Ordinary Differential Equations for Optical Attenuation as a Function of LocalRadius of Curvature

摘要

In this paper, we utilize simple approximate methods to compute the attenuationin an optical fiber as a function of its local radius of curvature. The fiber is initially wound around a bobbin of constant radius and subsequently payed out in dynamical motion. The time scale of electromagnetic phenomena is such that static attenuation values obtained from known models are acceptable for incorporation into the dynamic equations of motion derived by C. S. Kenney (Naval Weapons Center and the University of California at Santa Barbara) and M. Zak (Jet Propulsion Laboratory) for the SKYRAY Fiber Optics project. There are two very different types of loss mechanisms associated with fiber bending: (1) radiation loss caused by a uniform bend (i.e., when the fiber is wound around a bobbin of constant radius) and (2) the coupling loss from random changes of curvature as the result of surface roughness of the bobbin, mechanical stress, or cabling. The first loss mechanism is referred to as macrobending. In a qualitative sense, the attenuation caused by marcrobending increases as the radius of curvature decreases. The second loss mechanism caused by random bends (i.e., microbending) changes with 1/R squared. For each type of loss, we determine an associated ordinary differential equation for the attenuation as a function of the local radius of curvature. In the models associated with each type of loss, we assume that the fiber exhibits single-mode propagation, weak guidance, a step index of refraction, an infinitely thick cladding, and large local radius of curvature when compared to the fiber core radius.