Analysis of the tapered waveguide
This thesis describes analytical and numerical investigations of tapered waveguide problems, for integrated optics applications. A plane wave spectral analysis, models the propagation process of the tapered waveguide and introduces the concept of an Intrinsic spectral Integral, which turns out to be in good agreement with calculations in terms of Adiabatic modes. This allows us to extend the Intrinsic mode concept beyond the singularity where the Adiabatic mode concept breaks down. In this sense, the implementation of the resulting spectral formulation; for the case of homogeneous media, contains all information pertinent to the modal propagation mechanism, inside and outside the tapered waveguide; before and after the singularity caused by cut off of the Adiabatic mode. The thesis is mainly concerned with implementing the Intrinsic mode theory as a numerical computational tool. In this respect, very good agreement is demonstrated between this model and calculations performed numerically using the parabolic equation method. On the other hand, the new model contains far greater physical and analytical possibilities than previous methods.