Amgad Abdrabou

Purdue University West Lafayette | Purdue · Elmore Family School of Electrical and Computer Engineering

In this paper, a novel numerical method based on the sinc-collocation method is proposed for waveguide analysis. The modal characteristics waveguides are studied using a fullvectorial formulation. The scheme is formulated in terms of the transverse magnetic components. The field components are expanded using a set of products of one-dimentional sin...

There are many techniques available to numerically solve the biharmonic equation. In this paper we show that the sinc-Galerkin method is a very effective tool in numerically solving this equation. Hermite interpolation is used to treat the nonhomogeneous boundary conditions. Our method is tested on examples and comparisons with other methods are ma...

We propose an accurate and computationally efficient rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM) for modal analysis of optical waveguides. For the first time, we introduce rational Chebyshev basis functions to efficiently handle semi-infinite computational subdomains. In addition, the efficiency of these basis functions is enh...

We propose an accurate and computationally efficient numerical technique for solving the biharmonic eigenvalue problem. The technique is based on the sinc-Galerkin approximation method to solve the clamped plate problem. Numerical experiments for plates with various aspect ratios are reported, and comparisons are made with other methods in literatu...

Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that trans...

Photonic structures with high-Q resonances are essential for many practical applications, and they can be relatively easily realized by modifying ideal structures with bound states in the continuum (BICs). When an ideal photonic structure with a BIC is perturbed, the BIC may be destroyed (becomes a resonant state) or may continue to exist with a sl...

We propose and demonstrate a scheme to convert a topological state into a bound state in the continuum that still enjoys topological protection, applicable to any sub-symmetry-protected topological system embedded in a continuum bath.

In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wave vector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-Q resonances that either exist naturally for wave vectors near that of th...

Photonic structures with high-$Q$ resonances are essential for many practical applications, and they can be relatively easily realized by modifying ideal structures with bound states in the continuum (BICs). When an ideal photonic structure with a BIC is perturbed, the BIC may be destroyed (becomes a resonant state) or may continue to exist with a...

In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wavevectors near that of th...

Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was...

Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was...

Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e., a complex Bloch wavenumber, even when the periodic waveguide is lossless (no absorp...

Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially importa...

Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e. a complex Bloch wavenumber, even when the periodic waveguide is lossless (no absorpt...

Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially importa...

Plasmonics plays a vital role in realizing nanophotonic devices for integrated optics due to its strong light localization into subwavelength dimensions beyond the diffraction limit. Therefore, plasmonics has a wide range of applications such as sensing, solar cells, microscopy, etc. Plasmonics modelling techniques are necessary for understanding t...

A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline,...

Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counterintuitive wave phenomena and have potential applications in lasing, sensing, mode conversion, and spontaneous emission processes. For...

Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counter-intuitive wave phenomena, and have potential applications in lasing, sensing, mode conversion and spontaneous emission processes. For...

A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline,...

Many problems that arise in astrophysics, hydrodynamic and hydromagnetic stability, fluid dynamics, astronomy, beam and long wave theory are modeled as eighth-order boundary-value problems. In this paper we show that the sinc-Galerkin method is an efficient and accurate numerical scheme for solving these problems. The inner product approximations t...

A special kind of degeneracy, known as exceptional points (EPs), for resonant states on a dielectric periodic slab are investigated. Due to their unique properties, EPs have found important applications in lasing, sensing, unidirectional operations, etc. In general, EPs may appear in non-Hermitian eigenvalue problems, including those related to -pa...

A numerical scheme is developed to provide an approximate solution to the triharmonic boundary value problem. Based on the sinc inner product approximations, a direct discretization of the triharmonic operator Δ^3 reduces the problem to a generalized Sylvester equation. Numerical examples illustrate the pertinent features of the sinc-Galerkin metho...

A special kind of degeneracies known as the exceptional points (EPs), for resonant states on a dielectric periodic slab, are investigated. Due to their unique properties, EPs have found important applications in lasing, sensing, unidirectional operations, etc. In general, EPs may appear in non-Hermitian eigenvalue problems, including those related...

In this paper, a novel pseudo-spectral method with domain decomposition is introduced to study the modal characteristics of optical waveguides. The approach utilizes semi-vectorial formulation in terms of transverse magnetic field components Hx and Hy. Domain decomposition is employed where the computational domain is divided into a finite number o...