Metamaterials in Arbitrary Waveguiding Structures [Elektronische Ressource] / Yvonne Weitsch. Gutachter: Thomas Eibert ; Volkert Hansen. Betreuer: Thomas Eibert

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2011
• Nombre de lectures: 81
• Langue: Deutsch
• Poids de l'ouvrage: 6 Mo

Extrait

Technische Universität München
Lehrstuhl für Hochfrequenztechnik
Metamaterials in Arbitrary Waveguiding Structures
Yvonne Weitsch
Vollständiger Abdruck der von der Fakultät für Elektrotechnik und Informationstechnik
der Technischen Universität München zur Erlangung des akademischen Grades eines
– Doktor-Ingenieurs –
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Paolo Lugli, Ph.D.
Prüfer der Dissertation:
1. Univ.-Prof. Dr.-Ing. Thomas Eibert
2. Univ.-Prof. Dr.-Ing. Volkert Hansen (i.R.)
Bergische Universität Wuppertal
Die Dissertation wurde am 19.04.2011 bei der Technischen Universität München einge-
reicht und durch die Fakultät für Elektrotechnik und Informationstechnik am 12.07.2011
angenommen.Contents
Symbols and Acronyms v
1 Abstract 1
2 Introduction 3
3 Metamaterials 11
3.1 Maxwell’s Equations and Material Properties . . . . . . . . . . . . . . . . 11
3.2 Combined Right/Left-Handed Transmission Lines . . . . . . . . . . . . . . 15
3.3 Bloch-Floquet Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Leaky-Wave Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.1 Overview of Leaky-Wave Antenna Types . . . . . . . . . . . . . . 22
3.4.2 Bound or Leaky Wave - Slow or Fast Wave . . . . . . . . . . . . . 24
3.4.3 WorkingPrinciples: ConventionalVersusNovelFunctionalitieswith
Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Modal Series Expansion of Periodically Loaded Waveguides 29
4.1 Eigenproblem and Transfer Matrix Representation . . . . . . . . . . . . . 30
4.2 Scattering Matrix and Numerical Implementation . . . . . . . . . . . . . . 33
5 Solutions of Cylindrical Waveguides 37
5.1 Auxiliary Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Field Modes in Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 Five-Component Fields forE andH Modes . . . . . . . . . . . . . . . . . 42
5.4 General One-Dimensional Eigenvalue Problem . . . . . . . . . . . . . . . . 45
5.5 General Orthogonality Principle. . . . . . . . . . . . . . . . . . . . . . . . 47
5.6 Transverse Electromagnetic Field Type. . . . . . . . . . . . . . . . . . . . 50
5.7 Rectangular Hollow Waveguide . . . . . . . . . . . . . . . . . . . . . . . . 50
5.8 Energy Transfer of Evanescent Modes . . . . . . . . . . . . . . . . . . . . 58
5.9 H Waves andE Waves on the Grounded Dielectric Slab . . . . . . . . . . 60
5.10 Analytical Solution for the Shielded Three-Layer Model . . . . . . . . . . 64
6 Treatment of Open Region Problems 67
6.1 Integral Representation and Modal Expansion . . . . . . . . . . . . . . . . 67
6.2 TransformationofOpenRegionProblemtoEquivalentClosedRegionProb-
lem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2.1 Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2.2 Design of an Isotropic Absorbing Layer . . . . . . . . . . . . . . . 74
6.2.3 Influence of the Isotropic Absorbing Layer . . . . . . . . . . . . . . 75iv Contents
7 Closed Waveguide Realisations 81
7.1 Corrugated Rectangular Hollow Waveguide . . . . . . . . . . . . . . . . . 81
7.2 CRLH Waveguide in SIW Technology . . . . . . . . . . . . . . . . . . . . 87
7.2.1 Simulation, Prototype and Measurement Results . . . . . . . . . . 88
7.2.2 Dispersion Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2.3 Bloch Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8 Leaky-Wave Antenna Realisations 95
8.1 CRLH Leaky-Wave Antenna: Slotted Substrate Integrated Waveguide . . 95
8.1.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.1.2 Bloch Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8.1.3 Dispersion Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.1.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.2 CRLH Leaky-Wave Antenna: Interdigital Design . . . . . . . . . . . . . . 106
8.2.1 Comparison of Measurement and Simulation Results . . . . . . . . 106
8.2.2 NumericalComputationResultsbyModalSeriesExpansionApproach107
8.2.3 Dispersion Diagram and Radiation Performance . . . . . . . . . . 109
8.2.4 Bloch Impedance and Modal Field Distribution . . . . . . . . . . . 114
