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Disordered dielectric materials with structural correlations show unconventional optical behavior: They can be transparent to long-wavelength radiation, while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency in these materials is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here, we investigate band gaps, and we report Anderson localization in 2D disordered dielectric structures using numerical simulations of the density of states and optical transport statistics. The disordered structures are designed with different levels of positional correlation encoded by the degree of stealthiness χ. To establish a unified view, we propose a correlation-frequency (χ–ν) transport phase diagram. Our results show that, depending only on χ, a dielectric material can transition from localization behavior to a band gap crossing an intermediate regime dominated by tunneling between weakly coupled states.

During the last 30 years, the search for Anderson localization of light in three-dimensional (3D) disordered samples yielded a number of experimental observations that were first considered successful, then disputed by opponents, and later refuted by their authors. This includes recent results for light in TiO2 powders that Sperling et al now show to be due to fluorescence and not to Anderson localization (2016 New J. Phys. 18 013039). The difficulty of observing Anderson localization of light in 3D may be due to a number of factors: insufficient optical contrast between the components of the disordered material, near-field effects, etc. The way to overcome these difficulties may consist in using partially ordered materials, complex structured scatterers, or clouds of cold atoms in magnetic fields.

In this paper, we prove the long-time Anderson localization for the nonlinear random Schrödinger equation on Z d by using the Birkhoff normal form technique.

One of the most fascinating aspects of condensed matter is its ability to conduct electricity, which is particularly pronounced in conventional metals such as copper or silver. Such behavior stems from a strong tendency of valence electrons to delocalize in a periodic potential created by ions in the crystal lattice of a given material. In many advanced materials, however, this basic delocalization process of the valence electrons competes with various processes that tend to localize these very same valence electrons, thus driving the insulating behavior. The two such most important processes are the Mott localization, driven by strong correlation effects among the valence electrons, and the Anderson localization, driven by the interaction of the valence electrons with a strong disorder potential. These two localization processes are almost exclusively considered separately from both an experimental and a theoretical standpoint. Here, we offer an overview of our long-standing research on selected organic conductors and manganites, that clearly show the presence of both these localization processes. We discuss these results within existing theories of Mott–Anderson localization and argue that such behavior could be a common feature of many advanced materials.

In this paper, we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic (QP) Schrödinger operators. The resonances in the estimates can be described via a pair of symmetric zeros of certain functions and the estimates apply to the sub-exponential-type non-resonance conditions. As the application of quantitative Green’s function estimates, we prove both the arithmetic version of Anderson localization and the finite volume version of ( ( 1 2 − ) )-Hölder continuity of the integrated density of states (IDS) for such QP Schrödinger operators. This gives an affirmative answer to Bourgain’s problem in Bourgain (2000).

Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder – random fluctuations in material parameters – can suppress propagation and induce localization, analogous to Anderson localization. However, the statistical nature of this process remains incompletely understood. We present a comprehensive analytical and numerical study of electromagnetic wave propagation in spatially uniform media with randomly time-varying permittivity. Using the invariant imbedding method, we derive exact moment equations and identify three distinct statistical regimes for initially unidirectional input: gamma-distributed energy at early times, negative exponential statistics at intermediate times, and a quasi-log-normal distribution at long times, distinct from the true log-normal. In contrast, symmetric bidirectional input yields genuine log-normal statistics across all time scales. These findings are validated using two complementary disorder models – delta-correlated Gaussian noise and piecewise-constant fluctuations – demonstrating that the observed statistics are robust and governed by input symmetry. Momentum conservation constrains the long-time behavior, linking the statistical outcome to the initial conditions. Our results establish a unified framework for understanding statistical wave dynamics in time-modulated systems and offer guiding principles for the design of dynamically tunable photonic and electromagnetic devices.

This paper presents a detailed study investigating the effect of the material refractive index distribution at the local position of a glass–air disordered optical fiber (G-DOF) on its localized beam radius. It was found that the larger the proportion of the glass material, the smaller its localized beam radius, which means that the transverse Anderson localization (TAL) effect would be stronger. Accordingly, we propose a novel G-DOF with large-size glass elements doped in the fiber cross-section. The simulation results show that the doped large-size glass elements can reduce the localized beam radius in the doped region and has a very tiny effect on the undoped region, thus contributing to reducing the average localized beam radius of G-DOF.

We demonstrate a method to enhance the transverse Anderson localization (TAL) effect of the glass–air disordered optical fiber (G-DOF) by adjusting the number and diameter of air holes. This method does not need to enlarge the air-filling fraction of G-DOF, leading to the mitigation of fabrication complexity. By choosing the appropriate diameter and number of air holes, the average localized beam radius of G-DOF with the highest air-filling fraction of 30% can be successfully reduced by 18%. Moreover, the proposed method is always functional for the situations of the air-filling fraction lower than 50%. We also identify that, under the same air-filling fraction, a larger number of air holes in the G-DOF leads to the smaller standard deviation of the corresponding localized beam radius, indicating a stable fiber structure. The results will provide new guidance on the G-DOF design.

The electronic and transport properties of the monolayer black phosphorus and germanene nanoribbons are studied in the framework of the tight-binding model (TBM) based upon Landauer-Büttiker formalism using Green’s function method (GFM). The local density of states (LDOS) and electronic conductance of the phosphorene and germanene nanoribbons along zigzag and armchair directions are examined when the various types of defects are introduced into the system. It is found that the transport properties of zigzag phosphorene and germanene nanoribbons are strongly dependent on the number and location of the vacancies. Furthermore, it is shown that the one-/three-atom vacancy induces quasi-states in the conductance around the Fermi energy because of breaking the sublattice symmetry in the zigzag germanene nanoribbons (ZGeNRs). So the metal-semiconductor transition occurs when one-/three-atom vacancy is located at the edges of ZGeNRs; however, this transition is not observed in the zigzag phosphorene nanoribbons (ZPNRs). Besides, the results of the calculations indicate more sensitivity of ZPNRs on conductivity to the edge vacancy disorders than armchair phosphorene nanoribbons (APNRs). In addition, the conductance of ZPNRs decreases with the increment of the ribbon width in the presence of edge vacancy. Importantly, the disappearance of conductance around Fermi energy in ZPNR due to Anderson localization disorder highlights an important conclusion for the possibility of quenching of the conductance near the Fermi energy, making this class of materials appealing for applications in digital transistor devices.

The realization that electron localization in disordered systems 1 (Anderson localization) is ultimately a wave phenomenon 2 , 3 has led to the suggestion that photons could be similarly localized by disorder 3 . This conjecture attracted wide interest because the differences between photons and electrons—in their interactions, spin statistics, and methods of injection and detection—may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave 4 , 5 , 6 , 7 , 8 as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption 9 , 10 , 11 , and because absorption itself may suppress localization 3 . Here we show that the extent of photon localization can be determined by a different approach—measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminium spheres.