Soliton states in three coupled optical waveguide systems were studied: two linearly coupled waveguides with quadratic nonlinearity, two linearly coupled waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear waveguide with resonant gratings, which enable three-wave interaction. The methods adopted to tackle the problems were both analytical and numerical. The analytical method mainly made use of the variational approximation. Since no exact analytical method is available to find solutions for the waveguide systems under study, the variational approach was proved to be very useful to find accurate approximations. Numerically, the shooting method and the relaxation method were used. The numerical results verified the results obtained analytically. New asymmetric soliton states were discovered for the coupled quadratically nonlinear waveguides, and for the coupled waveguides with both cubic nonlinearity and Bragg gratings. Stability of the soliton states was studied numerically, using the Beam Propagation Method. Asymmetric couplers with quadratic nonlinearity were also studied. The bifurcation diagrams for the asymmetric couplers were those unfolded from the corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound states due to three-wave interaction were discovered for a quadratically nonlinear waveguide equipped with resonant gratings. Since the coupled optical waveguide systems are controlled by a larger number of parameters than in the corresponding single waveguide, the coupled systems can find a much broader field of applications. This study provides useful background information to support these applications.

<p>Flexible printed circuit boards (flex PCBs) are used in a wide range of electronic devices today due to their light weight, bendability, extensive wiring possibilities, and low-cost manufacturing techniques. The general trend in the flex PCB industry is further miniaturization alongside increasing functionality per device and reduced costs. To meet these demands, a new generation of low cost manufacturing technologies is being developed to enable structures with smaller lateral dimensions and higher packing densities.</p><p>Wet etching is today the most cost-efficient method for producing a large number of through-foil structures in flex PCBs. However, conventional wet etch techniques do not allow for through-foil structures with aspect ratios over 1 – a fact that either necessitates thin and mechanically weak foils or puts severe limitations on the packing density. The fabrication techniques presented in this thesis allow for through-foil structures with higher aspect ratios and packing densities using wet etching. To achieve high aspect ratios with wet etching, the flex PCB foils are pre-treated with irradiation by swift heavy ions. Each ion that passes through the foil leaves a track of damaged material which can be subsequently etched to form highly vertical pores. By using conventional flex PCB process techniques on the porous foils, high aspect ratio metallized through-foil structures are demonstrated.</p><p>The resulting structures consist of multiple sub-micrometer sized wires. These structures are superior to their conventional counterparts when it comes to their higher aspect ratios, higher possible packing densities and low metallic cross-section. Furthermore, metallized through-foil structures with larger areas and more complicated geometries are possible without losing the mechanical stability of the foil. This in turn enables applications that are not possible using conventional techniques and structures. In this thesis, two such applications are demonstrated: flex PCB vertical thermopile sensors and substrate integrated waveguides for use in millimeter wave applications.</p>

