Related papers: Evanescent modes in Sonic Crystals: Complex relati…
Complex Band Structures and Multiple Scattering Theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in Sonic Crystals. The Extended Plane Wave Expansion (EPWE) with supercell…
The complex band structures calculated using the Extended Plane Wave Expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical \omega(\vec{k}) methods, providing novel interpretations of…
This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the $k(\omega)$ problem reveal a complete…
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…
We present the mathematical and numerical theory for evanescent waves in subwavelength band gap materials. We begin in the one-dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance…
We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…
We give a general method to calculate photonic band structure in the form of wave number $k$ as a function of frequency $\omega$, which is required whenever we want to calculate signal intensity related with photonic band structure. This…
Photonic crystals with a finite size can support surface modes when appropriately terminated. We calculate the dispersion curves of surface modes for different terminations using the plane wave expansion method. These non-radiative surface…
Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together…
It is shown that negative electric permittivity and magnetic permeability recently discovered in a photonic crystal in the vicinity of the Gamma-point are properties of propagating modes only. The evanescent modes rather decay than increase…
Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in…
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions,…
The supercell approach enables us to treat the electronic structure of defective crystals, but the calculated energy bands are too complicated to understand or to compare with angle-resolved photoemission spectra because of inevitable zone…
A finite element method (FEM) for solving the complex valued k({\omega}) vs. {\omega} dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue…
The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and…
Omnidirectional light propagation in two-dimensional (2D) photonic crystals (PCs) has been investigated by extending the formerly developed 2D finite element analysis (FEA) of in-plane light propagation in which the corresponding band…
The recent results presented in arXiv:2202.05608 have led to significant developments in achieving stable approximations of Helmholtz solutions by plane wave superposition. The study shows that the numerical instability and ill-conditioning…
We have theoretically investigated two-band models of graded-gap superlattices within the envelope-function approximation. Assuming that the gap varies linearly with spatial coordinate, we are able to find exact solutions of the…
We derive the exact longitudinal plasmon dispersion relations, $\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb…
We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In…