Related papers: Hierarchical Band Gaps in Complex Periodic Systems
Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
Photonic band structure of metal-dielectric and semiconductor-dielectric layered structures are studied in the presence of a strong absorption. It is shown that absorption can enlarge some gaps by as much as 50%.
We study a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a configuration that can mimic…
Local resonance band gaps in acoustic metamaterials are widely known for their strong attenuation yet narrow frequency span. The latter limits the practical ability to implement subwavelength band gaps for broadband attenuation and has…
We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to…
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…
The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…
Hierarchical structures with constituents over multiple length scales are found in various natural materials like bones, shells, spider silk and others, all of which display enhanced quasi-static mechanical properties, such as high specific…
In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift…
Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and…
Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic…
We calculate the photonic band structure at normal incidence of highly deformable, self-assembling systems - cholesteric elastomers subjected to external stress. Cholesterics display brilliant reflection and lasing owing to gaps in their…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…
Metamaterials are arrangement of basic building blocks that repeat in space, time, or both. These material systems serve as an excellent platform for controlling waves, such as engineering wavenumber band gaps, flat bands, and…
We numerically study the statistical fluctuations of photonic band gaps in ensembles of stealthy hyperuniform disordered patterns. We find that at low stealthiness, where correlations are weak, band gaps of different system realizations…