Minimum Impulse Response in Graded-Index Fibers

It is known through simple first-order analysis that differential delay between the propagational modes in multimode optical fibers can be greatly reduced by grading the optical index of the core so t h a t t h e index n = m0(1 - AR 2 ), (1) where R is the fiber radius normalized to unity at the core-cladding boundary. It is also known that even less differential delay can be realized theoretically by slightly perturbing the gradient from this parabolic shape. We have taken some direct steps based on existing analyses to determine how much further improvement might be realized if the optimum gradient could be realized in an "ideal" fiber, where geometry is invariant over its length (no mode mixing) and where material dispersion is invariant with radius. T h e approach is very simple and will be so stated, but the algebra is tedious and what little has been included will be found in the appendix. 719 In their very nice analysis, Kawakami and Nishizawa 1 showed t h a t an improvement in fiberguide impulse response could be obtained by perturbing the parabolic profile through the addition of a small fourth-order variation in the index gradient. They suggested t h a t the minimum pulse width would be obtained when the fourth-order coefficient, 5, lies between the values %, where all meridional modes are synchronous, and 1, where circular spiral modes are synchronous. Minimum total pulse width, r, in fact occurs when 5 = %, and minimum rms width, a, occurs when