Optical resonators are structures that allow light to circulate and store energy for a duration of time. This work primarily looks at the fabrication, characterization, and application of whispering gallery mode microresonators and the analysis of organic photonic crystal-like structures and simulation of their resonant effects. Whispering gallery mode (WGM) microresonators are a class of cylindrically symmetric optical resonator which light circulates around the equator of the structure. These resonators are named after acoustic whispering galleries, where a whisper can be heard anywhere along the perimeter of a circular room. These optical structures are known for their ultra high Q-factor and their low mode volume. Q-factor describes the photon lifetime in the cavity and is responsible for the energy buildup within the cavity and sharp spectral characteristics of WGM resonators. The energy buildup is ideal for non-linear optics and the sharp spectral features are beneficial for sensing applications. Characterization of microbubble resonators is done by coupling light from a tunable laser source via tapered optical fiber into the cavity. The fabrication of quality tapered optical fiber on the order of 1-2 μm is critical to working on WGM resonators. The measurement of Q-factors up to 2x10⁸ and mode spectra are possible with these resonators and experimental techniques. This work focuses on microdisk and microbubble WGM resonators. The microdisk resonators are fabricated by femtosecond laser micromachining. The micromachined resonators are fabricated by ablating rotating optical fiber to generate the disk shape and then heated to reflow the surface to improve optical quality. These resonators have a spares mode spectrum and display a Q factor as high as 2x10⁶. The microbubble resonators are hollow microresonators fabricated by heating a pressurized capillary tube which forms a bubble in the area exposed to heat. These have a wall thickness of 2-5 μm and a diameter of 200-400 μm. Applications in pressure sensing and two-photon fluorescence of dye in microbubble resonators is explored. Photonic crystals can have engineered resonant properties by tuning photonic band gaps and introducing defects to create cavities in the photonic structure. In this work, a natural photonic crystal structure is analyzed in the form of diatoms. Diatoms are a type of phytoplankton which are identified by unique ornamentation of each species silica shell, called a frustule. The frustule is composed of a quasi-periodic lattice of pores which closely resembles manmade photonic crystals. The diatom frustules are analyzed using image processing techniques to determine pore-to-pore spacing and identify defects in the quasi-periodic structure which may contribute to optical filtering and photonic band gap effects. The data gathered is used to simulate light propagation through the diatom structure at different incident angles and with different material properties and to verify data gathered experimentally.

Photonic crystal waveguide (PCW) based device has been used in many applications in recent years due to its unique slow light effect. In this work, the application of PCW on sensing is presented. First, we present a PCW structure based Infrared (IR) spectroscopy combining with slot structure which has a large electric field enhancement for light-matter interaction for chemical sensing. The slow light effect and the electric field enhancement of our designed structure greatly enhance the absorption factor of chemical analytes by 1000. We then use multimode interference (MMI) optical splitter and Y junction combiner to connect two PCWs to show multiplexed detections of two chemicals on a single chip. Our results show the detection is down to 1 ppb for xylene in water and 100ppm for methane in nitrogen. We also present PCW microcavities structure for biological sensing in our work. Due to its high quality factor and easier immobilization of biomaterials, we are able to use ink jet printing method to bind the biomaterials on top of our chip. We choose linear-type 13 (L13, missing 13 holes) microcavities to do the biosensing for antibodies and cancer cell lysates because of its higher sensitivity combining with slow light effect. Our work achieves the cancer cell lysates detection down to 2 cells/μl., and further applications will be presented in our group in the future. / text

