E-beam writing. We demonstrated the design and process of a master pattern with a density range from 0.04 to 0.2 to maintain equal pressure over the stamp in the NIL step for an almost uniform residual thickness layer.:Abstract Introduction Design of Experiments Experimental Results and Discussions Conclusion

The reliable quantitative detection of biomarkers and pathogens at picomolar or even lower concentration would be a great help in point-of-care testing but is not readily available today. Integrated optical waveguides, which interact with the biochemical species to be monitored, are promising candidates for the detection of such ultra-low concentrations. The focus of this thesis is on optical waveguides in the shape of micro-ring or micro-racetrack resonators that are manufactured by UV-assisted nanoimprint lithography. This replica manufacturing technology is analyzed using analytical and numerical models in order to identify and quantify the main influence factors that determine the limit of detection of such biosensors. Potential biosensor applications are evaluated and general design rules are derived. The resulting measurements confirm the high potential of the chosen approach with respect to excellent sensitivity, low limit of detection and high dynamic range. With suitable optimization of the sensor layout, a further improvement of the performance by one to two orders of magnitude is possible.:Editor’s Preface Variables and constants Abbreviations 1 Introductions 1.1 Medical laboratory diagnostics 1.2 Biosensor technologies for point-of-care testing 1.3 Integrated optical waveguides and microresonators 1.4 Outline of the thesis 2 Basics 2.1 Guided waves in planar optical waveguides 2.1.1 Planar optical waveguides 2.1.2 Propagation of optical waves 2.1.3 Coupled modes in waveguides 2.2 Planar optical microresonators 2.2.1 Basic layouts and parameters 2.2.2 Manufacturing 2.2.3 Biosensing 2.3 Functionalization and biofunctionalization 3 UV-NIL Polymer Microresonator Biosensor Design 3.1 UV-assisted nanoimprint lithography 3.2 Waveguide cross-sections and refractive indices 3.2.1 Analytical waveguide modeling 3.2.2 Mode diagrams 3.2.3 Conclusions 3.3 Waveguide coupling 3.4 Waveguide losses 3.4.1 Absorption loss 3.4.2 Roughness loss 3.4..3 Substrate loss 3.4.4 Radiation loss due to bending 3.5 Sensitivity of the effective index to analyte binding 3.6 Overall sensitivity and detection limit 3.7 Generic design guidelines 3.8 Parameter selection for UV-NIL polymer waveguides 3.9 Comparison of polymer and silicon-based waveguides 3.9.1 Waveguide geometry 3.9.2 Radiation loss due to bending 3.9.3 Material damping 3.9.4 Surface roughness 3.9.5 Coupling channel widths and coupling coefficients 3.9.6 Conclusions 4 Characterization and Proof of Concept 4.1 Manufacturing-based design limits and chosen designs 4.2 Measurement setup and characterization process 4.3 Optical properties of UV-NIL polymer microresonators 4.4 Proof of concept 4.4.1 Sensitivity to bulk solutions 4.4.2 Reproducibility and drift 4.4.3 Comparison with theory 4.4.4 Comparison with literature 4.4.5 Sensitivity improvement 4.5 Asymmetry of the resonance curves 4.5.1 Cavity lifetime 4.5.2 Thermal influence 4.5.3 Summary 4.6 Conclusions 5 Integration into a biosensor platform 5.1 Chemical functionalization by oxygen plasma 5.2 Preparation of a biosensor characterization assay 5.2.1 Binding of fluorescent nanoparticles onto polymer surfaces 5.3 Microfluidic system 5.3.1 Programmable microfluidic system 5.3.2 System evaluation and improvement 5.4 Conclusions 6 Conclusions Declaration of authorship Acknowledgements Publications and awards / Der zuverlässige quantitative Nachweis von Biomarkern und Krankheitserregern in pikomolarer oder noch niedrigerer Konzentration wäre eine große Hilfe bei Tests am Point-of-Care, ist aber heute nicht ohne weiteres verfügbar. Integrierte optische Wellenleiter, die mit den zu überwachenden biochemischen Spezies interagieren, sind vielversprechende Kandidaten für den Nachweis solcher ultraniedriger Konzentrationen. Der Schwerpunkt dieser Arbeit liegt auf optischen Wellenleitern in Form von Mikro-Ring- oder Mikro-Spur-Resonatoren, die durch UV-unterstützte Nanoimprint-Lithographie hergestellt werden. Diese Replika-Herstellungstechnologie wird mit Hilfe analytischer und numerischer Modelle analysiert, um die wichtigsten Einflussfaktoren zu identifizieren und zu quantifizieren, die die Nachweisgrenze solcher Biosensoren bestimmen. Potenzielle Biosensoranwendungen werden bewertet und allgemeine Designregeln abgeleitet. Die daraus resultierenden Messungen bestätigen das hohe Potenzial des gewählten Ansatzes in Bezug auf ausgezeichnete Empfindlichkeit, niedrige Nachweisgrenze und hohen Dynamikbereich. Bei geeigneter Optimierung des Sensorlayouts ist eine weitere Verbesserung der Leistung um ein bis zwei Größenordnungen möglich.:Editor’s Preface Variables and constants Abbreviations 1 Introductions 1.1 Medical laboratory diagnostics 1.2 Biosensor technologies for point-of-care testing 1.3 Integrated optical waveguides and microresonators 1.4 Outline of the thesis 2 Basics 2.1 Guided waves in planar optical waveguides 2.1.1 Planar optical waveguides 2.1.2 Propagation of optical waves 2.1.3 Coupled modes in waveguides 2.2 Planar optical microresonators 2.2.1 Basic layouts and parameters 2.2.2 Manufacturing 2.2.3 Biosensing 2.3 Functionalization and biofunctionalization 3 UV-NIL Polymer Microresonator Biosensor Design 3.1 UV-assisted nanoimprint lithography 3.2 Waveguide cross-sections and refractive indices 3.2.1 Analytical waveguide modeling 3.2.2 Mode diagrams 3.2.3 Conclusions 3.3 Waveguide coupling 3.4 Waveguide losses 3.4.1 Absorption loss 3.4.2 Roughness loss 3.4..3 Substrate loss 3.4.4 Radiation loss due to bending 3.5 Sensitivity of the effective index to analyte binding 3.6 Overall sensitivity and detection limit 3.7 Generic design guidelines 3.8 Parameter selection for UV-NIL polymer waveguides 3.9 Comparison of polymer and silicon-based waveguides 3.9.1 Waveguide geometry 3.9.2 Radiation loss due to bending 3.9.3 Material damping 3.9.4 Surface roughness 3.9.5 Coupling channel widths and coupling coefficients 3.9.6 Conclusions 4 Characterization and Proof of Concept 4.1 Manufacturing-based design limits and chosen designs 4.2 Measurement setup and characterization process 4.3 Optical properties of UV-NIL polymer microresonators 4.4 Proof of concept 4.4.1 Sensitivity to bulk solutions 4.4.2 Reproducibility and drift 4.4.3 Comparison with theory 4.4.4 Comparison with literature 4.4.5 Sensitivity improvement 4.5 Asymmetry of the resonance curves 4.5.1 Cavity lifetime 4.5.2 Thermal influence 4.5.3 Summary 4.6 Conclusions 5 Integration into a biosensor platform 5.1 Chemical functionalization by oxygen plasma 5.2 Preparation of a biosensor characterization assay 5.2.1 Binding of fluorescent nanoparticles onto polymer surfaces 5.3 Microfluidic system 5.3.1 Programmable microfluidic system 5.3.2 System evaluation and improvement 5.4 Conclusions 6 Conclusions Declaration of authorship Acknowledgements Publications and awards

No description available.

