Efficient PML boundaries for anisotropic waveguide simulations using the finite element method

The application of integrated optics has broadened from well established areas, such as high-speed modulators for communication over optical fibre, to such diverse areas as radio frequency (RF) signal processing and antenna beam forming. Simulation tools that are general enough to model a wide range of RF and photonic devices, yet efficient enough to be used trivially are required.<br><br>The aim of this thesis is to investigate the use of the perfectly matched layer (PML) boundary condition as a means of improving the efficiency of eigenvalue simulations, and to extend their range of applicability to radiating waveguides. This work focuses in particular on the simulation of waveguides using the biaxial material Lithium Niobate. Major contributions made by this work include the derivation of a generalised PML suitable for matching biaxial materials, extension of analysis of numerical dispersion and reflection in the finite element method to biaxial media and derivation of closed form expressions for the numerical reflection from a PML interface. These expressions are used to investigate the major contributions to numerical errors in the implementation of the PML boundary and hence a significantly more efficient technique for enhancing the PML's performance with a minimal increase in unknowns is suggested and demonstrated in a practical simulation. Finally, the generalised PML is applied to three eigenvalue simulations, including a radiating waveguide bend, with greatly improved efficiency and accurate simulation of propagation loss. <br><br>In summary, the PML has been extended to biaxial materials and the sources of numerical errors in its implementation have been identified and an efficient means of reducing them devised. The new PML and implementation technique have been demonstrated in eigenvalue simulations of both lossless and lossy waveguides with accurate and efficient results being achieved.