8.3 Periodically Modulated Grounded Dielectric Slab . . . . . . . . . . . . . . 118
8.3.1 Design Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.3.2 Modal Solutions and Radiation Behaviour . . . . . . . . . . . . . . 118
9 Appendix 129
9.1 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.2 Eigenvalue Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.3 Pseudoinverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.4 Matrix Pencil Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.4.1 Determination of the Propagation Constants . . . . . . . . . . . . 131
9.4.2 Determination of the Amplitudes . . . . . . . . . . . . . . . . . . . 133Symbols and Acronyms
a inward normalised complex power wave amplitude
A complex amplitude
A magnetic vector potential
ABCD-matrix transmission matrix with respect to voltage and current
b outward normalised complex power wave amplitude
B magnetic flux density
C capacitance
′C per-unit-length capacitance
C left-handed capacitanceL
C right-handed capacitanceR
∗x conjugate complex of a numberx
C series capacitances
C shunt capacitancesh
8c =2.998·10 m/s, velocity of light0
CRLH composite right/left-handed
CST MWS computer simulation technology microwave studio
D electric flux density,
diagonal matrix
dB decibel
det(X) determinant of a matrixX
diag(X) diagonal of a matrixX
dim(X) dimension of a matrixX
E electric field strength
EQC equivalent circuit
EVD eigenvalue decomposition
f frequency
F electric vector potential
f cut-off frequencyc
FD finite difference
FDTD finite difference time domain
FE finite element
FIT finite integration technique
f(k (k )) amplitude functionz x
G Green’s function
HX conjugate transpose of a matrixX, Hermitian
H magnetic field strength
HFSS high frequency structure simulator
I electric current
I amplitude of forward travelling current wavefvi Symbols and Acronyms
I identity matrix
¯I identity dyad
Im imaginary part
J electric current density
J electric surface current densityA
j electric surface current density (instantaneous quantity)F
k Cartesian components of the wave vector, wavenumbersx,y,z
l length
L free-moving window length for the matrix pencil method,
inductance
′L per-unit-length inductance
L left-handed inductanceL
L right-handed inductanceR
L inductance in parallelp
L series inductances
L shunt inductancesh
LH left-handed
LWA leaky-wave antenna
M number of waves, modes
M magnetic current density
M magnetic surface current densityA
MP matrix pencil method
MWEs Maxwell’s Equations
n noise,
refractive index
n unit normal vector
p period or periodical length,
dimension
p generalised eigenvector
P power
PC photonic crystals
PCB printed circuit board
PEC perfectly electric conducting
PMC perfectly magnetic conducting
PML perfectly matched layer
q eigenvalue of E mode depending on transversal geometryE
q eigenvalue of H mode depending on transversal geometryH
Re real part
r reflection coefficient related to the Bloch impedanceB
r position vector
′r vector of source location
RH right-handed
S Poynting vector
S scattering parameter, relation between ingoing wave at portj to outgo-ij
ing wave at porti
S-matrix scattering matrixvii
SIW substrate integrated waveguide
SMA scattering matrix approach
SRR split-ring resonator
SVD singular value decomposition
TX transpose of a matrixX
t time
tanδ loss factor
TE transverse electric
TEM transverse electromagnetic
TL transmission line
TM transverse magnetic
T-matrix transfer matrix
U voltage
U amplitude of forward travelling voltage wavef
V mode voltage
v (eigen)vector
v group velocityg
v phase velocityph
w width
y representation of a signal
Y admittance
γtz =e , complex pole, eigenvalue of a matrixZ
z eigenvector of a matrixZ
Z impedance
Z Bloch impedanceB
Z characteristic impedancec
Z =120π Ω, field impedance of free spaceF0
Z characteristic impedance of E modeFE
Z characteristic impedance of H modeFH
Z transmission line impedanceL
Z (k ) impedancefunction for modei dependenton wavenumber inu-directioni uviii Symbols and Acronyms
α attenuation constant
β phase constant
δ Dirac impulse,
delta function distribution
Δ differential length
δ Kronecker symbolm,n
−12ε =8.854·10 As/(Vm), permittivity of free space0
ε effective permittivityeff
ε Neumann factorm
ε relative permittivityr
η e