The present work deals with the development and application of an acoustic long-period fiber grating (LPG) in conjunction with a special optical fiber (SF). The acoustic LPG converts selected optical modes of the SF. Some of these modes are characterized by complex, yet cylindrically symmetric polarization and intensity patterns. Therefore, they are the guided variant of so called cylindrical vector beams (CVBs). CVBs find applications in numerous fields of fundamental and applied optics. Here, an application to high-resolution light microscopy is demonstrated. The field distribution in the tight microscope focus is controlled by the LPG, which in turn creates the necessary polarization and intensity distribution for the microscope illumination. A gold nanoparticle of 30 nm diameter is used to probe the focal field with sub-wavelength resolution. The construction and test of the acoustic LPG are discussed in detail. A key component is the piezoelectric transducer that excites flexural acoustic waves in the SF, which are the origin of an optical mode conversion. A mode conversion efficiency of 85% was realized at 785 nm optical wavelength. The efficiency is, at present, mainly limited by the spectral positions and widths of the transducer’s acoustic resonances. The SF used with the LPG separates the propagation constants of the second-order polarization modes, so they can be individually excited and are less sensitive to distortions than in standard weakly-guiding fibers. The influence of geometrical parameters of the fiber core on the propagation constant separation and on the mode fields is studied numerically using the multiple multipole method. From the simulations, a simple mode coupling scheme is developed that provides a qualitative understanding of the experimental results achieved with the LPG. The refractive index profile of the fiber core was originally developed by Ramachandran et al. However, an important step of the present work is to reduce the SF’s core size to counteract the the appearance of higher-order modes at shorter wavelengths which would otherwise spoil the mode purity. Using the acoustic LPG in combination with the SF produces a versatile device to generate CVBs and other phase structures beams. This fiber-optical method offers beam profiles of high quality and achieves good directional stability of the emitted beam. Moreover, the device design is simple and can be realized at low cost. Future developments of the acoustic LPG will aim at applications to fiber-optical sensors and optical near-field microscopy. / Diese Arbeit behandelt die Entwicklung und Anwendung eines akustischen langperiodischen Fasergitters (LPG) in Verbindung mit einer optischen Spezialfaser (SF). Das akustische LPG wandelt ausgewählte optische Modi der SF um. Einige dieser Modi weisen eine komplexe, zylindersymmetrische Polarisations- und Intensitätsverteilung auf. Diese sind eine Form der so genannten zylindrischen Vektor-Strahlen (CVBs), welche in zahlreichen Gebieten der wissenschaftlichen und angewandten Optik zum Einsatz kommen. In dieser Arbeit wird eine Anwendung auf die hochauflösende Lichtmikroskopie demonstriert. Die fokale Feldverteilung wird dabei durch die Auswahl der vom LPG erzeugten Modi, welche zur Beleuchtung genutzt werden, eingestellt. Als Nachweis wird die entstehende laterale Feldverteilung mithilfe eines Goldpartikels (Durchmesser 30 Nanometer) vermessen. Aufbau und Test des akustischen LPGs werden im Detail besprochen. Eine wichtige Komponente ist ein piezoelektrischer Wandler, der akustische Biegewellen in der SF anregt. Diese sind die Ursache der Umwandlung optischer Modi. Die maximale Konversionseffizienz betrug 85% bei 785 nm (optischer) Wellenlänge. Die Effizienz ist derzeit hauptsächlich durch die Lage der akustischen Resonanzfrequenzen des Wandlers und deren Bandbreite begrenzt. Die benutzte SF spaltet die Ausbreitungskonstanten von Polarisationsmodi zweiter Ordnung auf, sodass diese individuell angeregt werden können und weniger anfällig gegen über Störungen der Faser sind, als das bei gewöhnlichen, schwach führenden Glasfasern der Fall ist. Das zu Grunde liegende Brechzahlprofil des Faserkerns wurde von Ramachandran et al. entwickelt. Für diese Arbeit wurde jedoch die Ausdehnung des Profils verkleinert – ein erster Schritt um Anwendungen bei kürzeren optischen Wellenlängen zu ermöglichen. Es werden numerische Simulationen mit der Methode der multiplen Multipole zur Berechnung der Modenfelder und den zugehörigen Propagationskonstanten vorgestellt. Diese zeigen u. a. den starken Einfluss von geometrischen Veränderungen des Faserkerns. Basierend auf den Simulationsergebnissen wird ein einfaches Kopplungsschema für die Modi entwickelt, welches ein qualitatives Verständnis der experimentellen Ergebnisse ermöglicht. In Kombination bilden die SF und das LPG ein vielseitiges Gerät zur Erzeugung von CVBs und anderen Strahlen mit komplexer Phasenstruktur. Die Methode besticht durch hohe Qualität des Strahlprofils, stabile Abstrahlrichtung, einfachen Aufbau, elektronische Steuerbarkeit und geringe Materialkosten. Zukünftige Weiterentwicklungen des akustischen LPGs zielen auf die Anwendung in faseroptischen Sensoren und in der optischen Nahfeldmikroskopie ab.

