dorsal/arxiv
View SchemaQ-based design equations for resonant metamaterials and experimental validation
| Authors | Steven A. Cummer, Bogdan-Ioan Popa, Thomas H. Hand |
|---|---|
| Categories | |
| ArXiv ID | physics/0703130 |
| URL | https://arxiv.org/abs/physics/0703130 |
| DOI | 10.1109/TAP.2007.912959 |
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 also shown that the $Q$ of the effective medium response is essentially equal to the $Q$ of an individual resonant particle. Thus, by measuring the $Q$ of a single fabricated metamaterial particle, the effective permeability or permittivity of a metamaterial can be calculated simply and accurately without requiring complex simulations, fabrication, or measurements. Experimental validation shows that the 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. This 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 $\tan \delta \approx 0.001$ 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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"abstract": "Practical design parameters of resonant metamaterials, such as loss tangent,\nare derived in terms of the quality factor $Q$ of the resonant effective medium\npermeability or permittivity. Through electromagnetic simulations of loop-based\nresonant particles, it is also shown that the $Q$ of the effective medium\nresponse is essentially equal to the $Q$ of an individual resonant particle.\nThus, by measuring the $Q$ of a single fabricated metamaterial particle, the\neffective permeability or permittivity of a metamaterial can be calculated\nsimply and accurately without requiring complex simulations, fabrication, or\nmeasurements. Experimental validation shows that the complex permeability\nanalytically estimated from the measured $Q$ of a single fabricated\nself-resonant loop agrees with the complex permeability extracted from $S$\nparameter measurements of a metamaterial slab to better than 20%. This $Q$\nequivalence reduces the design of a metamaterial to meet a given loss\nconstraint to the simpler problem of the design of a resonant particle to meet\na specific $Q$ constraint. This analysis also yields simple analytical\nexpressions for estimating the loss tangent of a planar loop magnetic\nmetamaterial due to ohmic losses. It is shown that $\\tan \\delta \\approx 0.001$\nis a strong lower bound for magnetic loss tangents for frequencies not too far\nfrom 1 GHz. The ohmic loss of the metamaterial varies inversely with the\nelectrical size of the metamaterial particle, indicating that there is a loss\npenalty for reducing the particle size at a fixed frequency.",
"arxiv_id": "physics/0703130",
"authors": [
"Steven A. Cummer",
"Bogdan-Ioan Popa",
"Thomas H. Hand"
],
"categories": [
"physics.optics"
],
"doi": "10.1109/TAP.2007.912959",
"title": "Q-based design equations for resonant metamaterials and experimental validation",
"url": "https://arxiv.org/abs/physics/0703130"
},
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