We study the temporal evolution of speckle patterns in transmission of shortwave pulses through a disordered waveguide. In the diffuse regime, theshort-range spatial structure of speckles is the same as for continuous wave(cw) illumination, whereas the long-range correlation between distant specklespots grows linearly with time and can exceed its cw value. We discuss thephysical origin of this phenomenon, compare our results to recent microwaveexperiments, and suggest that a similar linear growth with time should also becharacteristic for other mesoscopic interference phenomena.
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