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The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…
Planar photonic nanostructures have recently attracted a great deal of attention for quantum optics applications. In this article, we carry out full 3D numerical simulations to fully account for all radiation channels and thereby quantify…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing…
Bound states in the continuum (BICs) emerge throughout Physics as leaky/resonant modes that remain however highly localized. They have attracted much attention in Optics and Photonics, and especially in metasurfaces, i.e. planar arrays of…
Among different topological and related phases of condensed matter, nodal semimetals occupy a special place - the electronic band topology in these materials is related to three-dimensional bulk, rather than to surface, states. A great…
This work employs a new approach to analyze coupled-resonator circuits to design and manufacture a fully metallic dual polarization frequency selective surface (FSS). The proposed filtering structure is composed of a series of unit cells…
In this work we present a new mechanism for designing phase-gradient metasurfaces (PGMs) to control an electromagnetic wavefront with high efficiency. Specifically, we design a transmission-type PGM formed by a periodic subwavelength…
This paper aims to study the magneto-plasmons in an anisotropic graphene nano-waveguide with bigyrotropic cover and substrate. The substrate is backed by a perfect electromagnetic conductor (PEMC) layer, a general and ideal boundary, which…
This work investigates the propagation of electromagnetic waves in waveguides within static curved spacetimes. We develop a covariant formalism using Hertzian potentials to describe guided electromagnetic modes in spacetimes with metrics…
This paper deals with the existence of guided waves and edge states in particular two-dimensional media obtained by perturbing a reference periodic medium with honeycomb symmetry. This reference medium is a thin periodic domain (the…
We introduce and analyze an explicit formulation of fractional powers of the Lam\'e-Navier system of partial differential operators. We show that this fractional Lam\'e-Navier operator is a nonlocal integro-differential operator that…
In this paper we study the spectrum of low-energy edge excitations of a fractional quantum Hall (FQH) droplet. We show how to generate, by conformal field theory (CFT) techniques, the many-electron wave functions for the edge states. And we…
We explore exceptional points (EP) in a dual-mode symmetric planar optical waveguide with transverse variation of inhomogeneous loss profile; where modal evolution alongside an EP is reported in the context of selective optical mode…
We investigate theoretically properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpedicular magnetic field, the constriction functions as a spin filter with…
A generic problem of high frequency wave propagation along a metallic strip in parallel above a PEC ground plane is considered. The wave is excited by an elemental electric dipole at an arbitrary location above the PEC plane. The full wave…
Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC operators to the direct van der Waals simulation (DVS)…
An analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions…
This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with…
We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that…