Cylindrical dielectric waveguides such as the optical fiber and photonic crystal fiber are very important passive devices in optical communication systems. There are many kinds of commercial software and methods of simulation at present. In this thesis, we proposed the following four methods to analyze arbitrarily profiled cylindrical dielectric waveguides: The first two methods are modified from published work while the last two methods are entirely developed by ourselves. 1. Cylindrical ABCD matrix method: We take the four continuous electromagnetic field components as main variables and derive the exact four-by-four matrix (with Bessel functions) to relate the four field vector within each homogeneous layer. The electromagnetic field components of the inner and outer layer can propagate toward one of the selected interface of our choice by using the method of ABCD matrix. We can then solve for the £]-value of the waveguide mode with this nonlinear inhomogeneous matrix equation. 2. Runge-Kutta method: Runge-Kutta method is mostly used to solve the initial value problems of the differential equations. In this thesis, we introduce the Runge-Kutta method to solve the first-order four-by-four nonlinear differential equation of the electromagnetic field components and find the £]-value of the cylindrical dielectric waveguides in a similar way depicted in method one. 3. Coupled Ez and Hz method: It uses the axial electromagnetic filed components to solve cylindrical dielectric waveguides. The formulation is similar to cylindrical ABCD matrix method, but it requires less variables then cylindrical ABCD matrix method. The numerical solution obtained from this method is most stable, but it is more complicated to derive harder to write the program. 4. Simple basis expansion method: The simple trigonometric functions (sine or cosine) are chosen as the bases of the horizontal coupled magnetic field equation derived from the second-order differential equation of the transverse magnetic field components. We do not select the horizontal coupling electric field because the normal component of the electric field is discontinuous on the interface. But the normal and tangential components of the magnetic field are continuous across the interfaces. The modal solution problem is converted to a linear matrix eigenvalue-eigenvector equation which is solved by the standard linear algebra routines. We will compare these four numerical methods with one another. The characteristics and advantage as well as the disadvantage of each method will be studied and compared in detail.

Using the concept of the build-up cavity for second harmonic generation to produce 243nm laser light, an innovative cavity is theoretically explored using a 15mm length CLBO crystal. In order to limit the losses of the cavity, the number of effective optical surfaces is kept to only four and the use of a MgF2 crystal is adopted to separate the harmonic and fundamental laser beam from each other. The cavity is shown to have an expected round trip loss of five tenths of a percent or better, resulting in a conversion efficiency greater than 65%.

This thesis deals with transmission of data over power-line. There is theoretically described PLC technology and its classification, properties and used modulation techniques. A substantial part is focused on the mathematical description of distribution network using two methods, with multipath propagation and ABCD matrix. These methods are mutually compared. Furthermore, they are examined depending on the transfer functions of the topology and capabilities for unknown topology. Calculations of transfer functions are implemented using Matlab. The results were then processed graphically and evaluated.

The aim of this work was to model a four-port waveguide as a simple circuit,by first starting with a two-port then a three-port waveguide. Duethat the work was based on Nathan Marcuvitz book Waveguide handbook,an analytical solution for the circuit parameters was desired. In order toobtain an analytical solution three methods were studied; the Variationalmethod, the Integral equation method and the Static method. Out of thesethree methods the latter was chosen, because its strength of simplifying theboundary conditions. The goal to model a four-port and a three-portedwaveguide was too complicated. This led to that the goal was changed totrying to get a higher accuracy on the existing circuit model for a two-portwaveguide, by solving an extension to the circuit parameter. This was donebecause Marcuvitz only treated the first two modes correctly and it was notclear if the circuit model was stable for the higher orders of Taylor series. Inthe end a circuit model for a waveguide with an iris that treats the first 16modes correctly was solved. By looking at the dispersive properties of thecircuit a comparison with simulation software CST Microwave Studio couldbe done, which resulted in that the circuit model gave good results up to2b/ < 1. It was also showed that the accuracy was about the same as thecircuit model found in Waveguide handbook, but it can be mentioned thatthe accuracy is minimally better for the circuit model that was developed inthis work. Something that was discovered in this work is that the restrictionmentioned in Waveguide handbook for the case when the window is centeredis unreliable, it should be 2b/ < 1. It also appeared that the circuit modelremained stable for higher orders of the Taylor series, in this case up to the16:th order. / M°alet med detta arbete var att modellera en fyr-portars v°agledare somen simpel elektrisk krets, genom att f¨orst b¨orja med en tv°a-portars sedantre-portars -v°agledare. Detta arbete var baserat p°a Nathan Marcuvitz bokWaveguide handbook, d¨arav s¨oktes det en analytisk l¨osning f¨or kretsparametrarna.F¨or att kunna f°a en analytisk l¨osning, studerades tre metoder;Variationsmetoden, Integralsekvationsmetoden samt den Statiskametoden.Av dessa tre metoder valdes den sistn¨amnda, p°a grund av dess styrka medatt f¨orenkla randvillkoren. M°alet att modellera en fyr-portars samt en treportarsv°agledare var alldeles f¨or komplicerat. Detta ledde till att m°alet¨andrades till att f¨ors¨oka f°a en h¨ogre precision p°a den befintliga kretsmodellenf¨or en tv°a portars v°agledare, genom att l¨osa ut flera termer till kretsparametern.Detta gjordes d°a Marcuvitz endast hanterade de tv°a f¨orstamoderna korrekt, samt att det inte framgick ifall kretsmodellen ¨ar stabil f¨orh¨ogre ordningar av Taylor serier. I slut¨andan l¨ostes en kretsmodel f¨or env°agledare med en iris som hanterar de f¨orsta 16 moderna korrekt. Genomatt kolla p°a de dispersiva egenskaperna f¨or kretsen, kunde en j¨amf¨orelse medsimuleringsprogrammet CST Microwave Studio ske, d¨ar slutsatsen blev attkretsmodellen gav goda resultat upp till 2b/ < 1. Det visade ¨aven sig attprecisionen var ungef¨ar densamma som den kretsmodell som°aterfinns i Waveguidehandbook, men det kan n¨amnas att precisionen ¨ar minimalt b¨attref¨or den kretsmodell som togs fram i detta arbete. En sak som uppt¨acktes underdetta arbete var att restriktionen som n¨amns i Waveguide handbook f¨orfallet n¨ar gapet f¨or irisen ¨ar centrerad st¨ammer inte, den b¨or vara 2b/ < 1.Dessutom visade det sig att kretsmodellen fortfarande var stabil f¨or h¨ogreordningar av Taylorserier, i detta fall upp till den 16:e ordningen.