Local Field Configuration Modes in a Weakly Guiding Optical Fibre with a Conically Annular Core: An Analytical Study

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Abstract
An analytical study of the various field modes occurring in a weakly guiding tapered optical fibre having a conical annular core is presented. The boundaries of the core are determined by two flare angles. When the inner flare angle is equal to zero, the structure reduces to the familiar and widely studied conically tapered optical fibre. The analysis is made ab initio and does not follow the usual approximate treatment utilizing the perturbation effects on cylindrical geometry. One finds the occurrence of discrete local modes which are closely crowded together for structures with very small flare angles. For larger flare angles the discreteness of modes is maintained but in this case one cannot talk about an effective propagation along the axis.