Eine Nutzung der optischen Anisotropie dünner Schichten ist vor allem für die Displaytechnologie, die optische Datenspeicherung und für optische Sicherheitselemente von hoher Bedeutung. Diese Doktorarbeit befasst sich mit theoretischen und experimentellen Untersuchung von dreidimensionaler Anisotropie und dabei insbesondere mit der Untersuchung von lichtinduzierter dreidimensionaler Anisotropie in organischen dünnen Polymer-Schichten. Die gewonnenen Erkentnisse und entwickelten Methoden können wertvolle Beiträge für Optimierungsprozesse, wie bei der Kompensation der Blickwinkelabhängigkeit von Flüssigkristall-Displays, liefern.<br><br> Die neue Methode der Immersions-Transmissions-Ellipsometrie (ITE) zur Untersuchung von dünneren Schichten wurde im Rahmen dieser Dissertation entwickelt. Diese Methode gestattet es, in Kombination mit konventioneller Reflexions- und Transmissionsellipsometrie, die absoluten dreidimensionalen Brechungsindices einer biaxialen Schicht zu bestimmen. Erstmals gelang es damit, das dreidimensionale Brechungsindexellipsoid von transparenten, dünneren (150 nm) Filmen hochgenau (drei Stellen hinter dem Komma) zu bestimmen. Die ITE-Methode hat demzufolge das Potential, auch bei noch dünneren Schichten mit Gewinn eingesetzt werden zu können.<br><br> Die lichtinduzierte Generierung von dreidimensionaler Anisotropie wurde in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen, amorphen und flüssig-kristallinen Homo- und Copolymeren untersucht. Erstmals wurden quantitative Untersuchungen zur Änderung von lichtinduzierten, dreidimensionalen Anisotropien in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen Polymeren bei Tempern oberhalb der Glastemperatur durchgeführt.<br><br> Bei vielen der untersuchten Polymere war die dreidimensionale Ordnung nach dem Bestrahlen mit polarisiertem Licht und anschließendem Tempern oberhalb der Glastemperatur scheinbar von der Schichtdicke abhängig. Die Ursache liegt wohl in der, mit der neuentwickelten ITE-Methode detektierten, planaren Ausgangsorientierung der aufgeschleuderten dünneren Schichten.<br><br> Um Verkippungs-Gradienten in dickeren Polymerschichten in ihrem Verlauf zu bestimmen, wurde eine spezielle Methode unter Benutzung der Wellenleitermoden-Spektroskopie entwickelt.<br> Quantenchemisch bestimmte, maximal induzierbare Doppelbrechungen in flüssig-kristallinen Polymeren wurden mit den experimentell gefundenen Ordnungen verglichen. / The optical anisotropy of thin films is of great interest mainly in the display technology, the optical data storage and for optical security elements. The topic of this thesis was the theoretical and experimental investigation of three-dimensional anisotropy and especially the investigation of light-induced three-dimensional anisotropy in thin organic polymer films. The results and newly developed methods can contribute significantly to technical optimisation processes, e. g. for the compensation of the viewing angle dependence of liquid crystal displays.<br><br> The new method of immersion-transmission-ellipsometry (ITE) for the investigation of thinner layers was developed in the course of this PhD. The new method allows to determine the absolute three-dimensional refractive indices of a biaxial film. For the first time it has been possible to determine the three-dimensional indicatrix of transparent, 150 nm thin films with an accuracy of three digits after the decimal point. The ITE-method therefore has the potential to be used for the investigation of even thinner films.<br><br> The light-induced generation of three-dimensional anisotropy was investigated in thin films of azobenzene-containing and cinnamate containing, amorphous and liquid crystalline homo- and copolymers. For the first time, quantitative investigations of the changes of light-induced, three-dimensional anisotropies in thin films of azobenzene containing and cinnamate containing polymers, that were brought about by annealing above the glass transition temperatures, were carried out.<br><br> For many of the investigated polymers the three-dimensional order after irradiation with polarised light and subsequent annealing above the glass transition temperature seemed to be dependent on the film thickness. The reason could be the planar initial order of the spin-coated thinner films, which was detected with the new ITE-method.<br><br> For the characterisation of tilt gradients in thicker polymer films a special method using waveguide spectroscopy was developed. <br> Quantum chemically determined maximal values of inducible birefringence were compared with the experimentally determined values.

