In telecommunication, optical chips modulate, switch or amplify light, enabling a large amount of data to be transmitted through optical fibers. Moreover, such chips are also used in very sensitive medical and environmental sensors. Instead of electrons, optical chips handle photons; they manipulate light on micro- and nanoscales. Designers need to simulate how light behaves in their chips, but in most cases, calculating fully three-dimensional vectorial solutions of Maxwell's equations is computationally too expensive. This thesis attempts to reduce the computational cost of such simulations by globally expanding the field in one spatial direction in the modes of some cross-section(s). A variational procedure is applied to obtain a system of coupled partial differential equations in the other one or two directions - effectively reducing the dimensionality of the simulations by one. The system is solved by means of semi-analytical or finite element methods. The procedure is applied to scalar and vectorial mode solvers, and 2D and 3D scattering problems. For the scattering problems, special attention is paid to the boundary conditions; the boundaries of the calculation window are transparent for outgoing radiation, while allowing influx to be prescribed. When using one or a low number of modes in the expansion, the methods prove to be an improvement on other approximate techniques like the Effective Index Method, while using more modes yields results that converge to those of rigorous methods.
|Award date||25 Mar 2010|
|Place of Publication||Enschede|
|Publication status||Published - 25 Mar 2010|