The present work deals with the development and application of an acoustic long-period fiber grating (LPG) in conjunction with a special optical fiber (SF). The acoustic LPG converts selected optical modes of the SF. Some of these modes are characterized by complex, yet cylindrically symmetric polarization and intensity patterns. Therefore, they are the guided variant of so called cylindrical vector beams (CVBs). CVBs find applications in numerous fields of fundamental and applied optics. Here, an application to high-resolution light microscopy is demonstrated. The field distribution in the tight microscope focus is controlled by the LPG, which in turn creates the necessary polarization and intensity distribution for the microscope illumination. A gold nanoparticle of 30 nm diameter is used to probe the focal field with sub-wavelength resolution. The construction and test of the acoustic LPG are discussed in detail. A key component is the piezoelectric transducer that excites flexural acoustic waves in the SF, which are the origin of an optical mode conversion. A mode conversion efficiency of 85% was realized at 785 nm optical wavelength. The efficiency is, at present, mainly limited by the spectral positions and widths of the transducer’s acoustic resonances. The SF used with the LPG separates the propagation constants of the second-order polarization modes, so they can be individually excited and are less sensitive to distortions than in standard weakly-guiding fibers. The influence of geometrical parameters of the fiber core on the propagation constant separation and on the mode fields is studied numerically using the multiple multipole method. From the simulations, a simple mode coupling scheme is developed that provides a qualitative understanding of the experimental results achieved with the LPG. The refractive index profile of the fiber core was originally developed by Ramachandran et al. However, an important step of the present work is to reduce the SF’s core size to counteract the the appearance of higher-order modes at shorter wavelengths which would otherwise spoil the mode purity. Using the acoustic LPG in combination with the SF produces a versatile device to generate CVBs and other phase structures beams. This fiber-optical method offers beam profiles of high quality and achieves good directional stability of the emitted beam. Moreover, the device design is simple and can be realized at low cost. Future developments of the acoustic LPG will aim at applications to fiber-optical sensors and optical near-field microscopy.:Abstract / Kurzfassung iii Table of contents v 1 Introduction 1 2 Fundamentals of optical waveguides 5 2.1 Introduction 5 2.2 Maxwell’s equations and vector wave equations 5 2.3 Optical waveguides 7 2.3.1 Dielectric waveguides 7 2.3.2 Metallic waveguides 9 2.4 Numerical calculation of modes by the multiple multipole program 10 2.4.1 Representation of simulated mode fields 11 2.5 Overview of coupled mode theory 14 2.5.1 Coupled mode equations 14 2.5.2 Co-directional coupling 15 2.6 Summary and conclusions 16 3 Polarization control for fundamental and higher order modes 17 3.1 Introduction 17 3.2 Description of light polarization 18 3.2.1 Stokes parameters and the polarization ellipse 18 3.2.2 Polarization of light beams in free space 20 3.2.3 Polarization of light beams in optical fibers 21 3.3 Short overview of cylindrical vector beam generation 22 3.4 Excitation of cylindrical vector beams in optical fibers 27 3.4.1 Free-beam techniques 27 3.4.2 In-fiber techniques 29 3.5 Polarization control in optical fibers 30 3.5.1 Phase matching and the beat length 30 3.5.2 Polarization-maintaining single-mode fibers 32 3.5.3 Higher-order mode polarization-maintaining fibers 32 3.6 Summary and conclusions 34 4 Simulation of core-ring-fibers 36 4.1 Introduction 36 4.2 Model geometries for index-tailored optical fiber 37 4.2.1 Special fiber and fabrication 37 4.2.2 Elliptical core boundaries 39 4.2.3 Overview of the applied MMP Models 41 4.3 Simulation results for circular core geometry 43 4.3.1 Mode fields 43 4.3.2 Scaling of the core radii 43 4.3.3 Wavelength dependence 48 4.4 Simulation results for non-circular geometry 