A fibre drawer offers two straight step-index fibres with the same core index : fibre…

PHYSICS · Subjective · 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 fibre drawer offers two straight step-index fibres with the same core index

n_1 = 1.52

: fibre A has

n_2 = 1.490

and fibre B has

n_2 = 1.505

, so the index step of B is half that of A. Both have uniform indices and flat polished faces in air (index

1.00

); light in the core travels at

c/n_1

with

c = 3.00\times10^{8}

m s

^{-1}

. Consider meridional rays only, with the extreme guided ray incident on the wall at the critical angle. (a) From the zig-zag result

\Delta t/L = (n_1/c)(n_1/n_2 - 1)

and from

\mathrm{NA} = \sqrt{n_1^2 - n_2^2}

, show that to first order in the index step

\Delta n = n_1 - n_2

the modal spread is proportional to

\Delta n

while the NA is proportional to

\sqrt{\Delta n}

. (b) Evaluate the exact modal spread in ns km

^{-1}

and the numerical aperture of each fibre. (c) Give the ratio (A to B) of the spreads and of the numerical apertures, and say in one sentence what the customer buys and pays for by choosing B.

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