Physics Srr

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Synthesis of BulkMetamaterials

Advisor: Prof. Ruey-Beei WuStudent : Hung-Yi Chien

2010 / 04 / 01

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Outline

IntroductionScaling Plasma at Microwave FrequencySynthesis of Negative Magnetic PermeabilitySRR-Based Left-Handed Metamaterials

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IntroductionDeisng of bulk metamaterials with negative parameters

A combination of unit cells of small electrical size atfrequency of interest

Periodicity

A system of metallic wire and/or plates is used to obtainnegative dielectric permittivity.

A system of split ring resonators (SRRs) is used to obtainnegative magnetic permeability.

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Scaling Plasmas at Microwavefrequency

Simulation of plasmas at microwavefrequencies

Became an active field of research during 1960sSimulation of radio-communications with spaceships

during transit through the ionosphereModeling of plasma: Systems of metallic wires [1]

PlasmasExhibit negative dielectric permittivity belowplasma frequencyArtificial media with negative dielectricpermittivity[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 frequencyplasmons in metallic mesostructures. Phys. Rev. Lett., vol. 76, pp. 4773 4776, 1996 4


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Metallic Waveguide and Plates as1-D and 2-D Plasmas

Consider a hollow rectangular waveguide (TE mode)Cutoff frequencyWave impedancePropagation constant

Continuous media relations

A rectangular waveguide

1-D plasma with effective dielectric constant

Parallel metallic plates

2-D plasma with effective dielectric constant5


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Wire MediaIf the period of the wire mesh is smaller than the free-space wavelength, it should be approximately equivalentto the bunch of waveguides.Consider a TEM transmissionline loaded by metallic postPlasma frequency

ApproximationThe cutoff frequency of waveguide bunch

More accurate determination

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Spatial Dispersion in Wire MediaConsider a set of periodic parallel infinite wires

For TEM waves propagating perpendicular to the wires andpolarized with magnetic field also perpendicular to the wires

Dependence on kz

Spatial dispersion is expected

to appear when the unit cellsize is not small with regardto the wavelength.

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Synthesis of Negative MagneticPermeability

DiamagnetismCurrent would be induced in the closed circuits under theeffect of an external time-varying magnetic field.The secondary magnetic flux created by the induced

current would be opposite to that created by the externalfields.

Closed metallic ring

Self-inductance of a perfect conducting ring

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Synthesis of Negative MagneticPermeability

It does not seen possible to obtain an effective negativepermeability from the closed metallic ring.

( , )

Capacitive loaded metallic loopMagnetic polarizability of a closed loop can be enhanced by loadedthe loop with a capacitor.

Show a negative permeability just above the resonant frequency

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Analysis of Edge-Coupled SRREC-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 nonlinearphenomena. IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2075 2084, 1999 10


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Analysis of Edge-Coupled SRREC-SRR

Cross-polarizabilitiesUnwanted effect : bianisotropy

[19] R. Marque s, F. Mesa, J. Martel, and F. Medina Comparative analysis of edge and broadside coupled split ringresonators for metamaterial design. Theory and experiment. IEEE Trans. Antennas Propag., vol. 51, pp. 2572 2581,2003. 11


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Analysis of Edge-Coupled SRRThe frequency of resonance of an EC-SRR can bemeasured by placing the EC-SRR inside a rectangularwaveguide and measuring the transmission coefficient.

Electric and magnetic excitation

magnetic excitation

electric excitation

no excitation

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Other SRR DesignsBroadside-coupled SRR (BC-SRR)

Avoid the EC-SRR bianisotropyInversion symmetry

Additional advantage of much smaller electrical lengthThe capacitance for the BC-SRR approximately corresponds toa parallel plate capacitor.Thin substrate of high permeability can be used.

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Other SRR DesignsBroadside-coupled SRR (BC-SRR)

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Other SRR DesignsNonbianisotropy SRR (NB-SRR)

Avoid EC-SRR bianisotropyInversion symmetry

Keep a uniplanar designResonant frequency

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Other SRR DesignsDouble-split SRR (2-SRR)

Avoid EC-SRR bianisotropyInversion symmetry

The total capacitance of the circuit is four times smallerthan for the conventional EC-SRR.Resonant frequency: twice the frequency of resonanceof an EC-SRRLarger electrical size at resonance

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Other SRR DesignsSpirals

Resonant frequency: half the frequency of resonance of an EC-SRRSmaller 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 resonantelectromagnetic particles for metamaterial and filter design. Proc. ICEAA03, pp. 439 442, Torino, Italy, 2003 17


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Constitutive Relationship for BulkSRR Metamaterials

Effective constitutive parametersThe only necessary condition is that the size of the unitcell must be smaller than the wavelength.

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Zero-order appoximationIgnore couplings between adjacent elementsA rough approximation

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Lorentz appoximationcouplings between adjacent elements are considered ina rather simple way (Lorentz local field theory)Better approximation

Array of EC-SRR Array of BC-SRR20


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Higher-Order Resonances in SRRsCurrent distribution : symmetry or antisymmetry

Resonance of NB-SRR Resonance of EC-SRR21


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SRR-Based Left-HandedMetamaterials

1-D SRR-based left-handed metamaterialsNegative permittivity of the wire systemNegative 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 simultaneouslynegative permeability and permittivity. Phys. Rev. Lett., vol. 84, pp. 4184 4187, 2000. 22


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1-D SRR-based left-handed metamaterialsA single row of SRRs is placed inside a cutoff squarewaveguide

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 wavesin subwavelength split-ring-resonator- loaded metallic waveguides. Phys. Rev. Lett., vol. 89, paper 183901, 2002 23


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1-D SRR-based left-handed metamaterialsTwo hollow waveguides (one above and the other belowcutoff) 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 SRR -loaded waveguides. Proc. IEEE -AP/S Int. Symp. on Antennas and Propagation, pp. 106 109, 2003 24


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2-D SRR-based left-handed metamaterialsAn orthogonal arrangement of dielectric circuit boardswith 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: theoryand 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 two -dimensional, isotropic, left- handed metamaterial. Appl. Phys. Lett., vol. 78, pp. 489 491, 2001 25


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SuperpositionSystems providing negative permittivity and negativepermeability should be placed in the way that theinteraction between its elements through its quasistatic

fields is minimized.

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