50 4.4.1 Mode fields 50 4.4.2 Effects of individual rotation angles 53 4.4.3 Wavelength dependence 56 4.5 Summary and conclusions 61 5 Long period fiber gratings 63 5.1 Introduction 63 5.2 Principle of long-period fiber gratings 64 5.2.1 Results from coupled mode theory 64 5.2.2 Types of long-period gratings 65 5.2.3 Properties of acoustic long-period fiber gratings 67 5.3 Acoustic long-period grating setup 68 5.3.1 Transducer 69 5.3.2 Mechanical coupling 72 5.3.3 Acoustic dispersion of an optical fiber 75 5.3.4 Optical setup 77 5.3.5 Comparison to other acoustic LPG geometries 81 5.4 Experimental results 82 5.4.1 Transmission spectra 82 5.4.2 Discussion of transmission results 88 5.4.3 Direct mode field observation 93 5.4.4 Discussion of mode field observations 97 5.4.5 Time behavior and grating amplitude modulation 99 5.5 Summary and conclusions 101 6 Application of higher order fiber modes for far-field microscopy 104 6.1 Introduction 104 6.2 Complex beams in high-resolution far-field microscopy 104 6.3 Theoretical considerations 106 6.4 Experimental details 111 6.5 Results 114 6.6 Discussion 118 6.7 Summary and conclusions 122 7 Summary and outlook 124 Acknowledgments 139 Publications related to this work 142 List of figures 144 List of tables 150 List of acronyms 151 / Diese Arbeit behandelt die Entwicklung und Anwendung eines akustischen langperiodischen Fasergitters (LPG) in Verbindung mit einer optischen Spezialfaser (SF). Das akustische LPG wandelt ausgewählte optische Modi der SF um. Einige dieser Modi weisen eine komplexe, zylindersymmetrische Polarisations- und Intensitätsverteilung auf. Diese sind eine Form der so genannten zylindrischen Vektor-Strahlen (CVBs), welche in zahlreichen Gebieten der wissenschaftlichen und angewandten Optik zum Einsatz kommen. In dieser Arbeit wird eine Anwendung auf die hochauflösende Lichtmikroskopie demonstriert. Die fokale Feldverteilung wird dabei durch die Auswahl der vom LPG erzeugten Modi, welche zur Beleuchtung genutzt werden, eingestellt. Als Nachweis wird die entstehende laterale Feldverteilung mithilfe eines Goldpartikels (Durchmesser 30 Nanometer) vermessen. Aufbau und Test des akustischen LPGs werden im Detail besprochen. Eine wichtige Komponente ist ein piezoelektrischer Wandler, der akustische Biegewellen in der SF anregt. Diese sind die Ursache der Umwandlung optischer Modi. Die maximale Konversionseffizienz betrug 85% bei 785 nm (optischer) Wellenlänge. Die Effizienz ist derzeit hauptsächlich durch die Lage der akustischen Resonanzfrequenzen des Wandlers und deren Bandbreite begrenzt. Die benutzte SF spaltet die Ausbreitungskonstanten von Polarisationsmodi zweiter Ordnung auf, sodass diese individuell angeregt werden können und weniger anfällig gegen über Störungen der Faser sind, als das bei gewöhnlichen, schwach führenden Glasfasern der Fall ist. Das zu Grunde liegende Brechzahlprofil des Faserkerns wurde von Ramachandran et al. entwickelt. Für diese Arbeit wurde jedoch die Ausdehnung des Profils verkleinert – ein erster Schritt um Anwendungen bei kürzeren optischen Wellenlängen zu ermöglichen. Es werden numerische Simulationen mit der Methode der multiplen Multipole zur Berechnung der Modenfelder und den zugehörigen Propagationskonstanten vorgestellt. Diese zeigen u. a. den starken Einfluss von geometrischen Veränderungen des Faserkerns. Basierend auf den Simulationsergebnissen wird ein einfaches Kopplungsschema für die Modi entwickelt, welches ein qualitatives Verständnis der experimentellen Ergebnisse ermöglicht. In Kombination bilden die SF und das LPG ein vielseitiges Gerät zur Erzeugung von CVBs und anderen Strahlen mit komplexer Phasenstruktur. Die Methode besticht durch hohe Qualität des Strahlprofils, stabile Abstrahlrichtung, einfachen Aufbau, elektronische Steuerbarkeit und geringe Materialkosten. Zukünftige Weiterentwicklungen des akustischen LPGs zielen auf die Anwendung in faseroptischen Sensoren und in der optischen Nahfeldmikroskopie ab.:Abstract / Kurzfassung iii Table of contents v 1 Introduction 1 2 Fundamentals of optical waveguides 5 2.1 Introduction 5 2.2 Maxwell’s equations and vector wave equations 5 2.3 Optical waveguides 7 2.3.1 Dielectric waveguides 7 2.3.2 