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

Abstract

High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled-localized-states embedded inside the localized system, which are dubbed as "short necklace states". In this work, we define the essential quantities and then, based on these quantities, we investigate the short necklace states' properties statistically and quantitatively. Two different approaches are utilized and the results from them agree with each other very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of logarithmic transmission. In the second approach, we investigate statistical distributions of the peak/plateau-width measured in logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing the system length, the scaling property of typical plateau-width is very special since it almost does not decrease. The methods and the quantities defined in this work can be widely used on Anderson localization studies.

Hybridized/coupled multiple resonances in nacre

“…Hybridized states are further divided into two groups: i) mode spacing Δω < linewidths δω and ii) Δω ≥ δω. While both groups can be considered as coupled resonances with a different level of coupling, each can be identified using the accumulated phase shift 38 and the valleys between peaks in log 10 (T) 19 in addition to the fundamental localization parameters.…”

“…Thouless number or fundamental localization parameter): mode spacing Δω < linewidths δω and Δω ≥ δω. [13][14][15][16][17][18][19] Natural nacre can serve as intriguing low-dimensional photonic nanostructures to capitalize on hybridized multiple resonances for enhanced light-matter interactions. From a mechanical standpoint, as nanocomposites found in the inside layers of abalone shells, nacre has received considerable attention: [20][21][22][23][24][25] The mechanical and structural properties of nacre of abalone shells have been intensively studied to better understand how they deform and fracture in terms of plasticity and toughness.…”

Excitation of multiple resonances in 1D Anderson localized systems for efficient light amplification

“…Necklace states are often considered nonlocalized states, while dominating the transmission statistics due to relatively broad spectral bandwidths [3]. Recently, the concept of necklace states has been extended to include superposition of quasi-modes with several narrow peaks in transmission spectra [4][5][6][7][8]. Such hybridized states are also called extended quasi-modes or short necklace states.…”

“…This case is the classical necklace states. (ii) When Δω ≥ δω, hybridized states have multiple narrow peaks in transmission spectra (long-lived modes), and similar multiple peaks in space are extended [4][5][6][7][8]. This latter has lifetimes shorter yet comparable to single localized modes, and δω of the adjacent peaks is still narrow with low valleys.…”

“…Because the phase changes rapidly at the locations of resonances in 1D, h can be determined by the accumulated phase shift [white solid line in Fig. 3(b)] [16] and the relative height of valleys in log 10 T [5]. As shown in an example of Iz and T (Fig.…”