Advisor: Prof. Ruey-Beei Wu Student : Hung
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Transcript Advisor: Prof. Ruey-Beei Wu Student : Hung
Synthesis of Bulk
Metamaterials
Advisor: Prof. Ruey-Beei Wu
Student : Hung-Yi Chien 錢鴻億
2010 / 04 / 01
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Outline
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Introduction
Scaling Plasma at Microwave Frequency
Synthesis of Negative Magnetic Permeability
SRR-Based Left-Handed Metamaterials
Introduction
Deisng of bulk metamaterials with negative parameters
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A combination of unit cells of small electrical size at
frequency of interest
Periodicity
A system of metallic wire and/or plates is used to obtain
negative dielectric permittivity.
A system of split ring resonators (SRRs) is used to obtain
negative magnetic permeability.
Scaling Plasmas at Microwave
frequency
Simulation of plasmas at microwave
frequencies
Became an active field of research during 1960s
Simulation of radio-communications with spaceships
during transit through the ionosphere
Modeling of plasma: Systems of metallic wires [1]
Plasmas
Exhibit negative dielectric permittivity below
plasma frequency
Artificial media with negative dielectric
permittivity[2]
[1] W. Rotman “Plasma simulation by artificial dielectrics and parallel-plate media.” IRE
Trans. Antennas Propag., vol. 10, pp. 82–95, 1962
[2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs “Extremely low frequency
plasmons in metallic mesostructures.” Phys. Rev. Lett., vol. 76, pp. 4773–4776, 1996
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Metallic Waveguide and Plates as 1D and 2-D Plasmas
Consider a hollow rectangular waveguide (TE mode)
Cutoff frequency
Wave impedance
Propagation constant
Continuous media relations
A rectangular waveguide
1-D plasma with effective dielectric constant
Parallel metallic plates
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2-D plasma with effective dielectric constant
Wire Media
If the period of the wire mesh is smaller than the freespace wavelength, it should be approximately equivalent
to the bunch of waveguides.
Consider a TEM transmission
line loaded by metallic post
Plasma frequency
Approximation
The cutoff frequency of
waveguide bunch
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More accurate determination
Spatial Dispersion in Wire Media
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Consider a set of periodic parallel infinite wires
For TEM waves propagating perpendicular to the wires and
polarized with magnetic field also perpendicular to the wires
Dependence on kz
Spatial dispersion is expected
to appear when the unit cell
size is not small with regard
to the wavelength.
Synthesis of Negative Magnetic
Permeability
Diamagnetism
Current would be induced in the closed circuits under the
effect of an external time-varying magnetic field.
The secondary magnetic flux created by the induced
current would be opposite to that created by the external
fields.
Closed metallic ring
Self-inductance of a perfect conducting ring
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Synthesis of Negative Magnetic
Permeability
It does not seen possible to obtain an effective negative
permeability from the closed metallic ring.
(
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,
)
Capacitive loaded metallic loop
Magnetic polarizability of a closed loop can be enhanced by loaded
the loop with a capacitor.
Show a negative permeability just above the resonant frequency
Analysis of Edge-Coupled SRR
EC-SRR
Initially proposed by Pendry [3]
Resonant frequency
[3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart “Magnetism from conductors and enhanced nonlinear
phenomena.” IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2075–2084, 1999
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Analysis of Edge-Coupled SRR
EC-SRR
Cross-polarizabilities
Unwanted effect : bianisotropy
[19] R. Marque´s, F. Mesa, J. Martel, and F. Medina “Comparative analysis of edge and broadside coupled split ring
resonators for metamaterial design. Theory and experiment.” IEEE Trans. Antennas Propag., vol. 51, pp. 2572–2581,
2003.
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Analysis of Edge-Coupled SRR
The frequency of resonance of an EC-SRR can be
measured by placing the EC-SRR inside a rectangular
waveguide and measuring the transmission coefficient.
