Integral equation description of integrated dielectric waveguides

An equivalent polarization integral equation is advanced for use in the analysis of integrated dielectric waveguiding systems. This inhomogeneous Fredholm equation of the second kind in the unknown total waveguide core electric field provides a conceptually exact formulation of the guidance properties of a wide class of practical integrated dielectric waveguides. The integral equation is applied to a generalized axially uniform integrated dielectric waveguiding system. This axial uniformity renders the axial integral convolutional in nature, prompting the use of a spatial Fourier transform. This results in an inhomogeneous Fredholm equation for the unknown transformed total core field. Subsequent inversion of the transformed field with the aid of the residue theorem allows identification of two components of the total core field: the surface waves of the guide and the radiation spectrum. Application of moment method and Neumann series techniques to the integral equation is discussed.