Rib waveguide curvature loss: the scalar problem

The volume current method is used to obtain the curvature radiation loss from an integrated-optics dielectric rib waveguide in contact with the air. Following earlier workers, a single component of the electric field is assumed to satisfy a scalar Helmholtz equation. The electric field component is assumed to vanish on the air/dielectric interface; the introduction of this large discontinuity in the refractive index reduces the curvature loss considerably. The time and spatial decay constants appear as the product of two factors: a curvature factor CF and a shape discriminating factor DF. The factor CF is of lower order of magnitude than the curvature factor for an optical fibre, but contains similar features which may be compared. The discriminating factor DF may be calculated by the numerical solution of Helmholtz equations, but is discussed qualitatively here. Comparative shape studies are in agreement with physical intuition.