Eine Nutzung der optischen Anisotropie dünner Schichten ist vor allem für die Displaytechnologie, die optische Datenspeicherung und für optische Sicherheitselemente von hoher Bedeutung. Diese Doktorarbeit befasst sich mit theoretischen und experimentellen Untersuchung von dreidimensionaler Anisotropie und dabei insbesondere mit der Untersuchung von lichtinduzierter dreidimensionaler Anisotropie in organischen dünnen Polymer-Schichten. Die gewonnenen Erkentnisse und entwickelten Methoden können wertvolle Beiträge für Optimierungsprozesse, wie bei der Kompensation der Blickwinkelabhängigkeit von Flüssigkristall-Displays, liefern.<br /> <br /> Die neue Methode der Immersions-Transmissions-Ellipsometrie (ITE) zur Untersuchung von dünneren Schichten wurde im Rahmen dieser Dissertation entwickelt. Diese Methode gestattet es, in Kombination mit konventioneller Reflexions- und Transmissionsellipsometrie, die absoluten dreidimensionalen Brechungsindices einer biaxialen Schicht zu bestimmen. Erstmals gelang es damit, das dreidimensionale Brechungsindexellipsoid von transparenten, dünneren (150 nm) Filmen hochgenau (drei Stellen hinter dem Komma) zu bestimmen. Die ITE-Methode hat demzufolge das Potential, auch bei noch dünneren Schichten mit Gewinn eingesetzt werden zu können. <br /> <br /> Die lichtinduzierte Generierung von dreidimensionaler Anisotropie wurde in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen, amorphen und flüssig-kristallinen Homo- und Copolymeren untersucht. Erstmals wurden quantitative Untersuchungen zur Änderung von lichtinduzierten, dreidimensionalen Anisotropien in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen Polymeren bei Tempern oberhalb der Glastemperatur durchgeführt.<br /> <br /> Bei vielen der untersuchten Polymere war die dreidimensionale Ordnung nach dem Bestrahlen mit polarisiertem Licht und anschließendem Tempern oberhalb der Glastemperatur scheinbar von der Schichtdicke abhängig. Die Ursache liegt wohl in der, mit der neuentwickelten ITE-Methode detektierten, planaren Ausgangsorientierung der aufgeschleuderten dünneren Schichten.<br /> <br /> Um Verkippungs-Gradienten in dickeren Polymerschichten in ihrem Verlauf zu bestimmen, wurde eine spezielle Methode unter Benutzung der Wellenleitermoden-Spektroskopie entwickelt.<br /> <br /> Quantenchemisch bestimmte, maximal induzierbare Doppelbrechungen in flüssig-kristallinen Polymeren wurden mit den experimentell gefundenen Ordnungen verglichen. / The optical anisotropy of thin films is of great interest mainly in the display technology, the optical data storage and for optical security elements. The topic of this thesis was the theoretical and experimental investigation of three-dimensional anisotropy and especially the investigation of light-induced three-dimensional anisotropy in thin organic polymer films. The results and newly developed methods can contribute significantly to technical optimisation processes, e. g. for the compensation of the viewing angle dependence of liquid crystal displays. <br /> <br /> The new method of immersion-transmission-ellipsometry (ITE) for the investigation of thinner layers was developed in the course of this PhD. The new method allows to determine the absolute three-dimensional refractive indices of a biaxial film. For the first time it has been possible to determine the three-dimensional indicatrix of transparent, 150 nm thin films with an accuracy of three digits after the decimal point. The ITE-method therefore has the potential to be used for the investigation of even thinner films.<br /> <br /> The light-induced generation of three-dimensional anisotropy was investigated in thin films of azobenzene-containing and cinnamate containing, amorphous and liquid crystalline homo- and copolymers. For the first time, quantitative investigations of the changes of light-induced, three-dimensional anisotropies in thin films of azobenzene containing and cinnamate containing polymers, that were brought about by annealing above the glass transition temperatures, were carried out.<br /> <br /> For many of the investigated polymers the three-dimensional order after irradiation with polarised light and subsequent annealing above the glass transition temperature seemed to be dependent on the film thickness. The reason could be the planar initial order of the spin-coated thinner films, which was detected with the new ITE-method.<br /> <br /> For the characterisation of tilt gradients in thicker polymer films a special method using waveguide spectroscopy was developed.<br /> <br /> Quantum chemically determined maximal values of inducible birefringence were compared with the experimentally determined values.

