Calculations are presented of the transit times of guided and tunnelling rays in graded-index optical fibres. It is shown that 25% of the power launched by an incoherent source into a parabolic-index fibre is carried by leaky rays, which may increase the r.m.s. width of the impulse response by up to 41%. The profile which most effectively equalises the combined transit times of both guided and tunneling rays is given by alpha = 2-4 Delt
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