This thesis describes work carried out to demonstrate the use of photonic crystal fibres for the study of photochemistry reaction kinetics and fluorescence spectroscopy. Photonic crystal fibre allows the guidance of light, in a well-defined mode, over long path lengths. When the fibre’s microstructure is filled with a sample solution this, therefore, provides a greatly increased measurement path length and greater light-sample interaction than is possible in conventional spectroscopic systems, leading to enhanced sensitivity whilst greatly reducing the required sample volumes. The use of photonic crystal fibre as a micro reaction chamber for carrying out photochemical reactions and the study of their kinetics was achieved through monitoring the photoisomerisation of two azobenzene-based dyes, Disperse Red 1 and Disperse Orange 1, using real-time UV/Vis absorption spectroscopy. Both the 488 nm excitation laser and the broadband light source for the measurements were co-coupled through the fibre, giving perfect overlap of both with the sample. The fibre used for the measurements was a hollow core kagomé-type fibre with a core diameter of 19μm, giving a sample volume of 2.8 nL cm-1. The 30 cm path-length of the fibre allowed the use of sample concentrations down to 5×10-6 M, over an order of magnitude lower than in a conventional 1cm cuvette, with a sample volume of 90 nl in the core, a reduction of five orders of magnitude over conventional measurements. The kinetics of the photoisomerisation from the trans to the cis isomers of the dyes and the thermally driven cis-to-trans isomerisation could be tracked on the ms timescale, using a grating spectrometer which recorded the entire absorption spectrum of the dye. The data were numerically fitted using a custom model to take into account the properties of the fibre system. This led to the calculation of rate constants for the isomerisation processes in good agreement with those previously measured for these dye systems in bulk solution. Furthermore, the measurement of the dyes in pentane, in which they are highly insoluble, could be achieved due to the low concentrations that could be used; such measurements have not previously been reported. For the study of photonic crystal fibre as a system for the excitation and collection of fluorescence, two types of fibre were used; the same kagomé hollow-core fibre used for the photochemistry absorption measurements and a suspended-core “Mercedes” fibre. This allowed for the excitation of fluorophores in two contrasting environments. In the kagomé fibre fluorophores in bulk solution are excited whilst, in the Mercedes fibre, only fluorophores either on or in close proximity to the silica core interact with the evanescent field of the excitation light. The Fluorescein fluorophore was used initially to measure the detection limits in both fibre types and limits of 2x10-11 M in the kagomé and 10-9 M in the Mercedes fibre were obtained. This equates to 106 molecules in the kagomé fibre, which displays the lower detection limit due to greater light-sample interaction. Two-photon excitation of the Fluorescein fluorophore was then carried out using a mode-locked Ti-Sapphire laser as an excitation source, demonstrating the ability of the fibre system to sustain two-photon excitation of a long (30 cm) path length. The two-photon measurements showed remarkable detection sensitivity allowing detection of fluorescence from 10-9 M solutions of Fluorescein, showing the potential of using PCF for two-photon based experiments which are of particular interest in fields such as photodynamic therapy. A further study was carried out, using the two fibre types, for measurement of the fluorescence lifetime of the Rhodamine B fluorophore. Unperturbed lifetimes could be measured in the fibres showing no interference from the fibre. The measurements confirmed, in reference to known lifetime values, that in the kagomé fibre the excited fluorophores are in the bulk solution with only a minor influence from surface effects, whilst in the Mercedes fibre all of the excited molecules experience interaction with the surface of the silica core. This, therefore, gives a method of locating the fluorophores with respect to the fibre surface and the ability to choose between measurement of bulk solution and long path-length evanescent field-induced fluorescence.

Les travaux effectués dans le cadre de cette thèse s'inscrivent dans la suite des travaux réalisés par l'INL (Institut des Nanotechnologies de Lyon) sur les résonateurs optiques à base de cristaux photoniques membranaires pour la réalisation de composants actifs ou passifs intégrés sur silicium. Ces travaux se concentrent particulièrement sur le contrôle des propriétés de propagation des modes et des résonances guidés s'établissant dans les cristaux photoniques membranaires. Ils s'appuient notamment sur la nature partiellement ou totalement guidée de ces modes, ainsi que des propriétés de symétrie des structures (ou au contraire de dissymétrie) afin de pouvoir générer des dispersions photoniques à la demande. En effet, le contrôle des propriétés spectro-spatiales est primordiale à la réalisation de composants photoniques efficients. Par exemple l'établissement d'un régime d'émission laser dans un cristal photonique membranaire passe par un contrôle minutieux des propriétés temporelles de la résonance (fort facteur de qualité) mais aussi spatiales (fort ralentissement de la lumière) afin de pouvoir générer des densités d'états photoniques suffisamment importantes. Ainsi, de nombreuses stratégies de contrôle ont été mises en place