Photonic crystals (PhCs) are periodic dielectric structures that exhibit a photonic band gap; a range of wavelengths for which light propagation is forbidden. 2D PhCs exhibit most of the properties as their three dimension counterparts with a compatibility with standard semiconductor processing techniques such as epitaxial growth, electron beam lithography, Plasma deposition/etching and electromechanical lapping/polishing. Indium Phosphide (InP) is the material of choice for photonic devices especially when it comes to realization of coherent light source at 1.55 μm wavelength. Precise engineering of the nanostructures in the PhC lattice offers novel ways to confine, guide and control light in phonic integrated circuits (PICs). Strong confinement of light in PhCs offer novel opportunities in many areas of physics and engineering. Dry etching, a necessary process step in PhC device manufacturing, is known to introduce damage in the etched material. Process induced damage and its impact on the electrical and optical properties of PhCs depends on the etched material, the etching technique and process parameters. We have demonstrated a novel post-etch process based on so-called mass-transport (MT) technology for the first time on InP-based PhCs that has significantly improved side-wall verticality of etched PhC holes. A statistical analysis performed on several devices fabricated by MT process technology shows a great deal of improvement in the reliability of optical transmission characteristics which is very promising for achieving high optical quality in PhC components. Several PhC devices were manufactured using MT technology. Broad enough PhC waveguides that operate in the mono/multi-mode regime are interesting for coarse wavelength de-multiplexing. The fundamental mode and higher order mode interaction creates mini-stop band (MSB) in the dispersion diagram where the higher order mode has a lower group velocity which can be considered as slow light regime. In this thesis work, the phenomena of MSBs and its impact on transmission properties have been evaluated. We have proposed and demonstrated a method that enables spectral tuning with sub-nanometer accuracy which is based on the transmission MSB. Along the same lines most of the thesis work relates to broad enough PhC guides that operated in the multimode regime. Temperature tuning experiments on these waveguides reveals a clear red-shift with a gradient of dλ/dT=0.1 nm/˚C. MSBs in these waveguides have been studied by varying the width in incremental amounts. Analogous to semiconductors heterostructures, photonic heterostructures are composed of two photonic crystals with different band-gaps obtained either by changing the air-fill factor or by the lattice constant. Juxtaposing two PhC and the use of heterostructures in waveguide geometry has been experimentally investigated in this thesis work. In particular, in multimode line defect waveguides the “internal” MSB effect brings a new dimension in single junction-type photonic crystal waveguide (JPCW) and heterostructure W3 (HW3) for fundamental physics and applications. We have also fabricated an ultra-compact polarization beam splitter (PBS) realized by combining a multimode waveguide with internal PhC. MSBs in heterostructure waveguides have shown interesting applications such as designable band-pass flat-top filters, and resonance-like filters with high transmission. In the course of this work, InGaAsP suspended membrane technology was developed. An H2 cavity with a linewidth of ~0.4 nm, corresponding to a Q value of ~3675 has been shown. InGaAsP PhC membrane is an ideal platform to study coupled quantum well/dot-nanocavity system. / <p>QC 20120831</p>

Flexible printed circuit boards (flex PCBs) are used in a wide range of electronic devices today due to their light weight, bendability, extensive wiring possibilities, and low-cost manufacturing techniques. The general trend in the flex PCB industry is further miniaturization alongside increasing functionality per device and reduced costs. To meet these demands, a new generation of low cost manufacturing technologies is being developed to enable structures with smaller lateral dimensions and higher packing densities. Wet etching is today the most cost-efficient method for producing a large number of through-foil structures in flex PCBs. However, conventional wet etch techniques do not allow for through-foil structures with aspect ratios over 1 – a fact that either necessitates thin and mechanically weak foils or puts severe limitations on the packing density. The fabrication techniques presented in this thesis allow for through-foil structures with higher aspect ratios and packing densities using wet etching. To achieve high aspect ratios with wet etching, the flex PCB foils are pre-treated with irradiation by swift heavy ions. Each ion that passes through the foil leaves a track of damaged material which can be subsequently etched to form highly vertical pores. By using conventional flex PCB process techniques on the porous foils, high aspect ratio metallized through-foil structures are demonstrated. The resulting structures consist of multiple sub-micrometer sized wires. These structures are superior to their conventional counterparts when it comes to their higher aspect ratios, higher possible packing densities and low metallic cross-section. Furthermore, metallized through-foil structures with larger areas and more complicated geometries are possible without losing the mechanical stability of the foil. This in turn enables applications that are not possible using conventional techniques and structures. In this thesis, two such applications are demonstrated: flex PCB vertical thermopile sensors and substrate integrated waveguides for use in millimeter wave applications. / wisenet

La tesis estudia cinco formulaciones del método de modos acoplados para analizar guías con medios magnéticos en su interior. La formulación indirecta, de tipo general, se ha aplicado al análisis de desfasadores toroidales obteniéndose resultados similares a los obtenidos mediante un método numérico puro como es el de diferencias finitas. La tesis introduce igualmente una formulación del método de adaptación que junto con el método de modos acoplados permite analizar discontinuidades simples. La combinación de los métodos anteriores con la matriz de dispersión generalizada ha permitido analizar discontinuidades en guías de onda con ferritas transversalmente magnetizadas con discontinuidades en las tres direcciones del sistema de coordenadas.

