Transverse Coupling in Fiber Optics Part III: Bending Losses

Abstract

A general method is proposed to evaluate the radiation loss of bent open waveguides. This method consists in evaluating the coupling between the waveguide mode and the whispering-gallery modes that can be associated with the surrounding medium. The expression obtained for a reactive surface coincides with a previous result by Miller and Talanov. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> We investigate in detail the radiation loss of the fundamental (HE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> ) mode of a dielectric rod coupled to a slab. This arrangement, described in Part II of this article series, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> provides a useful mode-selection technique. The radiation loss is given by a simple closed-form expression. We find that for a wavelength of 1 µm and a rod radius of 5 µm in physical contact with the slab, the bending loss is less than 1 dB/km if the radius of curvature, in the plane of the slab, exceeds 22 mm.