No d'ordre : 4420 ANNEE 2012

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RENNES I ueh w

THESE I UNIVERSITE DE RENNES 1 sous le sceau de I'Universite Europeenne de Bretagne

pour le grade de

DOCTEUR DE L'UNIVERSITE DE RENNES 1 Mention : ~raitement du Signal et Telecommunications

Ecole doctorale Matisse

presentee par

Samsul Haimi DAHLAN Preparee a I'unite de recherche (UMR CNRS 6164, IETR)

lnstitut dlElectronique et de Telecommunications de Rennes Universite de Rennes 1

Contribution to the body of revolution finite-difference time domain (BoR-FDTD) method - Implementations of hybrid and multi- resolution approaches for fast simulation of electrically large axis- symmetrical antenna structures.

These soutenue a I'Universite de Rennes 1 le 13 Janvier 2012 devant le jury compose de :

Mme Elodie RICHALOT Professeur des Universites, Univenite de Paris-Est / rappoHeur

M. Michel NEY Professeur, Telecom Bretagne I rapporieur

M. Alain RElNElX Directeur de Recherche au CNRS, Universite de Limoges 1 examinateur

M. Renaud LOISON Professeurdes Universites, INSA de Rennes 1 examinateur

M. Anthony ROLLAND Docteur de I'Univenite de Rennes 1 I examinateur

M. Ronan SAULEAU Professeur des Universites, Univenite de Rennes 1 / directeur de these

Chapter 1 - General Introduction

Chapter 1

General Introduction

1.1 History and collaboration

This Ph.D thesis on the Body-of-Revolution Finite-Difference Time-Domain (BoR-

FDTD) was conducted at IETR (Inititute of Electronics and Telecommunications of Rennes).

It was supervised by Ronan SAULEAU (Professor at University Rennes 1). This work was

supported in part by the "Universit6 Europeenne de Bretagne" and the "Conseil Regional de

Bretagne" (project acronyms: OPTIMISE, CREATEICONFOCAL and GRAPPAS) and

UTHM (Universiti Tun Hussien Onn Malaysia) for the Ph.D scholarship.

The development of the BoR-FDTD simulator at IETR started in 2006 by Dr. Ming-

Sze Tong. He contributed in the development of the kernel programs of the simulator and

used it for electromagnetic study focusing on the electromagnetic band-gap structures (EBGs)

in BoR environment [I], [2].

This work was then continued by Anthony Rolland, who defended his Ph.D in 2009.

His thesis entitled "Conception d'antennes me'tallo-diklectriques par optimisation globule

base'e ssu le couplage entre la mkthode FDTD et les algorithmes gkne'tiques" combines the

BoR-FDTD simulator with an optimization technique which is based on the Genetic

Algorithms (GA) for the synthesis and the development of dielectric and lens antennas with

axis-symmetrical structure [3].

The BoR-FDTD is well known for fast and efficient method compared with the hl ly

three-dimensional (3D) FDTD simulator. In this present work, we explore and introduce

techniques to further reduce the computational effort especially for the simulation of large

body-of-revolution structures using the BoR-FDTD method.

Chapter 1 - General Introduction

References

[I] Ming Sze Tong, "Final report on body-of-revolution FDTD," (Unpublished)

[2] M. -S. Tong, R. Sauleau, A. Rolland, and T.-G. Chang, "Analysis of Electromagnetic

Band-Gap (EBG) waveguide structures using body-of-revolution finite difference time

domain method," Microwave and Optical Technology Letters, vol. 49, no. 9, pp. 467 -

469, Sept. 2007.

[3] A. Rolland, "Conception d'antennes me'tallo-di6lectriquespar optimisation globule base'e

sur le couplage entre la me'thode FDTD et les algorithmes ge'ne'tiques," These de

Doctorat, Universite de Rennes 1, Jan. 2009.

