A designer plans a link operating exactly at fused silica's zero-dispersion wavelength,

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

What an Instrument Can See, Ch The optical constants of a medium

Problem

A designer plans a link operating exactly at fused silica's zero-dispersion wavelength, 1.273 μm1.273\,\mu\mathrm{m}, using a source of spectral width Δλ=20 nm\Delta\lambda = 20\,\mathrm{nm} over a fibre of length L=100 kmL = 100\,\mathrm{km}. Reasoning that D=0D = 0 there, the designer argues that the pulse suffers no dispersive spreading at all, and that the bit rate can therefore be raised without limit. Near the zero-dispersion wavelength, DD itself is not constant: it varies with wavelength as the dispersion slope S=dD/dλ≈0.09 ps nm−2 km−1S = dD/d\lambda \approx 0.09\,\mathrm{ps\,nm^{-2}\,km^{-1}}. To leading order beyond the vanishing first-order term, the pulse spread is Δt≈12S(Δλ)2L\Delta t \approx \tfrac{1}{2}S(\Delta\lambda)^2 L. ((a)) Estimate the actual pulse spread for this link. ((b)) Say what is wrong with the designer's reasoning.

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