Electric and magnetic excitation
magnetic excitation
electric excitation
no excitation
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Other SRR Designs
Broadside-coupled SRR (BC-SRR)
Avoid the EC-SRR bianisotropy
Inversion symmetry
Additional advantage of much smaller electrical length
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The capacitance for the BC-SRR approximately corresponds to
a parallel plate capacitor.
Thin substrate of high permeability can be used.
Other SRR Designs
Broadside-coupled SRR (BC-SRR)
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Other SRR Designs
Nonbianisotropy SRR (NB-SRR)
Avoid EC-SRR bianisotropy
Inversion symmetry
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Keep a uniplanar design
Resonant frequency
Other SRR Designs
Double-split SRR (2-SRR)
Avoid EC-SRR bianisotropy
Inversion symmetry
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The total capacitance of the circuit is four times smaller
than for the conventional EC-SRR.
Resonant frequency: twice the frequency of resonance
of an EC-SRR
Larger electrical size at resonance
Other SRR Designs
Spirals
Resonant frequency: half the frequency of resonance of
an EC-SRR
Smaller electrical size at resonance
Present some degree of bianisotropy
[25] R. Marque´s, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martin “Novel small resonant
electromagnetic particles for metamaterial and filter design.” Proc. ICEAA’03, pp. 439–442, Torino, Italy, 2003
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Constitutive Relationship for Bulk
SRR Metamaterials
Effective constitutive parameters
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The only necessary condition is that the size of the unit
cell must be smaller than the wavelength.
Constitutive Relationship for Bulk
SRR Metamaterials
Zero-order appoximation
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Ignore couplings between adjacent elements
A rough approximation
Constitutive Relationship for Bulk
SRR Metamaterials
Lorentz appoximation
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couplings between adjacent elements are considered in
a rather simple way (Lorentz local field theory)
Better approximation
Array of EC-SRR
Array of BC-SRR
Higher-Order Resonances in SRRs
Current distribution : symmetry or antisymmetry
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Resonance of NB-SRR
Resonance of EC-SRR
SRR-Based Left-Handed
Metamaterials
1-D SRR-based left-handed metamaterials
Negative permittivity of the wire system
Negative permeability of the SRR system
[4] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz “Composite medium with simultaneously
negative permeability and permittivity.” Phys. Rev. Lett., vol. 84, pp. 4184–4187, 2000.
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SRR-Based Left-Handed
Metamaterials
1-D SRR-based left-handed metamaterials
A single row of SRRs is placed inside a cutoff square
waveguide
Negative permittivity: the cutoff waveguide
Negative permeability: EC-SRR
[46] R. Marque´s, J. Martel, F. Mesa, and F. Medina “Left-handed-media simulation and transmission of EM waves
in subwavelength split-ring-resonator-loaded metallic waveguides.” Phys. Rev. Lett., vol. 89, paper 183901, 2002
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SRR-Based Left-Handed
Metamaterials
1-D SRR-based left-handed metamaterials
Two hollow waveguides (one above and the other below
cutoff) are loaded by equispaced BC-SRRs
Passband : narrow waveguide
Stopband : wider waveguide
[51] J. D. Baena, R. Marque´s, J. Martel, and F. Medina “Experimental results on metamaterial simulation using SRRloaded waveguides.” Proc. IEEE-AP/S Int. Symp. on Antennas and Propagation, pp. 106–109, 2003
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SRR-Based Left-Handed
Metamaterials
2-D SRR-based left-handed metamaterials
An orthogonal arrangement of dielectric circuit boards
with EC-SRRs and metallic strips printed on each side
Negative permittivity : metallic strips
Negative permeability : EC-SRRs
[50] R. Marque´s, J. Martel, F. Mesa, and F. Medina “A new 2-D isotropic left-handed metamaterial design: theory
and experiment.” Microwave Opt. Tech. Lett., vol. 35, pp. 405–408, 2002.
[52] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial.” Appl. Phys. Lett., vol. 78, pp. 489–491, 2001
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SRR-Based Left-Handed
Metamaterials
Superposition
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Systems providing negative permittivity and negative
permeability should be placed in the way that the
interaction between its elements through its quasistatic
fields is minimized.