Metallic waveguides 9 2.4 Numerical calculation of modes by the multiple multipole program 10 2.4.1 Representation of simulated mode fields 11 2.5 Overview of coupled mode theory 14 2.5.1 Coupled mode equations 14 2.5.2 Co-directional coupling 15 2.6 Summary and conclusions 16 3 Polarization control for fundamental and higher order modes 17 3.1 Introduction 17 3.2 Description of light polarization 18 3.2.1 Stokes parameters and the polarization ellipse 18 3.2.2 Polarization of light beams in free space 20 3.2.3 Polarization of light beams in optical fibers 21 3.3 Short overview of cylindrical vector beam generation 22 3.4 Excitation of cylindrical vector beams in optical fibers 27 3.4.1 Free-beam techniques 27 3.4.2 In-fiber techniques 29 3.5 Polarization control in optical fibers 30 3.5.1 Phase matching and the beat length 30 3.5.2 Polarization-maintaining single-mode fibers 32 3.5.3 Higher-order mode polarization-maintaining fibers 32 3.6 Summary and conclusions 34 4 Simulation of core-ring-fibers 36 4.1 Introduction 36 4.2 Model geometries for index-tailored optical fiber 37 4.2.1 Special fiber and fabrication 37 4.2.2 Elliptical core boundaries 39 4.2.3 Overview of the applied MMP Models 41 4.3 Simulation results for circular core geometry 43 4.3.1 Mode fields 43 4.3.2 Scaling of the core radii 43 4.3.3 Wavelength dependence 48 4.4 Simulation results for non-circular geometry 50 4.4.1 Mode fields 50 4.4.2 Effects of individual rotation angles 53 4.4.3 Wavelength dependence 56 4.5 Summary and conclusions 61 5 Long period fiber gratings 63 5.1 Introduction 63 5.2 Principle of long-period fiber gratings 64 5.2.1 Results from coupled mode theory 64 5.2.2 Types of long-period gratings 65 5.2.3 Properties of acoustic long-period fiber gratings 67 5.3 Acoustic long-period grating setup 68 5.3.1 Transducer 69 5.3.2 Mechanical coupling 72 5.3.3 Acoustic dispersion of an optical fiber 75 5.3.4 Optical setup 77 5.3.5 Comparison to other acoustic LPG geometries 81 5.4 Experimental results 82 5.4.1 Transmission spectra 82 5.4.2 Discussion of transmission results 88 5.4.3 Direct mode field observation 93 5.4.4 Discussion of mode field observations 97 5.4.5 Time behavior and grating amplitude modulation 99 5.5 Summary and conclusions 101 6 Application of higher order fiber modes for far-field microscopy 104 6.1 Introduction 104 6.2 Complex beams in high-resolution far-field microscopy 104 6.3 Theoretical considerations 106 6.4 Experimental details 111 6.5 Results 114 6.6 Discussion 118 6.7 Summary and conclusions 122 7 Summary and outlook 124 Acknowledgments 139 Publications related to this work 142 List of figures 144 List of tables 150 List of acronyms 151

No description available.

In this paper a new equivalent circuit is presented which describes the dynamics of a prototype micro-gyro sensor. The concept takes advantage of the principles employed in vibratory gyro sensors and the ductile attributes of GalFeNOL to target high sensitivity and shock tolerance. The sensor is designed as a tuning fork structure. A GalFeNOL patch attached to the y-z surface of the drive prong causes both prongs to bending the x-z plane (about the y axis) and a patch attached to the x-z surface of the sensing prong detects Coriolis-force induced bending in the y-z plane (about the x axis). A permanent magnet is bonded on top of each prong to give bias magnetic fields. A solenoid coil surrounding the drive prong is used to produce bending in the x-z plane of both prongs. The sensing prong is surrounded by a solenoid coil with N turns in which a voltage proportional to the time rate of change of magnetic flux is induced. The equivalent circuit enables the efficient modeling of a gyro sensor and an electromechanical behavioral simulation using the circuit simulator SPICE. The prongs are modeled as wave guiding bending beams which are coupled to the electromagnetic solenoid coil transducer. In contrast to known network approaches, the proposed equivalent circuit is the first tuning fork model, which takes full account of the fictitious force in a constant rotating frame of reference. The Coriolis force as well as the centrifugal force on a concentrated mass are considered.

