Until this present work, the acoustics of waveguides has been divided into two broadly distinct fields---linear acoustics in ducts of complex geometry such as those with curvature or varying width, and nonlinear acoustics restricted to simple geometry ducts without curvature or flare. This PhD unites these distinct branches to give a complete mathematical description of weakly nonlinear wave propagation in a general shaped duct in both two and three dimensions. Such ducts have important applications---the clearest example is that of brass instruments, where it has been demonstrated that nonlinear wave steepening gives rise to the characteristic 'brassy' sounds of, for example, the trombone. As the ducts of these instruments have a very complicated geometry involving curvature, torsion and varying width, the goal of the PhD is to address what effect, if any, such changes in duct geometry have on the acoustic properties of such instruments. Other potential applications include the study of acoustics in curved aircraft engine intakes and even the nonlinear sound propagation through the trunk of an elephant. The first results chapter is focused on the exposition of the method used for the remainder of the paper, with the introduction of a new ``nonlinear admittance term'' as well as the associated algebra for it. An elegant notation for the nonlinear algebra is also developed, greatly simplifying the equations. The method is applied to one and two dimensional ducts and some analytical results are derived relating the work to previously published results. Numerical results are also presented and compared to other sources. The concept of nonlinear reflectance is also introduced---illustrating the effect of wave amplitude on the amount of energy reflected in a duct. The next results chapter builds on this work extending it to three dimensions. Numerical results are presented for three characteristic ducts---a curved duct, a horn and a helical duct, being one of the first works to study acoustics in helical pipes for both linear and nonlinear sound propagation. The final results chapter, utilising all of the previous work, addresses the problem of an open ended duct of finite length with nonlinear effects included. Results are compared with the linear results from the Wiener-Hopf method and new results are presented illustrating the effect of geometry and nonlinearity on the resonances of finite length waveguides culminating in the study of the resonances of a trombone.

Thesis (M.S.)--Montana State University--Bozeman, 2006. / Typescript. Chairperson, Graduate Committee: James P. Becker. Includes bibliographical references (leaves 120-121).

This thesis describes the fabrication and characterization of waveguides in the nonlinear, Raman-active optical crystal potassium gadolinium tungstate (KGW). Ion implantation and femtosecond laser writing techniques are used for the first time to fabricate waveguides in this material. The light ion implanted waveguides using hydrogen ions showed unexpected refractive index increases in the damage regions of approximately 0.3% of the nominal refractive index values for three of the four polarization orientations, with only the highest refractive index polarization exhibiting a refractive index decrease of approximately 0.2%. Waveguides fabricated using high-energy carbon, oxygen and fluorine ion irradiations resulted in strongly confining waveguides with wide amorphous damage regions. Carbon ion irradiation of KGW showed the most promise, with sharp step-like waveguides with a maximum refractive index change of delta-n=0.2 with excellent preservation of the Raman properties in the waveguide core. Microreflectivity measurements on the carbon ion irradiated sample revealed unexpected intermittent refractive index changes in the core region, a feature not detected using standard characterization techniques found in the literature. The oxygen ion irradiation of KGW also generated strongly confining waveguides with a maximum refractive index change of delta-n=0.17, however the Raman performance was shown to be reduced to less than 50% in the waveguide cores. Fluorine ion irradiations of KGW resulted in amorphous regions fabricated in the surface regions, offering promise for masking techniques for creating two-dimensional structures. The waveguides written using femtosecond laser writing processes were used to write buried channel waveguides using compressive stresses to form the waveguide. These waveguides exhibited low-losses down to to 2.0 dB/cm in the telecommunications spectrum, with high coupling efficiency to SMF fiber, and excellent Raman properties in the waveguide core. These channel waveguides also successfully showed SRS generation into the 1.8-1.9 \mu m infrared region using a high power picosecond pump source in the telecommunications band. The use of the microreflectivity and micro-Raman spectroscopy measurement techniques were demonstrated to be valuable characterization tools for each of the fabrication methods.

