Related papers: Bloch Waves in High Contrast Electromagnetic Cryst…
Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well-known…
Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational…
Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable…
We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion…
The refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical inclusions. The band-structure, group…
We develop a semi-analytical model to describe bound states in the continuum (BICs) in photonic crystal slabs. We model leaky modes supported by photonic crystal slabs as a transverse Fabry-Perot resonance composed of a few propagative…
Bloch equations give a quantum description of the coupling between an atom and a driving electric force. In this article, we address the asymptotics of these equations for high frequency electric fields, in a weakly coupled regime. We prove…
We introduce a new approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasi-periodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective…
An analytical approach based on the parametric representation of the wave propagation in nonuniform media was considered. In addition to the previously developed theory of parametric antiresonance describing the field attenuation in stop…
Calculations of propagating quantum trajectories associated to a wave function provide new insight into quantum processes such as particle scattering and diffraction. Here, hydrodynamic calculations of electron beam imaging under conditions…
A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum…
The density of Bloch electromagnetic states inside a one dimensional photonic crystal (1D PC) is formulated based on its dispersion relations. The formulation applied to any anisotropic medium with known dispersion relations and…
We estimate the electromagnetic fields generated by a cluster of dielectric nanoparticles embedded into a background made of a vacuum. The dielectric nanoparticles are small scaled but enjoy high contrast of their relative permittivity.…
We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
We apply a Bloch-bands approach to the analysis of pulsed optical standing wave diffractive elements in optics and interferometry with ultracold atoms. We verify our method by comparison to a series of experiments with Bose-Einstein…
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the…
We study the local dynamics of $L^{2}\left(\mathbb{R}\right)$-perturbations to the zero solution of spatially $2\pi$-periodic coefficient reaction-diffusion systems. In this case the spectrum of the linearization about the zero solution is…
A metamaterial with frequency dependent double negative effective properties is constructed from a sub-wavelength periodic array of coated rods. Explicit power series are developed for the dispersion relation and associated Bloch wave…