Slotted waveguide array (SWGA) antennas find application in systems which require planarity, low profile, high power handling capabilities such as radars. In this thesis, a planar, low sidelobe, phased array antenna, capable of electronically beam scanning in E-plane is designed, manufactured and measured. In the design, slot characterization is done with HFSS and by measurements, and mutual coupling between slots are calculated analytically. A MATLAB code is developed for the synthesis of the SWGA antenna. Grating lobe problem in the scanning array, which is caused by the slot positions, is solved using baffles on the array. A high power feeding section for the planar array, having an amplitude tapering to get low sidelobes is also designed using a corrugated E-plane sectoral horn. The power divider is designed analytically, and simulated and optimized with HFSS.

Wave propagation is a common phenomenon in aircraft structures resulting from high velocity transient loadings like bird hit, gust etc. Apart from understanding the behavior of structures under such loading, wave propagation analysis is also important to gain knowledge about their high frequency characteristics, which have several applications. The applications include structural health monitoring using diagnostic waves and control of wave transmission for reduction of noise and vibration. Transient loadings with high frequency content are associated with wave propagation. As a result, the higher modes of the structure participate in the response. Finite element (FE) modeling for such problem requires very fine mesh to capture these higher modes. This leads to large system size and hence large computational cost. Wave propagation problems are usually solved in frequency domain using fast Fourier transform (FFT) and spectral finite element method is one such technique which follows FE procedure in the transformed frequency domain. In this thesis, a novel wavelet based spectral finite element (WSFE) is developed for wave propagation analysis in finite dimension structures. In WSFE for 1-D waveguides, the partial differential wave equations are reduced to a set of ODEs using orthogonal compactly supported Daubechies scaling functions for temporal approximation. The localized nature of the Daubechies basis functions allows finite domain analysis and imposition of the boundary conditions. The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equation and hence, the exact elemental dynamic stiffness matrix is derived. Thus, In the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FE and after solution, the time domain responses are obtained using the inverse wavelet transform. The developed technique circumvents several serious limitations of the conventional FFT based Spectral Finite Element (FSFE). In FSFE, the wave equations are reduced to ODEs using FFT for time approximation. The remaining part of the formulation is quite similar to that of WSFE. The required assumption of periodicity in FSFE, however, does not allow modeling of finite length structures. It results in “wrap around” problem, which distorts the response simulated using FSFE and a semi-infinite (“throw-off”) element is required for imparting artificial damping. This artificial damping occurs as the “throw off” element allows leakage of energy. In some cases, a very high damping can also be considered instead of “throw off” element to remove wrap around effects. In either cases, the damping introduced is much larger than any inherent damping that may be present in the structure. It should also be mentioned that even in presence of the artificial damping, a larger time window is required for removing the distortions completely. The developed WSFE method is completely free from such problems and can efficiently handle undamped finite length structures irrespective of the time window considered. Apart from this, FSFE allows imposition of only zero initial condition and in contrary any initial conditions can be used in WSFE. Though FSFE has problem in modeling finite length undamped structures for time domain analysis, it is well suited for performing frequency domain study of wave characteristics, namely, the determination of spectrum and dispersion relations. WSFE is also capable of extracting these frequency dependent wave properties, however only up to a certain fraction of the Nyquist frequency. This constraint results from the loss in frequency resolution due to the increase in time resolution in wavelet analysis, where the basis functions are bounded both in time and frequency. A price has to be paid in frequency domain in order to obtain a bound in the time domain. The consequence of this analysis is to impose a constraint on the time sampling rate for the simulation with WSFE, to avoid spurious dispersion. WSFE for 2-D waveguides are formulated using Daubechies scaling functions for both temporal and spatial approximations. The initial and boundary conditions, however, are imposed using two different methods, which are wavelet extrapolation technique and periodic extension or