Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior

Bertolotti, Jacopo; Galli, Mattéo; Sapienza, Riccardo; Ghulinyan, Mher; Gottardo, S.; Andreani, LC; Pavesi, L.; Wiersma, D.S.

doi:10.1103/physreve.74.035602

Cited by 39 publications

(42 citation statements)

References 28 publications

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“…Such a periodic on average model is an optical counterpart of the Anderson model of electronic systems and is widely used for localization studies 12,14,15,19,25 . The transmission coefficients of optical waves are calculated by standard transfer matrix method 25 .…”

Section: The Modelmentioning

confidence: 99%

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

Chen

Jiang

2013

J. Phys.: Condens. Matter

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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.

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Section: The Modelmentioning

confidence: 99%

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

Chen

Jiang

2013

J. Phys.: Condens. Matter

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“…Therefore, the phase measurement is a valid tool to isolate the spectrum singularities in either periodic [12] or random systems [8]. This way, in Ref.…”

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“…In such conditions, the wavefunctions become localized within an extension ξ and decay exponentially with distance l. Being essentially an interference phenomenon, Anderson localization has been studied as for electromagnetic and acoustic waves [5], as well as for degenerate atomic gases [6]. Very recently, Anderson localization of optical waves in the microwave regime has been demonstrated in experiments on 1D random multilayer dielectric stacks [7,8].Initially, it has been widely accepted that the conductivity (transmittivity) of a disordered chain is mainly supported by states which are closer situated to the sample center [9]. Later, this was questioned, since for long enough specimen, the states in the center possess significantly reduced probability to support a two-step hopping transport through these states.…”

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Formation of optimal-order necklace modes in one-dimensional random photonic superlattices

Ghulinyan

2007

Phys. Rev. A

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We study the appearance of resonantly coupled optical modes, optical necklaces, in Anderson localized one-dimensional random superlattices through numerical calculations of the accumulated phase. The evolution of the optimal necklace order m * shows a gradual shift towards higher orders with increasing the sample size. We derive an empirical formula that predicts m * and discuss the situation when in a sample length L the number of degenerate in energy resonances exceeds the optimal one. We show how the extra resonances are pushed out to the miniband edges of the necklace, thus reducing the order of the latter by multiples of two.Wave interference phenomena play a crucial role in transport properties of various physical systems from periodic [1] to disordered [2,3]. Among these, originally studied for electronic systems, Anderson localization seems the more intriguing one [4]. It predicts a phase transition form metallic-like conductivity to an insulating regime, when the transport can come to halt with increasing the randomness. On the other hand, in a onedimensional (1D) disordered system, such a transition happens when the sample size L extends beyond the socalled localization length ξ. In such conditions, the wavefunctions become localized within an extension ξ and decay exponentially with distance l. Being essentially an interference phenomenon, Anderson localization has been studied as for electromagnetic and acoustic waves [5], as well as for degenerate atomic gases [6]. Very recently, Anderson localization of optical waves in the microwave regime has been demonstrated in experiments on 1D random multilayer dielectric stacks [7,8].Initially, it has been widely accepted that the conductivity (transmittivity) of a disordered chain is mainly supported by states which are closer situated to the sample center [9]. Later, this was questioned, since for long enough specimen, the states in the center possess significantly reduced probability to support a two-step hopping transport through these states. In late 80's, Pendry [10] and Tartakovskii et al. [11], independently, argued that the conductivity in such systems should be dominated by so-called necklaces -few homogeneously distributed through the sample states, degenerate in energy, and coupled resonantly to delocalize and extend through the chain. The number m of resonant states forming a necklace, was calculated to scale as L 1/2 , while the probability of their occurrence was shown to drop as exp(−L 1/2 ), thus predicting them to be increasingly improbable events in long samples [10]. Therefore, for a certain sample length, a trade-off between the expected number m and their occurrence probability would determine the optimal order of the necklace.In this Letter we study the appearance of optical necklaces in finite 1D random superlattices through numerical calculations of the accumulated phase and follow the evolution of the optimal necklace order when increasing the sample size. We suggest an empirical formula which predicts the optimal necklace order m *...

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“…The phenomenon can be studied also in lower-dimensional systems like random dielectric multi-layers (1D) [56][57][58], see fig. 3a, or random holes distribution in thin films (2D) [25], see fig.…”

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Complex photonic structures for energy efficiency

Burresi

Wiersma

2013

EPJ Web of Conferences

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Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior

Cited by 39 publications

References 28 publications

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

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

Formation of optimal-order necklace modes in one-dimensional random photonic superlattices

Complex photonic structures for energy efficiency

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