Field distribution near an abrupt bend in single-mode waveguides: a simple model

We present a simple model for wave propagation effects near an abrupt bend of a single-mode waveguide. An abrupt bend generates a radiating field that interacts with the guided-mode component in a region near the bend. As a result, the phase front of the total field rocks. In the presence of a second bend, the launching efficiency of the guided-mode component of the third waveguide is seriously influenced by the interference between the two. In this paper we approximate the radiation component by the first-order Hermite-Gaussian wave that propagates in a uniform medium. We derive closed form expressions for the phase-front rocking and the coherent coupling efficiency. We compare them to the numerical results by the propagating beam method. Their agreement is satisfactory.