This thesis describes the fabrication and characterization of waveguides in the nonlinear, Raman-active optical crystal potassium gadolinium tungstate (KGW). Ion implantation and femtosecond laser writing techniques are used for the first time to fabricate waveguides in this material. The light ion implanted waveguides using hydrogen ions showed unexpected refractive index increases in the damage regions of approximately 0.3% of the nominal refractive index values for three of the four polarization orientations, with only the highest refractive index polarization exhibiting a refractive index decrease of approximately 0.2%. Waveguides fabricated using high-energy carbon, oxygen and fluorine ion irradiations resulted in strongly confining waveguides with wide amorphous damage regions. Carbon ion irradiation of KGW showed the most promise, with sharp step-like waveguides with a maximum refractive index change of delta-n=0.2 with excellent preservation of the Raman properties in the waveguide core. Microreflectivity measurements on the carbon ion irradiated sample revealed unexpected intermittent refractive index changes in the core region, a feature not detected using standard characterization techniques found in the literature. The oxygen ion irradiation of KGW also generated strongly confining waveguides with a maximum refractive index change of delta-n=0.17, however the Raman performance was shown to be reduced to less than 50% in the waveguide cores. Fluorine ion irradiations of KGW resulted in amorphous regions fabricated in the surface regions, offering promise for masking techniques for creating two-dimensional structures. The waveguides written using femtosecond laser writing processes were used to write buried channel waveguides using compressive stresses to form the waveguide. These waveguides exhibited low-losses down to to 2.0 dB/cm in the telecommunications spectrum, with high coupling efficiency to SMF fiber, and excellent Raman properties in the waveguide core. These channel waveguides also successfully showed SRS generation into the 1.8-1.9 \mu m infrared region using a high power picosecond pump source in the telecommunications band. The use of the microreflectivity and micro-Raman spectroscopy measurement techniques were demonstrated to be valuable characterization tools for each of the fabrication methods.

Dielectric waveguides are crucial devices in the making of integrated-optical circuits. It is very important to analyze this type of waveguides so we can optimize the design for better performance. Analysis of bent waveguides has been a difficult problem in the past. In a bent waveguide, two coordinate systems are needed to fully describe the ongoing complex scattering process in the transition region of the waveguide. It is extremely hard to analyze such problems for methods built on a single coordinate system such as the finite-difference,finite-element methods and the beam propagation method (BPM). In this thesis, we adopt dual mode-field representations (for all the low and higher-order modes), one for the incident and reflected waves and the other for the transmitted waves, to study bending effects. To calculate the wave fields, we apply the analytic continuity principle to allow the waves to analytically extend and join smoothly on the bordering line. By matching the two continuity conditions of both the fields and their normal derivatives we get two matrix equations for the reflection and transmission coefficients. For symmetrical bending waveguide, the task can be further reduced to solving two smaller problems each with even or odd symmetry on the bordering line. As the bent angle increases the governing matrix equation becomes more singular. As a result, all the elements in the matrix are calculated with closed-form formulae to minimize the stability problem. In addition, special numerical methods are used to extend the range of the bending angles that this method can handle. In conclusion, our theory can calculate microwave bending waveguides up to 30 degrees and for dielectric slab waveguide with 15 degree bent angle. With this method we are able to compute small reflection coefficients of about -60dB and less.

No description available.

Waveguides are used to transmit electromagnetic signals.Their geometry is typically long and slender their particularshape can be used in the design of computational methods. Onlyspecial modes are transmitted and eigenvalue and eigenvectoranalysis becomes important. We develop a .nite-element code for solving theelectromagnetic .eld problem in closed waveguides .lled withvarious materials. By discretizing the cross-section of thewaveguide into a number of triangles, an eigenvalue problem isderived. A general program based on Arnoldi’s method andARPACK has been written using node and edge elements toapproximate the .eld. A serious problem in the FEM was theoccurrence of spurious solution, that was due to impropermodeling of the null space of the curl operator. Therefore edgeelements has been chosen to remove non physical spurioussolutions that arises. Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. For the more complicated inhomogeneouswaveguides with and without striplines, comparison has beendone with results found in literature together with gridconvergence studies. The code has been implemented to be used in an industrialenvironment, together with full 3-D time and frequency domainsolvers. The2-D simulations has been used as input for full3-D time domain simulations, and the results have been comparedto what an analytical input would give. / NR 20140805