[4] Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's

equations in isotropic media," IEEE Trans. Antennas and Propagation, vol. 14, 1966, pp.

302-307.

[5] M. Celuch and W. K. Gwarek, "Industrial design of axis-symmetrical devices using a

customized solver from RF to optical frequency bands," IEEE Microwave Mag., vol. 9,

no. 6, pp. 150 - 159, Dec. 2008.

[6] A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference

Time-Domain Method, 2nd ed., Artech House, Inc., 2000.

[7] S. H. Dahlan, A. Rolland, R. Sauleau, "Application of the dual-grid scheme in BoR

FDTD for the simulation of dual reflector antennas", European Con$ on Antennas and

Propagation, EuCAP 2011, pp. 1345-1348, Rome, Italy, 11-15 Apr. 201 1.

[8] S. H. Dahlan, A. Rolland, R. Sauleau, "Schkmas d'analyse rapide de problemes

axisymitriques par la mkthode FDTD b symitrie de rkvolution (BoR-FDTD)", Dix-

septidmes Journe'es Nationales Micro-ondes, Brest, 4 pages, 18-20 May 201 1.

[9] S. A. Muhammad, A. Rolland, S. H. Dahlan, R. Sauleau and H. Legay, "Comparison

between Scrimp horns and stacked Fabry-Perot cavity antennas with small apertures,'"

European Con$ on Antennas and Propagation, EuCAP 2012, (Submitted).

[lo] Romain Pascaud, "Nouveaux schdmas rapides pour la mdthode des Diffirences Finies

dans le Domaine Temporel (FDTD). Application b la simulation d'antennes environnkes,"

These de Doctorat, Institut National des Sciences Appliquies de Rennes, Dec. 2007.

Chaoter 2 - The Finite Difference Time Domain Method - General Overview

effect however could be reduced by implementation of some extension technique

called the Mur superabsorbation [6] which is much less sensitive to variation of an

incident angle. The major property of the Mur ABC is that it can accurately

matched incoming wave at a particular direction, by changing the effective

permittivity of the Mur absorption. This property will deteriorates to some extent

for incoming wave at angles different compared to the matched one.

2. The total field-scattered field (TF-SF) decomposition

This technique is very useful in antenna and radar analysis. The FDTD problem

space is divided into two separate regions by virtual TF-SF boundaries which then

known as the total field (TF) region and the scattered field (SF) region [3]. An

incident plane wave is excited inside the total field region. It can be a direct or an

oblique plane wave depending on the problem analysis. Whenever there is no

scatterer or obstacle in the TF region, the applied incident plane wave will not

radiate outside the TF region into the SF region. On the other hand, with the

present of obstacle inside the TF region, only the scattered part of the

electromagnetic wave will be radiated outside the region into the SF region.

3. Near-field to far-field transformation (NTFF)

An important technique for calculating the far field characteristics of a radiating

source based on the near field information without having to extend the radiation

space to the far field region. The near-to-far field transformation is performed

around a surrounding transformation surface enclosing the radiating source in the

near field region. It is a post-processing technique that calculates the contributions

of the radiated fields over time for gaining the far field information either in time

or frequency domain. It is widely applied in antenna design [7].

4. Media

Media such as losslessflossy, linearlnonlinear, isotropic/nonisotropic and

dispersivelnondispersive can be treated using the FDTD method. Nonlinear media

can be treated naturally in FDTD since it is a time-domain approach. For

dispersive media, special model such as the Debye, Drude and Lorentz models [3]

are commonly applied to represent the characteristic. A single FDTD run could

provide results for the whole spectrum range.

34

Cha~ter 2 - The Finite Difference Time Domain Method - General Overview

could handle this eficiently in FDTD such as by applying the multi-resolution

approach. In this thesis a new multi-resolution approach based on the dual grid

method is introduced in the subsequent chapter for handling such issue in the

bodies of revolutions FDTD (BoR-FDTD) environment. The explanation about

BoR-FDTD is detailed in the next chapter.

