Losses and Impulse Response of a Parabolic Index Fiber With Random Bends

Abstract

The coupling coefficients of the modes of a parabolic index fiber with randomly curved axis are derived and are used to compute its excess losses and impulse response. It is found that bends with a period comparable to the natural ray oscillation period in the parabolic index medium are catastrophic. The average radius of curvature R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> of a guide composed of circular sections with an average length of 1 cm must not decrease below approximately R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> = 1 m. Mode coupling by random bends has the tendency to reduce the width of the impulse response function. However, this improvement is accompanied by losses. Reducing the width of the impulse response for coupled mode operation to half its uncoupled width causes 0.7 dB additional loss, a ten-fold reduction of the pulse width costs 18 dB.