Near an atomic resonance a probe beam experiences a refractive index at angular frequency

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Optics & Photonics · Wave propagation and light in media

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

Problem

Near an atomic resonance a probe beam experiences a refractive index n=1.00n = 1.00 at angular frequency ω=4.0×1015 rad s−1\omega = 4.0\times10^{15}\,\mathrm{rad\,s^{-1}}, with slope dn/dω=5.0×10−12 s\mathrm{d}n/\mathrm{d}\omega = 5.0\times10^{-12}\,\mathrm{s} there. ((a)) Find the group index ng=n+ω dn/dωn_{\rm g} = n + \omega\,\mathrm{d}n/\mathrm{d}\omega. ((b)) Find the group velocity vg=c/ngv_{\rm g} = c/n_{\rm g}, taking c=2.998×108 m s−1c = 2.998\times10^{8}\,\mathrm{m\,s^{-1}}.

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