**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Numerical modeling of planar periodic structures in electromagnetics

Abstract

Periodic structures, such as frequency-selective surfaces (FSSs) and photonic band-gap (PBG) materials, exhibit total reflection in specific frequency bands while total transmission in other bands. They find numerous applications in a large field of the electromagnetic (EM) spectrum. For example, in the microwave region, they are used to increase the efficiency of reflector antennas. In the far-infrared region they are used in designing polarizers, beam splitters, mirrors for improving the pumping efficiency in molecular lasers, as components of infrared sensors, etc. To set a solid basis for the analysis of periodic structures, we have first studied the most commonly used technique, the integral equation (IE) solved by the method of moments (MoM). IE-MoM is particularly well-suited for the analysis of printed planar structures. In any IE-MoM numerical implementation the efficient evaluation of the corresponding Green's functions (GFs) is of paramount importance. This is especially true for IE analysis of periodic structures whose GFs are slowly converging infinite sums. The systematic study of existing acceleration algorithms of general and specific types, used to accelerate the evaluation of periodic GFs, has been performed. We propose a new and efficient method for acceleration of multilayered periodic GFs that successfully combines the advantages of Shanks' and Ewald's transform. In structures operating at higher frequencies (thin films in millimeter and submillimeter wave bands or with self supporting metallic plates) the thickness of metallic screens must be taken into account. The existing full-wave approaches for simulating these structures double the number of unknowns as compared to that one of the zero-thickness case. Moreover, the thick aperture problem asks for the computation of cavity Green's functions, which is a difficult and time-consuming task for apertures of arbitrary cross-sections. This thesis addresses the problem of scattering by periodic apertures in conducting screens of finite thickness by introducing an approximate and computationally efficient formulation. This formulation consists in treating the thick aperture as an infinitely thin one and in using the correction term in integral equation kernel that accounts for the screen thickness. The number of unknowns remains the same as in the zero-thickness screens and evaluation of complicated cavity Green's functions is obviated, which yields computationally efficient routines.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (8)

Periodic table

The periodic table, also known as the periodic table of the elements, arranges the chemical elements into rows ("periods") and columns ("groups"). It is an organizing icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which says that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks.

Integral equation

In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals.

Photonic crystal

A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices (crystal structure) of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications.