Anomalous dispersion is an interval in which the real refractive index decreases with increasing frequency, opposite to normal dispersion. It commonly occurs near a material resonance, where optical absorption also changes rapidly.
The frequency dependence of the complex refractive index determines both propagation phase and attenuation. A rapidly changing real part can give unusual group velocity, but that value alone does not specify the speed of a new signal in an absorbing medium. Measuring transmitted intensity together with phase or deviation across the band is therefore more informative than fitting a real refractive index while ignoring losses.

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