Q-Based Design Equations and Loss Limits for Resonant Metamaterials and Experimental Validation
Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor Q of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is first shown that the Q of the effective...
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Published in | IEEE transactions on antennas and propagation Vol. 56; no. 1; pp. 127 - 132 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.01.2008
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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Abstract | Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor Q of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is first shown that the Q of the effective medium response is essentially equal to the Q of an individual resonant particle. This implies that by measuring the Q of a single fabricated metamaterial particle, the effective permeability or permittivity of a meta-material can be estimated simply and accurately without complex simulations, fabrication, or measurements. Experimental validation shows that the frequency-dependent complex permeability analytically estimated from the measured Q of a single fabricated self-resonant loop agrees with the complex permeability extracted from S parameter measurements of a metamaterial slab to better than 20 %. This Q equivalence reduces the design of a metamaterial to meet a given loss constraint to the simpler problem of the design of a resonant particle to meet a specific Q constraint. The Q-based analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. It is shown that tan delta ap 0.001 is a strong lower bound for magnetic loss tangents for frequencies not too far from 1 GHz. The ohmic loss of the metamaterial varies inversely with the electrical size of the metamaterial particle, indicating that there is a loss penalty for reducing the particle size at a fixed frequency. |
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AbstractList | Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor Q of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is first shown that the Q of the effective medium response is essentially equal to the Q of an individual resonant particle. This implies that by measuring the Q of a single fabricated metamaterial particle, the effective permeability or permittivity of a meta-material can be estimated simply and accurately without complex simulations, fabrication, or measurements. Experimental validation shows that the frequency-dependent complex permeability analytically estimated from the measured Q of a single fabricated self-resonant loop agrees with the complex permeability extracted from S parameter measurements of a metamaterial slab to better than 20 %. This Q equivalence reduces the design of a metamaterial to meet a given loss constraint to the simpler problem of the design of a resonant particle to meet a specific Q constraint. The Q-based analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. It is shown that tan delta ap 0.001 is a strong lower bound for magnetic loss tangents for frequencies not too far from 1 GHz. The ohmic loss of the metamaterial varies inversely with the electrical size of the metamaterial particle, indicating that there is a loss penalty for reducing the particle size at a fixed frequency. The Q-based analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. |
Author | Popa, B.-I. Hand, T.H. Cummer, S.A. |
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Cites_doi | 10.1103/PhysRevB.70.113102 10.1103/PhysRevB.72.165102 10.1103/PhysRevE.71.036617 10.1103/PhysRevE.70.016608 10.1103/PhysRevB.65.195104 10.1063/1.1655673 10.1103/PhysRevB.65.144440 10.1103/PhysRevLett.90.107401 10.1109/22.798002 10.1063/1.1823595 10.1103/PhysRevE.73.036609 10.1103/PhysRevE.68.065602 |
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Keywords | Lower bound Design criterion Frequency dependence Parameter estimation Electromagnetism Q factor S-parameters metamaterials Complex media Simulation Quality factor Analytical method Permittivity Metamaterial |
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Snippet | Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor Q of the resonant effective medium... The Q-based analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. |
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SubjectTerms | Applied classical electromagnetism Complex media Design engineering Electromagnetic wave propagation, radiowave propagation Electromagnetism; electron and ion optics Equations Exact sciences and technology Frequency estimation Frequency measurement Fundamental areas of phenomenology (including applications) Magnetic materials Magnetic resonance Mathematical analysis Metamaterials Ohmic Particle measurements Permeability Permeability measurement Permittivity Permittivity measurement Physics Q factor Q measurement Simulation Studies Tangents |
Title | Q-Based Design Equations and Loss Limits for Resonant Metamaterials and Experimental Validation |
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