2. Long computation of high-Q structures

Performing simulation for a high-Q structure using the time domain approach

might require very long computation time. This is due to the slow field

dissipations. The problem can be more challenging when involving finer

resolution in time and space. This issue however is not only restricted to FDTD

alone but other analysis methods are also face similar problem.

2.3 Conclusion

In summary, a brief discussion of the general FDTD method has been presented.

Some of its major properties as well as its inherent limitations have been pointed out. Next

chapter will present the bodies of revolution (BoR) FDTD, a FDTD approach based on

cylindrical coordinate system to handle axis-symmetrical electromagnetic problems. The

BoR-FDTD is the main method used throughout this work.

Chavter 3 -Bodies of Revolution Finite Difference Time Domain (BoR-FDTD) Simulator

3.2 Specification and presentation of BoR-FDTD method

3.2.1 The governing equations

The BoR structures are symmetric about the axis and this leads to the natural use of

the cylindrical coordinates @,y,z) as illustrated in Figure 3.1.

xd

Figure 3.1 - Cylindrical coordinate system

To derive the governing equations for the BoR-FDTD we should go back to the

Maxwell curl equations given in (2.1) to (2.2) from the previous chapter. In cylindrical

coordinates system, the Maxwell equations can be rewritten as:

Chapter 3 -Bodies of Revolution Finite Difference Time Domain (BoR-FDTD) Simulator

From equation (3.3) to (3.8) it can be noted that the cylindrical space is discretized in

three dimensional manners along the p, p, and z directions. However, thanks to the

rotationally symmetric structures where fields variations in the azimuthal (p ) directions can

be solved analytically. In order to do that, we first expand the electric and magnetic fields in

the rotationally symmetric geometries using the infinite Fourier series expansion [6], [8]. It is

written as:

where m is the azimuthal mode number. The subscript even and odd denotes the

Fourier coefficients for the cosinusoidal or sinusoidal dependence respectively. Originally the

electric and magnetic fields are a function of p, p and z at all time. However, once expanded

in Fourier series, the fields are now dependent only on p and z components but varied with

cos(myl) and sin(myl).

Without losing generality, we can now assume that the angular variation of the

electromagnetic fields has either a cos(mp) or sin(mylj variation. In our case we choose the

field variations as:

Chanter 3 -Bodies of Revolution Finite Difference Time Domain (BoR-FDTD) Simulator

govern the electromagnetic fields in bodies of revolution (BoR) structure in its normal FDTD

computational space.

3.2.2 Discretization of the governing equations

3.2.2.1 Gridding scheme in three dimensional cylindrical coordinate

The governing equations need to be discretized for used in the FDTD scheme and the

update equations must be derived based on the grid definition. In the FDTD method the

electric field and the magnetic fields are located at offset position from one another in the

designated space. For reference, the general three dimensional FDTD cell in cylindrical

coordinate system is as illustrated in Figure 3.2. The positions of all electric field components

are at the cell borders tangential to each other and effectively located half cells apart from the

reference point (i,j,k). The magnetic fields components on the other hand are defined

normally to the surface of the cylindrical cell and are half cells apart from the electric fields

in the cell.

(i,i,k)

Figure 3.2 - The three dimensional FDTD cell in cylindrical coordinates.

44

Chavter 3 -Bodies of Revolution Finite Difference Time Domain @OR-FDTD) Simulator

Figure 3.4 - Cell definitions on the BoR-FDTD grid system

From Figure 3.4, we show some cells and field components on the BoR-FDTD grid

system. The definitions of the cell sizes and the half cells are given. Note that BoR-FDTD

lattice has uniform size in z direction but distributed non-uniformly in p direction. The

following defines the cell sizes and half cells coordinate for both directions:

Apf = pi+l - p i for i = 0-Np - 1

P i + ~ / z = pi + A p f / 2 for i = 1-N, - 3

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