This thesis with the research development in design and modeling of the lithium niobate (LiNbO₃) optical waveguides. In particular, the material and modal properties of the titanium (Ti)-indiffusion and annealed proton-exchange (APE) are investigated thoroughly. By linking the relation of the design and fabrication parameters with modal properties of the LiNbO₃ waveguides, a comparative study on modaling and characterization of diffused optical waveguides is presented. First we investigate the diffusion, exchange, and annealing processes analytically and numerically. Through comparing different models of index change with concentration of the related species such as titanium and hydrogen, the material properties can be calculated. The accuracy and the scope of validity for the analytical methods are also investigated. Some important fabrication and design parameters are abstracted and used for calculating the index distribution of the optical waveguides. Then, by applying a rigorous finite difference method, the modal properties of the diffused waveguides, such as modal profile, effective index, and coupling loss with the standard fiber, can be calculated. The modal properties of the optical waveguides directly link to the fabrication parameters of corresponding waveguides. Based on modal properties of optimized waveguides, the device performances of the related devices can be easily obtained. Based on the analysis of general LiNbO₃ optical waveguides, the detail material and modal properties of the titanium-indiffusion and APE LiNbO₃ optical waveguides are further investigated. Their fabrication processes are reviewed and typical process parameters are given. Furthermore, by comparing with measurement results of the titanium-diffusion and APE LiNbO₃ optical waveguides made in McMaster University, the relation between the waveguide modal performance and design parameters is built through some effective methods and ready to be applied in the design of optical devices. Finally, we reconstruct the refractive index distribution of the optical waveguides by using the measurement results of modal properties. / Thesis / Master of Engineering (ME)

In this work, we investigate several aspects of photonic crystal waveguides through modeling and simulation. We introduce a one-dimensional model for two-dimensional photonic crystal fibers (PCFs), analyze tapered PCFs, analyze planar photonic crystal waveguides and one-dimensional PCFs with infinite periodic cladding, and investigate transmission properties of a novel type of fiber, referred to as Fresnel fiber. A simple, fast, and efficient one-dimensional model is proposed. It is shown that the model is capable of predicting the normalized propagation constant, group-velocity dispersion, effective area, and leakage loss for PCFs of hexagonal lattice structure with a reasonable degree of accuracy when compared to published results that are based on numerical techniques. Using the proposed model, we investigate tapered PCFs by approximating the tapered section as a series of uniform sections along the axial direction. We show that the total field inside the tapered section of the PCF can be evaluated as a superposition of local normal modes that are coupled among each other. Several factors affecting the adiabaticity of tapered PCFs, such as taper length, taper shape, and number of air hole rings are investigated. Adiabaticity of tapered PCFs is also examined. A new type of fiber structure, referred to as Fresnel fiber, is introduced. This fiber can be designed to have attractive transmission properties. We present carefully designed Fresnel fiber structures that provide shifted or flattened dispersion characteristics, large negative dispersion, or large or small effective area, making them very attractive for applications in fiber-optic communication systems. To examine the true photonic crystal modes, for which the guidance mechanism is not based on total internal reflection, photonic crystal planar waveguides with infinite periodic cladding are studied. Attention will be focused on analytical solutions to the ideal one-dimensional planar photonic crystal waveguides that consist of infinite number of cladding layers based on an impedance approach. We show that these solutions allow one to distinguish clearly between light guidance due to total internal reflection and light guidance due to the photonic crystal effect. The analysis of one-dimensional PCFs with infinite periodic cladding is carried out in conjunction with an equivalent T-circuits method to model the rings that are close to the core of the fiber. Then, at sufficiently large distance from the core, the rest of the cladding rings are approximated by planar layers. This approach can successfully estimate the propagation constants and fields for true photonic crystal modes in both solid-core and hollow-core PCFs with a high accuracy. <i>Original file (released May 10, 2007) replaced Oct. 3, 2012 GMc per DePauw]</i> / Ph. D.

Miniaturization of electronic circuits and systems continue to pose great difficulties in meeting the demand and anticipated growth for information services and their associated electronics. Of the several information processing techniques under consideration for devices of the future, optical systems are considered to offer significant advantages in terms of speed and bandwidth. Unfortunately, at the dimensions of contemporary electronics, optical waveguides will fail to assist significantly due to the fact that standard optical waveguides will have dimensions below the diffraction limit and hence optical waveguiding at such scales will be impractical. In order to circumvent this, recent work in the area of using nano-sized protrusions to guide light below the diffraction limit has been receiving a decent amount of attention. Such systems have typically involved using electron beam lithography to create these perturbations on metallic surfaces called plasmonic waveguides. While these waveguides are fairly efficient, in the amounts required to make real circuits this method would be impractically slow and prohibitively expensive. However, such waveguides could be made much more cheaply if means could be found to arrange colloidal nanoparticles on suitable substrates. In this project, nanoscale self-assembly has been investigated with the aim of achieving such ends. Colloidal nanoparticles have been synthesized and self-assembled onto substrates such that they show near field interactions necessary for plasmonic waveguiding without any aggregation. Absorption peak shifts, which were obtained during the experimental phase of this project confirmed that such nanoparticle assemblies can be achieved and that they do demonstrate some plasmonic waveguiding action. With this first step, it is hoped that films like these may find use for quick and cheap plasmonic waveguiding sometime in the near future. / Master of Science