Related papers: Evanescent modes in Sonic Crystals: Complex relati…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
We discuss the properties of the transmission function in the k-space for a generic multi-layered structure. In particular we analytically demonstrate that a transmission greater than one in the evanescent spectrum (amplification of the…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search…
In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity…
Phononic crystals enable precise manipulation of elastic wave propagation through engineered bandgaps; however, designing defect states within these bandgaps for frequency-selective applications remains a significant challenge. Existing…
Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of…
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…
The first principles calculations of band gaps and bulk moduli of cesium lead halide perovskite solid solutions, $CsPb(I_{1-x}Cl_x)_3$ and $CsPb(I_{1-x}Br_x)_3$, are performed at the level of general gradient approximation of the density…
The structural and electronic properties of a single pentacene molecule and a pentacene molecular crystal, an organic semiconductor, are examined by a first-principles method based on the generalized gradient approximation of density…
With the Marchenko method, Green's functions in the subsurface can be retrieved from seismic reflection data at the surface. State-of-the-art Marchenko methods work well for propagating waves but break down for evanescent waves. This paper…
Pseudopotentials, tight-binding models, and $k\cdot p$ theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here we present the first new method in decades, which we call…
The Semi-Analytical Finite Element (SAFE) method is widely used for computing guided wave dispersion curves in waveguides of arbitrary cross-section. Accurate mode tracking across consecutive wavenumber steps remains challenging,…
Metallic nano-structures characterised by multiple geometric length scales support low-frequency surface-plasmon modes, which enable strong light localization and field enhancement. We suggest studying such configurations using singular…
We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in…
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…
We examine harmonic oscillator defects coupled to a photon field in the environs of an optical fiber. Using techniques borrowed or extended from the theory of two dimensional quantum fields with boundaries and defects, we are able to…
In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…