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
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Periodicity
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A system of metallic wire and/or plates is used to obtain
negative dielectric permittivity.
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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
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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
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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)
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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
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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
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For TEM waves propagating perpendicular to the wires and
polarized with magnetic field also perpendicular to the wires
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Dependence on kz
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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
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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
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It does not seen possible to obtain an effective negative
permeability from the closed metallic ring.
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Capacitive loaded metallic loop
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Magnetic polarizability of a closed loop can be enhanced by loaded
the loop with a capacitor.
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Show a negative permeability just above the resonant frequency
Analysis of Edge-Coupled SRR
 EC-SRR
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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
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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)
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Avoid the EC-SRR bianisotropy
 Inversion symmetry
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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)
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Avoid EC-SRR bianisotropy
 Inversion symmetry
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Keep a uniplanar design
Resonant frequency
Other SRR Designs
 Double-split SRR (2-SRR)
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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
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Resonant frequency: half the frequency of resonance of
an EC-SRR
Smaller electrical size at resonance
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Present some degree of bianisotropy
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[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
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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
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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
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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
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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.