The presence of photonic band gap in an arbitrarily shaped photonic structure, particularly structures that are fabricated by exploiting rolled-up nanotechnology, can be understood from the density of optical states. In this thesis, the density of optical states and the local density of optical states in finite-sized photonic structures are calculated using the finite difference time domain method together with a parallelized message passing interface. With this approach, a software package suitable for high-performance computing on multi-platform was published under GNU GPL license. When light is guided to propagate along a rolled-up thin film, whispering gallery mode resonances can be formed in a microtubular structure. Dynamic probing and tuning via a plasmonic nanoparticle-coated glass tip are investigated to demonstrate the transition from dielectric-dielectric to dielectric-plasmonic coupling in the tubular microcavity. The competition of these two coupling mechanisms allow the tuning of the optical cavity modes towards lower and then higher energies in a single coupling system. Moreover, three dimensionally confined higher order axial modes can be selectively coupled and tuned by the glass tip due to their unique spatial distribution of the optical field along the tube axis. In addition, the interaction between sharp optical cavity modes and broad plasmonic modes supported by silver nanoparticles leads to the occurrence of Fano resonance. In particular, Fano resonances occurring at higher-order axial modes has been observed as well. The experimental results are supported by numerical simulations based on the finite difference time domain method. In photonic lattice structures, light propagation behavior can be influenced and defined by the photonic band structure. By designing the unit cell with glide mirror symmetry, topologically protected edge states operating in the visible spectral range have been proposed in two dimensional photonic crystals which can be made of feasible materials. Topological phenomena such as unidirectional waveguiding and/or effective zero refractive index are presented. In addition, a scheme to study topological phase transition in a single photonic crystal device is proposed and studied via unevenly stretching photonic lattice. Moreover, a new method is explored to distinguish the topological phase from the bulk modes. The research presented in this thesis concerns molding the flow of light in specially designed photonic devices for various potential applications. The software package can be used to design and investigate finite-sized photonic structures with an arbitrary shape, which is much faster in terms of computation than other reported techniques and software packages. The rolled-up microcavities can be employed to trap and store light in the way of whispering gallery mode resonances, and the resonant light can be tuned and modulated by a plasmonic nanoparticles-coated glass tip. This research is particularly interesting for optical signal processing, slowing light via Fano resonances, and high sensitive sensing. In addition, the topological photonic crystal design and examination scheme presented in this thesis provide a simplified yet more efficient way to obtain non-trivial topological phase from a tunable photonic crystal that can be verified not only by edge modes but also by bulk modes.:Bibliographic record 1 Abstract 1 LIST OF ABBREVIATIONS and Symbols 3 1 Introduction 9 1.1 Introduction and Motivation 9 1.2 Objectives 11 1.3 Organization of the thesis 12 2 Density of optical states in rolled-up photonic crystals and quasi crystals 15 2.1 Introduction 15 2.1.1 background 17 2.1.2 Infinitely extended ideal photonic crystal 17 2.2 Finite-sized photonic crystal, photonic quasicrystal, and arbitrary photonics structures 20 2.2.1 Numerical algorithm 25 2.2.2 Rolled-up photonic crystals and quasi crystals 30 2.3 Software package 33 2.3.1 Computational performance 33 2.3.2 FPS User interface 35 2.3.3 Detailed tutorial 37 2.3.4 Alternative rolled-up photonic crystals 47 2.3.5 Beyond 3D photonic crystals. 