Standard single-mode optical fibre at has group-velocity dispersion

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Optics & Photonics · Waves in two and three dimensions, dispersion and wave packets

Modes, Packets and Media, Ch Dispersion and the propagation of wave packets

Problem

Standard single-mode optical fibre at 1550 nm1550\,\mathrm{nm} has group-velocity dispersion β2=−21.7 ps2 km−1\beta_2 = -21.7\,\mathrm{ps^2\,km^{-1}}. A transform-limited pulse of duration T0=5.0 psT_0 = 5.0\,\mathrm{ps} is launched into it. ((a)) Find the dispersion length LD=T02/∣β2∣L_{\rm D} = T_0^2/|\beta_2|. ((b)) Find the pulse duration after propagating z=5.0 kmz = 5.0\,\mathrm{km}, using T(z)=T01+(z/LD)2T(z) = T_0\sqrt{1 + (z/L_{\rm D})^2}.

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