durant les années 2000, permettant l'établissement d'un régime laser dans des structures diverses. Néanmoins, si les méthodes de fabrication et la maîtrise dans la conception de ces structures se sont améliorées au fil de leur développement, ces dispositifs restent difficilement compétitifs face à d'autres technologies. Démontrer la versatilité de ces structures par l'ajout de fonctionnalités tels que le \emph{beam steering} ou d'autres capacités serait alors une véritable plus-value. Récemment, de nouvelles stratégies de contrôle de la lumière ont émergé. Ces stratégies se basent sur une approche totalement différente des procédés de contrôle habituels. Ainsi, on peut citer les nouveaux phénomènes de localisation de la lumière basés sur des procédés inédits de découplage de la lumière du continuum radiatif, ou des dispersions en cône de Dirac qui pourraient permettre la réalisation de composants originaux tels que des lasers mono-modes à grande surface active. Ces nouveaux phénomènes permettent d'envisager d'autres approches pour la réalisation de lasers à cristaux photoniques et pourraient apporter les nouvelles fonctionnalités recherchées. Parallèlement, l'utilisation de membranes photoniques multi-modes reste encore peu répandue dans la littérature. L'utilisation conjointe de modes d'ordres différents offre pourtant des possibilités supplémentaires dans le contrôle des propriétés de propagation de la lumière dans les cristaux photoniques membranaires. Ce contrôle supplémentaire peut se traduire par des capacités de ralentissement de la lumière accrues ou par la réalisation de dispersions plus exotiques. Le but de cette thèse est alors de mettre en place les briques conceptuelles nécessaires à la génération de ces dispersions particulières. Pour cela, un modèle théorique permettant d'appréhender les dynamiques de couplage opérant dans les cristaux photoniques membranaires étudiés est mis en place. Ce modèle est ensuite confronté aux résultats de simulation ainsi qu'aux caractérisations optiques des structures fabriquées. En parallèle, une étude prospective des applications possibles est menée pour chacune des dispersions générées. / Work carried out in this thesis is part of the overall work done at INL on optical resonators based on photonic crystals for the design of passive as well as active components integrated on silicon chips. These works especially focus on spectral properties and propagation control of guided modes and resonances settled in photonic crystal slabs. They rely partly on the guided nature of these modes as well as their symmetry properties to generate on-demand photonic dispersions. Indeed, control of the spectro-spatial properties is overriding for the design of efficient photonic components. For instance, obtaining a laser effect with a photonic crystal requires a precise control of both spectral properties (high quality factor) and spatial ones (high light slow-down) so that large photonic densities of states are achieved. Thereby, numerous strategies of control have been developed during the 2000s, allowing a laser effect to occur with various structures. Nonetheless, despite both manufacture and design qualities have been improved, these components still remain hardly competitive compared to other technologies. Demonstrating the versatility of these structures by achieving novel functionalities like beam steering or other capacities would be a real betterment. Recently, new strategies to control light using photonic crystals have been discovered. These strategies are based on completely new phenomena. For instance, new possibilities to localize light based on novel light decoupling processes from the continuum have arisen and Dirac cone dispersions could allow the formation of monomode larger-area photonic crystal lasers. These new phenomena enabled to consider new approaches to design photonic crystal laser that could lead to the novel functionalities sought. In parallel, the use of multimode photonic membranes still remains uncommon in the literature. The use of several guided orders gives additional possibilities to the control of light propagation within photonic crystal membrane thought. This additional control can lead to improved slowing-down capabilities or exotic dispersion generation. The goal of this thesis is to set up the fundamental blocks on which these particular dispersions are based on. In this purpose, a theoretical model allowing apprehending the coupling dynamic occurring in photonic crystal membranes is established. Then, this model is compared to simulation results and experimental characterizations of the manufactured structures.

This thesis presents the development of photonic tools towards the realisation of an optical intensity waveform synthesiser and of an attosecond pulse synthesiser based on the generation and Fourier synthesis of a continuous-wave coherent spectral comb spanning more than 3 octaves (UV to mid-IR) by use of a gas-filled hollow core photonic crystal fibre (HC-PCF).

