Dynamics of Anderson Localization in Open 3D Media

Skipetrov, S. E.; Tiggelen, B. A. van

doi:10.1103/physrevlett.96.043902

Cited by 113 publications

(101 citation statements)

References 41 publications

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“…Current experiments [65][66][67] control either the frequency domain or the spatial domain, but not both. An optical TRM will open up an entirely new class of time-reversed optics experiments, yielding new fundamental insights into wave-scattering phenomena [22][23][24]27,121 . Important applications of TRMs are expected in the field of ultrafast nano-optics 68,120,122 .…”

Section: Applications and Perspectivementioning

confidence: 99%

Controlling waves in space and time for imaging and focusing in complex media

et al. 2012

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Section: Applications and Perspectivementioning

confidence: 99%

Controlling waves in space and time for imaging and focusing in complex media

et al. 2012

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“…(6) [5]. Such an approach can be more or less successful in making qualitative predictions in the spirit of the scaling theory of localization [17], but it becomes insufficient when one is interested in fine details of multiple wave scattering close to the mobility edge and in the localized regime: coherent backscattering cone [6], dynamics of short pulses [7,8], or precise scaling of the transmission coefficient with the size of disordered sample [9]. A plausible generalization of SC theory to media of finite size can be obtained by noticing that, by virtue of Eq.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Although SC equations (7) and (8) appear to be a powerful tool to study Anderson localization in realistic situations [6,7,8,9], they still remain a conjecture and lack microscopic justification. Derivation of these equations from the first principles is the main purpose of the present paper.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size

Cherroret

Skipetrov

2008

Phys. Rev. E

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“…In the present work, we assume that internal reflection is negligible following previous work 33 , since the dielectric constant of the constituting material is small. Thus, z 0 is set to 0.667.…”

Section: Methodsmentioning

confidence: 99%

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

2017

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Wave transport is one of the most interesting topics related to quasicrystals. This is due to the fact that the translational symmetry strongly governs the transport properties of every form of wave. Although quasiperiodic structures with 1-4 or without 1,5-7 disorder have been studied, a clear mechanism for wave transport in three-dimensional quasicrystals including localization is missing 8,9 . To study the intrinsic quasiperiodic e ects on wave transport, the time invariance of the lattice structure and the loss-free condition must be controlled 10,11 . Here, using finite-di erence methods, we study the di usive-like transport and localization of photonic waves in a three-dimensional icosahedral quasicrystal without additional disorder. This result appears at odds with the well-known theory 12 of wave localization (Anderson localization), but we found that in quasicrystals the short mean free path of the photonic waves makes localization possible.The first discovery of a quasicrystal 13 disproved the long-standing conjecture in condensed matter physics that only crystalline materials with translational symmetry could be densely packed and highly ordered. In crystalline materials the waves with wavelengths commensurate with the crystal's periodicity can transmit without scattering loss, leading to ballistic transmission. Disordered materials can be contrasted with ordinary crystals. Because of frequent scattering, wave transport in disordered materials is usually described by random walks leading to diffusive transmission, for example, Ohm's law 14 . Considering the wave nature of electrons, Anderson predicted that if the degree of structural randomness is sufficiently large, the wave interference will result in complete halting of electrons, the so-called Anderson localization 15 , and the transmission coefficient will decrease exponentially with increasing sample thickness 16 . Because of the mixed structural characteristics-for example, the lack of translational symmetry of the disordered media and the highly ordered structure of the ordinary crystals-a critical question has been raised regarding wave transport in quasicrystals, including localization, which has not been thoroughly answered 17 .To the best of our knowledge, this is the first demonstration of the intrinsic localization of photonic waves in a three-dimensional (3D) quasicrystal without additional disorder. Photonic wave localization in a 3D icosahedral quasicrystal is carefully investigated by photonic wave transmission utilizing finite-difference methods. The diffusive transport and localization of photonic waves in the quasicrystal are revealed by widely accepted approaches 18,19 . We characterize the localization phenomena by analysing the spatial and temporal evolution of photonic waves. The localization mechanism is elucidated using the photonic band structures of quasicrystal approximants.An icosahedral quasicrystal structure can be built according to the substitution rules 20 as shown in Fig. 1a-i and further detailed in Supplementary ...

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Dynamics of Anderson Localization in Open 3D Media

Cited by 113 publications

References 41 publications

Controlling waves in space and time for imaging and focusing in complex media

Controlling waves in space and time for imaging and focusing in complex media

Microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

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