Embedding approach to modelling the electromagnetic behavior of simple objects in a complex environment

(1)

Embedding approach to modelling the electromagnetic

behavior of simple objects in a complex environment

Citation for published version (APA):

Tijhuis, A. G., Beurden, van, M. C., Korkmaz, E., & Franchois, A. I. M. (2004). Embedding approach to modelling

the electromagnetic behavior of simple objects in a complex environment. In I. M. Pinto, V. Galdi, & L. B. Felsen

(Eds.), Electromagnetics in a Complex World : Challenges and Perspectives (pp. 287-288). (Springer

Proceedings in Physics; Vol. 96). Springer.

Document status and date:

Published: 01/01/2004

Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be

important differences between the submitted version and the official published version of record. People

interested in the research are advised to contact the author for the final version of the publication, or visit the

DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page

numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

providing details and we will investigate your claim.

(2)

Embedding

Approach

to

Modeling

the

Electromagnetic Behavior of Simple Objects

in

a

Gomplex

Environment'

A. G. _{Tijhuis ',}

M.

C. van Beurden r, B. Korkmaz r, and

A.

Franchois 2

I _{Eindhoven University of Technology, Eindhoven,}_The_Netherlands 2

Ghent University, Ghent, Belgium

Abstract

One of the most promising techniques for modeling the electromagrretic

behav-ior of

two- and three-dimensional dielectric and/or metallic objects is a

combina-tion of

the conjugate-gradient method

with

a special extrapolation technique

for

generating the

initial

estimate. The procedure

is

effective

for

almost any varying physical parameter. The basic idea is to write this

initial

estimate as a linear com-bination

of

a few previous

"final"

results and minimize the integfated squared

er-ror for the "new" value of the varying physical parameter.

By

choosing the physical parameter as an angle ofincidence

or

a source

posi-tion on a contour or surface, the scattering operator

ofa

simple object (a dielectric

volume

or

a metallic patch) can be characterized completely at the cost

of

a few

complete

field

computations

"from

scratch". This allows us

to

combine the

elec-tromagnetic response

of

this object

with

the previously determined characteristics of a complex environment.

The

first

application was the 2D inverse-scattering problem

ofa

dielectric cyl-inder embedded

in

a water-filled metal container. Here, the computational

prob-lem is

that the presence

of

the metal container breaks the translation symmetry that allows the application

of

FFT operations to evaluate the operators

in

the

im-plementation

of

the conjugate-gradient scheme. Since the container has circular symmetry, spectral theory can be used to

identiff

the scattering and reflection

op-erators for the interior object and the surrounding environment.

Presently, the approach is being generalized

to

large, almost periodic systems

consisting

of

many identical

"building

blocks".

Typical

examples are a large,

fi-nite

array

or

a

photonic-bandgap

optical

waveguide. Each

individual

building block is now considered as being "embedded" by an environment

of

similar build-ing blocks and simple regions

like

a homogeneous or layered dielectric. The con-torn separating the individual regions is no longer circular and, hence, the

scatter-ing operators need to be determined with the aid of the equivalence principle.

(3)

288

A. G. Tijhuis et a/.

The implementation amounts to solving a conventional EFIE by marching on in source position.

In the presentation, we

will

review the development summarized above. Repre-sentative results

will

be given

of

the

first

tbree steps, and the formulation behind