This thesis introduces the linear and nonlinear properties of photonic crystal fibre (PCF), describes the fabrication and characterisation of different PCFs, and demonstrates their applications to supercontinuum (SC) generation and single-photon sources. The linear properties of PCF include endlessly single-mode transmission, highly controllable dispersion and birefringence. These unique properties have made PCFs the best media to demonstrate all kinds of nonlinear effects such as self-phase modulation (SPM), cross-phase modulation (XPM), Raman effects, four-wave mixing and modulation instability (FWM and MI), and soliton effects. The combination of these nonlinear effects has led to impressive spectral broadening known as SC generation in PCFs. The intrinsic correlation of signal and idler photons from FWM has brought PCF to the application of single-photon generation. Four projects about SC generation were demonstrated. The first was visible continuum generation in a monolithic PCF device, which gave a compact, bright (-20 dBm/nm), flat and single-mode visible continuum source extending to short wavelength at 400 nm. The second was polarised SC generation in a highly bire-fringent PCF. A well linearly polarised continuum source spanning 450-1750 nm was achieved with >99% power kept in a single linear polarisation. This polarised continuum source was then applied to tuneable visible/UV generation in a BIBO crystal. The third was residual pump peak removal for SC generation in PCFs. The fourth was to design an all-fibre dual-wavelength pumping for spectrally localised continuum generation. Two projects about photon pair generation using FWM were then demonstrated. One was an all-fibre photon pair source designed in the telecom band for quantum communication. This source achieved >50% heralding efficiency which is the highest in fibre photon pair sources reported so far. Another one was to design birefringent PCFs for naturally narrow band photon pair generation in the Si SPAD high detection efficiency range. 0.122 nm bandwidth signal photons at 596.8 nm were generated through cross polarisation phase matched FWM in a weakly birefringent PCF pumped by a picosecond Ti:Sapphire laser at 705 nm in the normal dispersion regime.

This thesis presents the development of photonic microcells for use as the host for coherent optics phenomena and related applications. A photonic microcell consists of a length of hollow-core photonic crystal fibre (HC-PCF) with a gas-filled core that is spliced to conventional optical fibre at either end to seal the gas within the fibre. Towards the goal of demonstrating and assessing the coherence properties of quantum optical effects in photonic microcells, the fabrication of two types of HC-PCF is presented. The established photonic bandgap HC-PCF offers extremely low transmission loss of ~10 dB/km over kilometre distances. However, the fibre has a limited transmission bandwidth of ~50 THz and exhibits modal coupling unfavourable for many applications. Work is presented on the tailoring of this fibre by control and shaping of the core-surround in order to improve its modal properties. A second type of HC-PCF is based on a large-pitch lattice, whose guidance relies on a new mechanism. This fibre exhibits a much improved bandwidth (>1000 THz) and has a relatively higher but still practical loss of ~1 dB/m. The development of photonic microcells at microbar pressure level and with low optical insertion loss is shown, an important step in the improvement of the technology for coherent optics applications which will take advantage of the extreme gas-laser interaction efficiency achieved in HC-PCF. Finally, quantum optical effects are demonstrated in HC-PCF and photonic microcells loaded with both the molecular gas acetylene and atomic vapour rubidium. The observation of electromagnetically induced transparency (EIT) in acetylene-filled HC-PCF represents the first such observation in a molecular gas, while the use of a photonic microcell allows a comparison of many experimental configurations to explore the coherence properties of coherent optical systems in the core of a HC-PCF. Furthermore, EIT is observed unambiguously in a rubidium loaded HC-PCF for the first time, and the anti-relaxation effects of a polymer coating demonstrated in this configuration.

This thesis explores the generation and the coherence properties of Raman frequency combs that are initiated from vacuum fluctuations using hydrogen-filled hollow-core photonic crystal fibre (HC-PCF). The motivation is to explore a novel route for generating attosecond pulses and waveform synthesis. To this end, work has been undertaken in the design and fabrication of HC-PCF, in the generation of Raman comb with a compact set-up and finally in an experimental demonstration of the mutual coherence between the comb spectral components. Here, the well-established photonic bandgap (PBG) HC-PCF is further developed. Surface mode spectral positions are controlled by chemical etching technique, and a single piece of fibre with two robust bandgaps is fabricated. Furthermore, the second established class of HC-PCF; namely large-pitch Kagome-lattice HC-PCF, has experienced challenging developments. This led to the fabrication of a hypocycloid-core seven-cell Kagome HC-PCF with comparable attenuation value to that of PBG HC-PCF while offering much larger bandwidth. Using the fabricated HC-PCF, different Raman frequency comb systems are developed. In addition to the previously-generated multi-octave Raman frequency comb from a large 1064 nm Nd:YAG Q-switch laser, several more compact version of Raman comb sources have been developed, including one whose lines lay in the visible and UV for applications in forensics and biomedicine. The Raman frequency comb generated inside a length of hydrogen-filled HC-PCF is further investigated by studying the coherence of the Raman lines. Despite of vacuum-fluctuation-initiation, it is demonstrated that the comb has self- and mutualcoherence properties within each single shot, bringing thus the possibility of generating attosecond pulses with non-classical properties.

