A technician compares two light guides of the same core glass, : a bare rod…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Beams, resonators and guided-wave photonics · Beams, resonators and guided-wave photonics

Optics and Photonics, Ch Optical fibres in communication and endoscopy

Problem

A technician compares two light guides of the same core glass, n1=1.48n_1 = 1.48: a bare rod surrounded by air (n2=1.00n_2 = 1.00), and a step-index fibre with the same core clad in glass of index n2=1.46n_2 = 1.46. "The bare rod has a much bigger numerical aperture," she says, "so it must be the better fibre." ((a)) Calculate the numerical aperture NA=n12−n22\mathrm{NA} = \sqrt{n_1^2 - n_2^2} for the bare rod and for the clad fibre. Explain in one sentence what a numerical aperture greater than 11 means physically for the bare rod's end face. ((b)) Calculate the modal spread per kilometre, Δt/L=(n1/c)(n1/n2−1)\Delta t/L = (n_1/c)(n_1/n_2 - 1), for both cases. ((c)) Using your numbers from (a) and (b), explain why the clad fibre is the one that actually carries a usable signal over a real distance, even though it accepts far less light.

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