restraint matrix respectively. The 2-D WSFE is bounded in both the spatial directions unlike 2-D FSFE, which is essentially unbounded in one spatial direction. Apart from this, 2-D WSFE is also free from “wrap around” problem similar to 1-D WSFE due to the localized nature of the basis functions used for temporal approximation. In this thesis, WSFE is developed for isotropic 1-D and 2-D waveguides for time and frequency domain analysis. These include elementary rod, Euler-Bernoulli and Timoshenko beams in 1-D modeling, and plates and axisymmetric cylinders in 2-D modeling. The wave propagation responses simulated using WSFE for these waveguides are validated using FE results. The advantages of the proposed technique over the corresponding FSFE method are also highlighted all through the numerical examples. Next part of the thesis involves the extension of the developed WSFE technique for modeling composite and nano-composite structures to study their wave propagation behavior. Due to their anisotropic nature, analysis of composite structures, particularly high frequency transient analysis is much more complicated compared to the corresponding metallic structures. This is due to the presence of stiffness coupling in these structures. Superior mechanical properties of composites, however, are making them integral parts of an aircraft and thus they often experience such short duration, high velocity impact Loadings. Very few literatures report the response of composite structures subjected to such high frequency excitations. Here, WSFE is formulated for a higher order composite beam with axial, flexural, shear and contractional degrees of freedom. WSFE is also formulated for composite plates using classical laminated plate theory with axial and flexural degrees of freedom. Simulations performed using these WSFE models are used to study the higher order and elastic coupling effects on the wave propagation responses. Carbon nanotubes (CNTs) and their composites are attracting a great deal of experimental and theoretical research world-wide. The recent trend in the literature shows a great interest in the dynamic and wave characteristics of CNTs and nano-composites because of their several applications. In most of these applications, CNTs are used in the embedded form as it does not requires precise alignment of the nano-tubes. In addition, the extraordinary mechanical properties of CNTs are being exploited to achieve high strength nano-composite. Apart from the experimental studies and atomistic simulation to study the mechanical properties of CNTs and nano-composites, continuum modeling is also receiving much attention, mainly due to its computational viability. In this thesis, a 1-D WSFE is formulated for multi-wall carbon nanotube (MWNT) embedded composite modeled as beam using higher order layer-wise theory. This theory allows to model partial interfacial shear stress transfer, which normally occurs due to improper dispersion of CNTs in nano-composites. The effects of different matrix materials and fraction of shear stress transfer on the wave characteristics are studied. The responses obtained using other beam theories are also compared. The beam modeling does not allow capturing the radial motions of the CNT, which are important for several applications. These can be effectively captured by modeling the CNT using a 2-D axisymmetric model. Hence, a 2-D WSFE model is constructed to capture the high frequency characteristics of single-walled carbon nanotubes (SWNTs). The response of SWNT simulated using the developed model is validated with experimental and atomistic simulation results reported in the literature. The comparison are done for dispersion relation and also radial breathing mode frequencies. The effects of geometrical parameters, namely the radius and the wall thickness of the SWNT on the higher radial, longitudinal and coupled radial-longitudinal vibrational modes are analyzed. These behaviors are studied in both time and frequency domains. Such time domain analyses of finite length SWNT are not possible with the Fourier transform based techniques reported in literature, although, such analyses are important particularly for sensor applications of SWNT. Spectral finite element method is very much suited for solution of inverse problems like force reconstruction from the measured wave response. This is because the technique is based on the concept of transfer function between the displacements (output) and applied forces (input). In the present work, WSFE is implemented for identification of impact force from the wave propagation responses simulated with FE and used as surrogate experimental results. The results show that WSFE can accurately reconstruct the impulse load applied to 1-D waveguides which include rod, Euler-Bernoulli beam and connected 2-D frame, even with highly truncated response. This is unlike FSFE, where the accuracy of the identified force depends largely on the time window of the measured responses. The detection of damage from the wave propagation analysis is another class of inverse