Observation of bending wave localization and quasi mobility edge in two dimensions

Localization and delocalization of light in photonic moiré lattices

Moiré lattices consist of two superimposed identical periodic structures with a relative rotation angle. Moiré lattices have several applications in everyday life, including artistic design, the textile industry, architecture, image processing, metrology and interferometry. For scientific studies, they have been produced using coupled graphene-hexagonal boron nitride monolayers^1,2, graphene-graphene layers^3,4 and graphene quasicrystals on a silicon carbide surface⁵. The recent surge of interest in moiré lattices arises from the possibility of exploring many salient physical phenomena in such systems; examples include commensurable-incommensurable transitions and topological defects², the emergence of insulating states owing to band flattening^3,6, unconventional superconductivity⁴ controlled by the rotation angle^7,8, the quantum Hall effect⁹, the realization of non-Abelian gauge potentials¹⁰ and the appearance of quasicrystals at special rotation angles¹¹. A fundamental question that remains unexplored concerns the evolution of waves in the potentials defined by moiré lattices. Here we experimentally create two-dimensional photonic moiré lattices, which-unlike their material counterparts-have readily controllable parameters and symmetry, allowing us to explore transitions between structures with fundamentally different geometries (periodic, general aperiodic and quasicrystal). We observe localization of light in deterministic linear lattices that is based on flat-band physics⁶, in contrast to previous schemes based on light diffusion in optical quasicrystals¹², where disorder is required¹³ for the onset of Anderson localization¹⁴ (that is, wave localization in random media). Using commensurable and incommensurable moiré patterns, we experimentally demonstrate the two-dimensional localization-delocalization transition of light. Moiré lattices may feature an almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool for controlling the properties of light patterns and exploring the physics of periodic-aperiodic phase transitions and two-dimensional wavepacket phenomena relevant to several areas of science, including optics, acoustics, condensed matter and atomic physics.

Dynamics of wave packets in two-dimensional random systems with anisotropic disorder

A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain "lucky shots" associated with the long-living resonant modes localized inside the sample.

Localized modes in a finite-size open disordered microwave cavity

We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths, and we successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensional open random media.

Quasi-two-dimensional transfer of elastic waves

A theory for multiple scattering of elastic waves is presented in a heterogeneous plate bounded by two flat free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. We derive a time-dependent, quasi-two-dimensional radiative transfer equation (i.e., two horizontal dimensions with a finite number of vertical mode) that describes the coupling of the eigenmodes of the layer (surface Rayleigh waves, shear horizontal waves, and Lamb waves). The fundamentally different element is that the traction-free boundary conditions are treated on the level of the wave equation, whereas at the same time elastic transfer can be considered over macroscopic horizontal distances. Expressions are found that relate the small-scale fluctuations to the lifetime of the modes and to their mode-coupling rates. We discuss the diffusion approximation that simplifies the mathematics of this model significantly, and which should apply at large lapse times. Finally, this model facilitates a study of coherent backscattering near the plate surface for different sources and for different detection configurations.

Optical properties of an ionic-type phononic crystal

An ionic-type phononic crystal composed of two ferroelectric media with opposite spontaneous polarization aligned periodically in a superlattice structure was studied theoretically and experimentally. The coupling between vibrations of the superlattice and the electromagnetic waves results in various long-wavelength optical properties, such as microwave absorption, dielectric abnormality, and polariton excitation, that exist originally in ionic crystals. The results show that this artificial crystal structure can be used to simulate the microscopic physical processes in real crystals.