A data link between two buildings runs of the step-index fibre of this chapter ( ,

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Optics and Photonics, Ch Optical fibres in communication and endoscopy

Problem

A data link between two buildings runs

L = 1.2\ \mathrm{km}

of the

50\ \mu\mathrm{m}

step-index fibre of this chapter (

n_1 = 1.48

n_2 = 1.46

, core radius

a = 25\ \mu\mathrm{m}

), whose loss at

850\ \mathrm{nm}

2.0\ \mathrm{dB\,km^{-1}}

. The source is an LED at

850\ \mathrm{nm}

of spectral width

40\ \mathrm{nm}

, whose emitting face is a

100\ \mu\mathrm{m}

square radiating

5.0\ \mathrm{mW}

as a Lambertian source into the hemisphere in front of it; the face is held in air against the polished end of the fibre. The receiver needs at least

2.0\ \mu\mathrm{W}

, and the link must carry

10\ \mathrm{Mbit\,s^{-1}}

. Take

|D_\lambda| = 85\ \mathrm{ps\,nm^{-1}\,km^{-1}}

850\ \mathrm{nm}

c = 2.998\times10^8\ \mathrm{m\,s^{-1}}

, and treat each end face as a glass-air surface at normal incidence (Chapter 6). ((a)) Using the etendue count of this chapter (Chapter 3), find the largest power the LED can deliver into the fibre's guided cone. ((b)) Find the modal spread and the material spread over the link, combine them, and find the bit-rate ceiling. Does the link meet

10\ \mathrm{Mbit\,s^{-1}}

? ((c)) Write the loss budget in decibels, the fibre plus the reflection at each of the two end faces, and find the power reaching the receiver. Does it meet

2.0\ \mu\mathrm{W}

? ((d)) The fibre is replaced by one of the same core size with

n_2 = 1.47

, half the index step. Repeat (a) to (c) and decide whether the link now meets both requirements.

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