Disorder-Enhanced Transport in Photonic Quasicrystals

Levi, Liad; Rechtsman, Mikael C.; Freedman, Barak; Schwartz, Tal; Manela, Ofer; Segev, Mordechai

doi:10.1126/science.1202977

Cited by 178 publications

(130 citation statements)

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“…The beam width increases slowly indicating stronger confinement, and the slope of the curve smoothly changes. The calculated exponents for 30 • , 45 • and 90 • are close to 0.5, indicating that wave propagation in the quasicrystal is diffusive-like 3,26 .…”

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confidence: 69%

“…However, the bandgap is very narrow and loosely defined thus exhibiting characteristics of pseudogaps 16 . Indeed, a previous study 3 demonstrated that a quasicrystal has pseudogaps. Since localized states can exist in the pseudogap regime 16 , the wave localization is expected to occur in the low-intensity spectral regime of the quasicrystal.…”

mentioning

confidence: 98%

“…The exponents of the width variation are approximately 1.05 for 0 • rotation and 0.89 for 90 • rotation. A value close to 1.0 indicates ballistic transport 3,26 . The beam width change of the quasicrystal is substantially different from that of the diamond.…”

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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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Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

2017

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“…The method of parabolic equation approximation was first applied by Leontovich in study of radio-waves spreading [16] and later developed in detail by Khokhlov [17] (see also [18]). In modern experimental and theoretical research, it naturally appears in investigations of a wave propagation in random optical lattices [19][20][21][22].…”

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confidence: 99%

Lévy Transport in Slab Geometry of Inhomogeneous Media

Iomin

Sandev

2016

Math. Model. Nat. Phenom.

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We present a physical example, where a fractional (both in space and time) Schrödinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the parabolic equation approximation that corresponds to the paraxial small angle approximation of the fractional Helmholtz equation. The obtained effective quantum dynamics is fractional in both space and time. As an example, Lévy flights in an infinite potential well are considered numerically. An analytical expression for the effective wave function of the quantum dynamics is obtained as well.

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“…In optics, for instance, photonic quasicrystals have attracted strong interest [3] for their specific behaviour, induced by the particular spectral properties, in light transport [4][5][6], plasmonic [7] and laser action [8]. Very recently, one of the most salient spectral feature of quasicrystals, namely the gap labelling [9], has been observed for a polariton gas confined in a one dimensional quasi-periodic cavity [10].…”

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Energy landscape in a Penrose tiling

et al. 2016

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Since their spectacular experimental realisation in the early 80's [1], quasicrystals [2] have been the subject of very active research, whose domains extend far beyond the scope of solid state physics. In optics, for instance, photonic quasicrystals have attracted strong interest [3] for their specific behaviour, induced by the particular spectral properties, in light transport [4][5][6], plasmonic [7] and laser action [8]. Very recently, one of the most salient spectral feature of quasicrystals, namely the gap labelling [9], has been observed for a polariton gas confined in a one dimensional quasi-periodic cavity [10]. This experimental result confirms a theory which is now very complete in dimension one [11,12]. In dimension greater than one, the theory is very far from being complete. Furthermore, some intriguing phenomena, like the existence of self-similar eigenmodes can occur [13]. All this makes two dimensional experimental realisations and numerical simulations pertinent and attractive. Here, we report on measurements and energy-scaling analysis of the gap labelling and the spatial intensity distribution of the eigenstates for a microwave Penrose-tiled quasicrystal. Far from being restricted to the microwave system under consideration, our results apply to a more general class of systems.Quasicrystals are alloys that are ordered but lack translational symmetry. In dimension two, they can be modelled with a collection of polygons (tiles) that cover the whole plane, so that each pattern (a sub-collection of tiles) appears, up to translation, with a given density but the tiling is not periodic. A typical example is given by the Penrose tiling [14]. Here, we implement a microwave realisation of a Penrose-tiled lattice using a set of coupled dielectric resonators [see Fig. 1 (a)]. The microwave setup used has shown its versatility by successfully addressing various physical situations ranging from Anderson localisation [15] to topological phase transition in graphene [16], and provided the first experimental realisation of the Dirac oscillator [17].We establish a two-dimensional tight-binding regime [18], where the electromagnetic field is mostly confined within the resonators. For an isolated resonator, only a single mode is important in a broad spectral range around the bare frequency E b 6.65 GHz. This mode spreads out evanescently, so that the coupling FIG. 1:Microwave Penrose-tiled quasicrystal. (a) Diamond-vertex Penrose-tiled quasicrystal, where the tiling is superposed to guide the eye (thin diamonds in green). The sites of the lattice are occupied by dielectric resonators (ceramic cylinders of 5 mm height and 8 mm diameter) with a high index of refraction (n = 6). The lattice is sandwiched between two aluminium plates (the upper one is not shown). The microwaves are excited by a movable loop antenna. (b) Experimentally obtained DOS as a function of frequency, the white and gray zones indicate the main frequency bands, Ei, and the gaps, ∆Ei, respectively. The bare frequency E b is indicated by the wh...

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Disorder-Enhanced Transport in Photonic Quasicrystals

Cited by 178 publications

References 29 publications

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

Lévy Transport in Slab Geometry of Inhomogeneous Media

Energy landscape in a Penrose tiling

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