Cancer is a major health problem in the world today. Almost all cancers have a significantly better chance for therapy and recovery if detected at their early stage. The capability to perform disease diagnosis at an early stage requires high-resolution imaging that can visualise the physiological and morphological changes at a cellular level. However, resolving powers of current medical imaging systems are limited to sub-millimeter sizes. Furthermore, the majority of cancers are associated with morphological and functional alterations of cells in epithelial tissue, currently assessed by invasive and time-consuming biopsy. Optical imaging enables visualisations of tissue microstructures at the level of histology in non-invasive means. Optical imaging is suitable for detecting neoplastic changes with sub-cellular resolution in vivo without the need for biopsy. Nonlinear optical microscopy based on multi-photon absorption and higher harmonic generation has provided spectacular sights into visualisation of cellular events within live tissue due to advantages of an inherent sectioning ability, the relatively deep optical penetration, and the direct visualisation of intrinsic indicators. Two-photon excited uorescence (TPEF) from intrinsic cell components and second harmonic from asymmetric supermolecular structures can provide complementary information regarding functionalities and morphologies in tissue environments, thus enabling premalignant diagnosis by detecting the very earliest changes in cellular structures. During the past sixteen years, nonlinear optical microscopy has evolved from a photonic novelty to a well-established laboratory tool. At present, in vivo imaging and long-term bedside studies by use of nonlinear optical microscopy have been limited due to the fact that the lack of the compact nonlinear optical instrument/imaging technique forces the performance of nonlinear optical microscopy with bulk optics on the bench top. Rapid developments of fibre-optics components in terms of growing functionalities and decreasing sizes provide enormous opportunities for innovation in nonlinear optical microscopy. Fibre-based nonlinear optical endoscopy will be the soul instrumentation to permit the cellular imaging within hollow tissue tracts or solid organs that are inaccessible with a conventional optical microscope. Lots of efforts have been made for development of miniaturised nonlinear optical microscopy. However, there are major challenges remaining to create a nonlinear optical endoscope applicable within internal cavities of a body. First, an excitation laser beam with an ultrashort pulse width should be delivered eciently to a remote place where ecient collection of faint nonlinear optical signals from biological samples is required. Second, laser-scanning mechanisms adopted in such a miniaturised instrumentation should permit size reduction to a millimeter scale and enable fast scanning rates for monitoring biological processes. Finally, the design of a nonlinear optical endoscope based on micro-optics must maintain great exibility and compact size to be incorporated into endoscopes to image internal organs. Although there are obvious diculties, development of fibre-optic nonlinear optical microscopy/endoscopy would be indispensible to innovate conventional nonlinear optical microscopy, and therefore make a significant impact on medical diagnosis. The work conducted in this thesis demonstrates the new capability of nonlinear optical endoscopy based on a single-mode fibre (SMF) coupler or a double-clad photonic crystal fibre (PCF), a microelectromechanical system (MEMS) mirror, and a gradientindex (GRIN) lens. The feasibility of all-fibre nonlinear optical endoscopy is also demonstrated by the further integration of a double-clad PCF coupler. The thesis concentrates on the following key areas in order to exploit and understand the new imaging modality. It has been known from the previous studies that an SMF coupler is suitable for twoii photon excitation by transmitting near infrared illumination and collecting uorescence at visible wavelength as well. Although second harmonic generation (SHG) wavelength is farther away from the designed wavelength of the fibre coupler than that of normal TPEF, it is demonstrated in this thesis that both SHG and TPEF signals can be collected simultaneously and eciently through an SMF coupler with axial resolution of 1.8 um and 2.1 um, respectively. The fibre coupler shows a unique feature of linear polarisation preservation along the birefringent axis over the near infrared and the visible wavelength regions. Therefore, SHG polarisation anisotropy can be potentially extracted for probing the orientation of structural proteins in tissue. Furthermore, this thesis shows the characterisation of nonlinear optical microscopy based on the separation distance of an SMF coupler and a GRIN lens. Consequently, the collection of nonlinear signals has been optimised after the investigation of the intrinsic trade-off between signal level and axial resolution. These phenomena have been theoretically explored in this thesis through formalisation and numerical analysis of the three-dimensional (3D) coherent transfer function for a SHG microscope based on an SMF coupler. It has been discovered that a fibreoptic SHG microscope exhibits the same spatial frequency passband as that of a fibreoptic reection-mode non-uorescence