Coupling length due to random bending in multimode optical fibres

Mode coupling coefficients and coupling lengths are determined for multimode fibres with general index distributions in the case where random bending is the main cause of mode coupling. It is shown that the product of the coupling length and the coupling-induced loss is determined only by the shape of the index distribution, and that the coupling length of the focusing fibre is about four times longer than that of the step-index fibre when the coupling-induced losses of both fibres are equal.