Surface roughness and the attenuation length of guided waves in optical fibers

We consider the influence of surface roughness on the attenuation length of electromagnetic waves guided by a dielectric cylinder. Fluctuations in the radius of the cylinder allow the guided wave to radiate energy into the vacuum outside the guide. We find that a perfectly sinusoidal modulation of the radius of the guide leads to a contribution to the attenuation coefficient propertional to ω2, if the wavelength of the guided mode is small compared to the radius of the guide, and if the spatial period of the sinusoid is in the appropriate range. Random fluctuations in the radius on a spatial scale small compared to the wavelength of the mode lead to a contribution proportional to ω3, in the limit of large guide radius. Our theoretical results will be compared to the data reported by Harrington, who studied the scattering produced by waves with wavelength in the 2–10 μm range in thallium halide fibers.