Analysis of finite rib waveguides by matrix methods

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Abstract
The modal structure of finite lateral extent waveguides differs from that of the associated infinite structures by the presence of additional guided modes arising from the boundary conditions and by the discrete representation of the continuum modes. These differences are analyzed for a rib waveguide using matrix methods. The origin of the additional modes and their evolution with changing system parameters are discussed. The development of localized modes from delocalized modes is of particular interest, as is the evolution of radiation modes into discrete, localized modes of higher order as the rib increases in height. These developments are followed in detail and the changes in modal character are related to the properties of the finite system's dispersion curves. Illustrations of the effect of increasing system size on the localized and delocalized modes are given.