microscope. When the numerical aperture of the fibre is much larger than the convergent angle of the illumination on the fibre aperture, the performance of fibre-optic SHG microscopy behaves as confocal SHG microscopy. Furthermore, it has been shown in both analysis and experiments that axial resolution in fibre-optic SHG microscopy is dependent on the normalised fibre spot size parameters. For a given illumination wavelength, axial resolution has an improvement of approximately 7% compared with TPEF microscopy using an SMF coupler. Although an SMF enables the delivery of a high quality laser beam and an enhanced sectioning capability, the low numerical aperture and the finite core size of an SMF give rise to a restricted sensitivity of a nonlinear optical microscope system. The key innovation demonstrated in this thesis is a significant signal enhancement of a nonlinear optical endoscope by use of a double-clad PCF. This thesis has characterised properties of our custom-designed double-clad PCF in order to construct a 3D nonlinear optical microscope. It has been shown that both the TPEF and SHG signal levels in a PCF-based system that has an optical sectioning property for 3D imaging can be significantly improved by two orders of magnitude in comparison with those in an SMF-based microscope. Furthermore, in contrast with the system using an SMF, simultaneous optimisations of axial resolution and signal level can be obtained by use of double-clad PCFs. More importantly, using a MEMS mirror as the scanning unit and a GRIN lens to produce a fast scanning focal spot, the concept of nonlinear optical endoscopy based on a double-clad PCF, a MEMS mirror and a GRIN lens has been experimentally demonstrated. The ability of the nonlinear optical endoscope to perform high-resolution 3D imaging in deep tissue has also been shown. A novel three-port double-clad PCF coupler has been developed in this thesis to achieve self-alignment and further replace bulk optics for an all-fibre endoscopic system. The double-clad PCF coupler exhibits the property of splitting the laser power as well as the separation of a near infrared single-mode beam from a visible multimode beam, showing advantages for compact nonlinear optical microscopy that cannot be achieved from an SMF coupler. A compact nonlinear optical microscope based on the doubleclad PCF coupler has been constructed in conjunction with a GRIN lens, demonstrating high-resolution 3D TPEF and SHG images with the axial resolution of approximately 10 m. Such a PCF coupler can be useful not only for a fibre-optic nonlinear optical probe but also for double-clad fibre lasers and amplifiers. The work presented in this thesis has led to the possibility of a new imaging device to complement current non-invasive imaging techniques and optical biopsy for cancer detection if an ultrashort-pulsed fibre laser is integrated and the commercialisation of the system is achieved. This technology will enable in vivo visualisations of functional and morphological changes of tissue at the microscopic level rather than direct observations with a traditional instrument at the macroscopic level. One can anticipate the progress in bre-optic nonlinear optical imaging that will propel imaging applications that require both miniaturisation and great functionality.

<p>This thesis concerns some experimental and theoretical issues in fiber optics. In particular, properties and devices based on photonic crystal fibers (PCFs) are investigated.</p><p>The work can be grouped into three parts. In the first part we use sound to control light in PCFs. The lowest order flexural acoustic mode of various PCFs is excited using an acoustic horn. The acoustic wave acts as a traveling long-period grating. This is utilized to couple light from the lowest order to the first higher order optical modes of the PCFs. Factors affecting the acoustooptic coupling bandwidth are also investigated. In particular, the effect of axial variations in acoustooptic phase-mismatch coefficient are studied.</p><p>In the second part of the thesis we use an electric field to control transmission properties of PCFs. Tunable photonic bandgap guidance is obtained by filling the holes of an initially index-guiding PCF with a nematic liquid crystal and applying an electric field. The electric field introduces a polarization-dependent change of transmission properties above a certain threshold field. By turning the applied field on/off, an electrically tunable optical switch is demonstrated.</p><p>The third part consists of two theoretical works. In the first work, we use relativistic causality, i.e. that signals cannot propagate faster than the vacuum velocity of light, to show that Kramers-Kronig relations exist for waveguides, even when material absorption is negligible in the frequency range of interest. It turns out that evanescent modes enter into the Kramers-Kronig relations as an effective loss term. The Kramers-Kronig relations are particularly simple in weakly guiding waveguides as the evanescent modes of these waveguides can be approximated by the evanescent modes of free space. In the second work we investigate dispersion properties of planar Bragg waveguides with advanced cladding structures. It is pointed out that Bragg waveguides with chirped claddings do not give dispersion characteristics significantly different from Bragg waveguides with periodic claddings.</p>