Abstract

In many fiber and integrated optical devices one needs either to connect two waveguides of different cross-sections, or to join several waveguides at a single junction. A knowledge of the coupling efficiencies of such a junction is clearly important and depends on our understanding of propagation in tapered waveguide sections. We consider paraxial propagation in the z-direction in a graded index waveguide whose refractive index is given by By suitably choosing the function c(z) we can describe tapers with linear, hyperbolic or parabolic geometries in the xz plane. We have used the Feynman Path integral method¹ to obtain exact expressions for the coupling efficiency of such tapers without resorting to approximate numerical techniques. Our closed form analytical results for the coupling efficiencies reveal detailed structure which other methods of analysis do not show. Some recent experimental evidence would indicate support for the results of our calculations.²

© 1990 Optical Society of America