Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media

Abstract

We have measured pulsed microwave transmission through quasi-one-dimensional ͑quasi-1D͒ samples with lengths up to three times the localization length as determined from measurements of the variance of intensity fluctuations. Measurements are analyzed using four complementary approaches, each appropriate in a specific time range: ͑i͒ diffusion theory; ͑ii͒ self-consistent localization theory ͑SCLT͒ with a renormalized diffusion coefficient in space and frequency, D͑z , ⍀͒; ͑iii͒ a dynamic single parameter scaling ͑DSPS͒ model, which reflects the decay of localized modes which do not overlap in space and frequency; and ͑iv͒ simulations of 1D random media. For times up to twice the diffusion time D , diffusion theory gives an excellent fit to the data. For times up to 4 D , the slowing of the decay rate of transmission is in accord with SCLT. For longer times, transmission decays more slowly than the predictions of the SCLT, indicating the inability of this modified diffusion theory to capture the decay of long-lived localized states. Beyond the Heisenberg time, the decay rate approaches the predictions of the DSPS model, reflecting the increasing proportion of wave energy in longlived localized states. The decay rates obtained from 1D simulations are then in good agreement with measurements in quasi-1D samples and coincide with decay rates given by the DSPS model.

Characterization of short necklace states in the logarithmic transmission spectra of localized systems

“…Their fundamental characters and statistical consequences to the transmission are widely studied 12,[14][15][16][17] . Recently, it is demonstrated that the NSs have evident contribution to the short-time transport of wave package [19][20][21][22] and the dynamics of fluctuations of localized waves 23 . More profoundly, the number of NS can increase dramatically as approaching the Anderson transition point, which strongly supports a modes-coupling induced quantum percolation scenario for the Anderson localization-delocalization transition 24,25 .…”

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

“…77 It was found that while the self-consistent theory can account very well for the propagation at intermediate times, it fails at longer times when the transport occurs by hopping between localized regions.…”

Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach

“…In practice the contribution of the dwell time can be difficult to observe due to weak or strong localization effects [31][32][33][34][35]. Note that the calculation of the dwell time relies on the ladder approximation that misses contributions in the development of the irreducible kernel such as crosseddiagrams.…”