48 2.4 Conclusion 49 3 Rolled-up microesonator 51 3.1 Introduction 51 3.2 Rolled-up microresonators 52 4 Tip-assisted photon-plasmon coupling in three-dimensionally confined microtube cavities 57 4.1 Introduction 57 4.2 Tube and plasmonic particle preparation and characterization 60 4.3 Results and discussion 62 4.4 Axial mode tuning 64 4.5 Fano resonance 65 4.5.1 Background 65 4.5.2 Fano resonance in the tip assisted coupling setup 68 4.6 Conclusion 71 5 Topological photonics 73 5.1 Introduction and motivation 73 5.2 Topological phase transition point 77 5.2.1 Fundamental phase transition point 77 5.2.2 Zero refractive index material 79 5.3 Non-trivial topology in realistic materials 80 6 Topological phase transition in stretchable photonic crystals 85 6.1 Introduction and motivation 85 6.2 SSH model 88 6.3 Photonic crystal 91 6.4 Band structure and end modes of the photonic crystal 99 6.5 Conclusion 101 7 Summary and outlook 103 7.1 Summary 103 7.2 Outlook 104 Bibliography 111 List of figures 127 Publications 133 Acknowledgments 136 Selbständigkeitserklärung 137 Curriculum Vitae 138

Das Thema dieser Arbeit ist eine mögliche Steuerung eines optischen Solitons in nichtlinearen optischen Fasern. Es gelang, die interessierenden Solitonparameter wie Intensität, Dauer und Zeitverschiebung durch die Wechselwirkung mit einer dispersiven Welle geringer Intensität kontrollierbar zu modifizieren. Es wird eine neue analytische Theorie vorgestellt für die Wechselwirkung zwischen Solitonen und dispersiven Wellen, die auf der Kreuzphasenmodulation in nichtlinearen Fasern beruht. Das vorgestellte Modell kombiniert quantenmechnische Streutheorie und eine Erweiterung der Störungstheorie für Solitonen aus der nichtlinearen Optik. Damit wurden folgende neue Ergebnisse erzielt: (1) Die Entwicklung aller Solitonparameter wird korrekt vorhergesagt. Insbesondere wird die mögliche Verstärkung der Solitonamplitude erfolgreich bestimmt. (2) Passende Intervalle der Kontrollparameter, die eine effektive Solitonmanipulation garantieren, können quantitativ bestimmt werden. (3) Der Raman-Effekt wurde in die Modellbeschreibung eingebunden. Die klassische Abschätzung der Eigenfrequenzverschiebung des Solitons durch den Raman-Effekt wurde verbessert und erweitert durch eine neue Relation für den einhergehenden Amplitudenverlust. Weiterhin wurden solche Kontrollpulse bestimmt, die dieser Schwächung des Solitons entgegenwirken. Im Unterschied zu früheren Versuchen liefert die hier entwickelte Modellbeschreibung die passenden Parameterbereiche für eine stabile Auslöschung des Raman-Effektes. (4) Obwohl die Wechselwirkung selbst auf der Kreuzphasenmodulation basiert, spielt der ”self-steepening“- Effekt, der die Bildung von optischen Schocks beschreibt, eine entscheidende Rolle für eine effiziente Veränderung der Solitonparameter. / This work discusses the problem how to control an optical soliton propagating along a non- linear fiber. The approach chosen here is to change soliton delay, duration and intensity in a simple, predictable manner by applying low-intensity velocity-matched dispersive light waves. A new analytic theory of cross-phase modulation interactions of solitons with dispersive control waves is presented which combines quantum mechanical scattering theory, a modified soliton perturbation theory and a multi-scale approach. This led to the following new results: (1) The evolution of all soliton parameters is correctly predicted. In particular the possible amplitude enhancement of solitons is successfully quantified, which could not be obtained by the standard formulation of the soliton perturbation theory. (2) General ranges for control parameters are quantitatively determined, which ensure an effective interaction. (3) The Raman effect is incorporated into the theory. The classical estimation of the Raman self-frequency shift is refined and expanded by a new relation for the amplitude loss arising with the Raman self-frequency shift. Furthermore, control pulses are identified which cancel soliton degradation due to Raman effect. In contrast to previously reported attempts with the interaction scheme under consideration, even parameter ranges are found which lead to a stable cancellation of the Raman effect. (4) New qualitative insights into the underlying process emerged. The prominent role of the self-steepening effect could be isolated. Though the pulse interaction is mediated by cross-phase modulation, the self-steepening effect causes an essential enhancement leading to much stronger changes in soliton parameters.