problems considered in this thesis and is of utmost importance in the area of aircraft structural health monitoring. Here, the detection scheme is based on arrival time of the waves reflected from the damage. A novel detection technique based on wavelet filtering is proposed here and it is shown to work efficiently even in the presence of noise in the measured wave responses. Detection of damage requires an efficient damage model to simulate the mode of structural failure. In this regard, two spectrally formulated wavelet elements are proposed, one to model isotropic beam with through-width notch and the second to model composite beam with embedded de-lamination. In the first case, the response of the damaged beam is considered as the perturbation of the undamaged response and the linear perturbation analysis leads to a completely new set of dynamic stiffness matrix. In the second case, the delamination is modeled by subdividing the de-laminated region into separate waveguides and full damage model is established by imposing the kinematics. These models help to simulate wave propagation in such damaged beams to study the effect of damage on the wave response. Noise and vibration are often transmitted from the source to the other parts of the structure in the form of wave propagation. Thus, control of such wave transmission is essential for reduction of noise and vibration, which are the main cause of discomfort and in many cases cause failure of structure. Here, techniques for both passive and active controls of wave are proposed. For active control, a closed loop system is modeled using WSFE with magnetostrictive actuator for control of axial and flexural wave propagations in connected isotropic 1-D waveguides. The feedback is negative velocity and/or acceleration measured at different sensor points. A very new application of CNT reinforced composite for passive control of vibration and wave response is explored in this thesis. For this, a novel concept of nano-composite inserts is proposed. This insert can be made from CNTs dispersed in polymer. The high stiffness of the inserts helps to regulate the power flow in the form of wave propagation from the point of application of the loads to other parts of the structures. The length of the insert, volume fraction of CNTs and position are changed to achieve the required reduction in wave amplitudes. The entire thesis is split up into eight chapters. Chapter 1 presents a brief introduction, the motivation and objective of the thesis. Chapters 2 and 3 give a detail account of wavelet spectral finite element formulation for 1-D and 2-D isotropic waveguides, while Chapter 4 gives the same for composite waveguides. Chapter 5 brings out essential wave characteristics in carbon nanotubes and nano-composite structures, while Chapters 6 and 7 exclusively deal with application of WSFE to some real world problems. The thesis ends with summary and directions of future research. In summary, the thesis has brought out several new aspects of wave propagation in isotropic, composite and nano-composite structures. In addition to establishing wavelet spectral finite element as a useful tool for wave propagation analysis, several new techniques are presented, several new algorithm are proposed and several new concepts are explored.

Optical biosensors are increasingly being considered for lab-on-a-chip applications due to their benefits such as small size, biocompatibility, passive behaviour and lack of the need for fluorescent labels. The light guiding mechanisms used by many of them result in poor overlap of the optical field with the target molecules, reducing the maximum sensitivity achievable. This thesis presents a new platform for optical biosensors, namely slotted photonic crystals, which engender higher sensitivities due to their ability to confine, spatially and temporally, the peak of optical mode within the analyte itself. Loss measurements showed values comparable to standard photonic crystals, confirming their ability to be used in real devices. A novel resonant coupler was designed, simulated, and experimentally tested, and was found to perform better than other solutions within the literature. Combining with cavities, microfluidics and biological functionalization allowed proof-of-principle demonstrations of protein binding to be carried out. High sensitivities were observed in smaller structures than most competing devices in the literature. Initial tests with cellular material for real applications was also performed, and shown to be of promise. In addition, groundwork to make an integrated device that includes the spectrometer function was also carried out showing that slotted photonic crystals themselves can be used for on-chip wavelength specific filtering and spectroscopy, whilst gas-free microvalves for automation were also developed. This body of work presents slotted photonic crystals as a realistic platform for complete on-chip biosensing; addressing key design, performance and application issues, whilst also opening up exciting new ideas for future study.