We study the effect of localization on the propagation of a pulse through a multimode disordered waveguide. The correlator 〈u(ω₁)u*(ω₂)〉 of the transmitted wave amplitude u at two frequencies differing by δω has for large δω the stretched exponential tail ∝exp(-√τDδω/2). The time constant τD=L²/D is given by the diffusion coefficient D, even if the length L of the waveguide is much greater than the localization length ξ. Localization has the effect of multiplying the correlator by a frequency-independent factor exp(-L/2ξ), which disappears upon breaking time-reversal symmetry.
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Beenakker et al. (1999) studied this question.
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