1. 
 Gustafsson, Mats, et al.
(författare)

Constraints on the temporal dispersion of passive metamaterials
 2011

Konferensbidrag (refereegranskat)abstract
 Metamaterial applications such as cloaking, perfect lenses, and artificial permeability are restricted by the frequency dependence of the permittivity, permeability, and index of refraction. Here, causality and passivity together with integral identities for Herglotz functions are used to construct sum rules. The sum rules relate the frequency dependence of the material parameters with their high and lowfrequency values. The corresponding physical bounds determine the minimum variations of the material parameters over a frequency interval. The results are illustrated with a numerical example for artificial permeability.


2. 
 Gustafsson, Mats, et al.
(författare)

On the radiation resistance for small capacitive dipole antennas
 2011

Konferensbidrag (refereegranskat)abstract
 A relation between the radiation resistance and the quasistatic polarizability, input capacitance, and input inductance for small electric dipole antennas is investigated. The relation follows from the forward scattering sum rule and sum rules for the input impedance together with resonance models for the partial realized gain and the reflection coefficient.


3. 
 Gustafsson, Mats, et al.
(författare)

Optical theorem and forward scattering sum rule for periodic structures
 2011

Rapport (övrigt vetenskapligt)abstract
 Based on energy conservation, an optical theorem is constructed for a slab having an arbitrary periodic microstructure in a plane. A sum rule for low pass structures is derived using analytic properties of Herglotz functions based on causality and passivity. The sum rule relates the extinction cross section to the static polarizability per unit cell, and quantifies the interaction between the slab and electromagnetic fields possible over all wavelengths. The results are illustrated with several numerical and experimental examples.


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5. 
 Gustafsson, Mats, et al.
(författare)

Physical bounds and sum rules for highimpedance surfaces
 2010

Rapport (övrigt vetenskapligt)abstract
 Highimpedance surfaces are artificial surfaces synthesized from periodic structures. The high impedance is useful as it does not short circuit electric currents and reflects electric fields without phase shift. Here, a sum rule is presented that relates frequency intervals having high impedance with the thickness of the structure. The sum rule is used to derive physical bounds on the bandwidth for highimpedance surfaces. Numerical examples are used to illustrate the result, and show that the physical bounds are tight.


6. 
 Gustafsson, Mats, et al.
(författare)

Physical bounds on the partial realized gain
 2010

Konferensbidrag (refereegranskat)abstract
 An antenna identity, derived from the forward scattering sum rule, shows that the partial realized gain of an antenna is related to the polarizability of the antenna structure. The partial realized gain contains the mismatch, directivity, efficiency, and polarization properties of the antenna. The antenna identity expresses how the performance depends on the electrical size and shape of the antenna structure. It is also the starting point for several antenna bounds. In this paper, the identity, its associated physical bounds, and computational aspects of the polarizability dyadics are discussed.


7. 
 Gustafsson, Mats, et al.
(författare)

Sum rules and physical bounds in electromagnetic theory
 2010

Konferensbidrag (refereegranskat)abstract
 Sum rules are useful in many branches of physics and engineering as they relate all spectrum parameter values with their asymptotic expansions. Properties of the dynamic response can hence be inferred by the, in many cases much simpler, static response. This has e.g., been used for lossless matching networks, radar absorbers, extinction cross section, partial realized gain of antennas, highimpedance surfaces, transmission cross section, transmission coefficients, and temporal dispersion of metamaterials. Here, several sum rules and their associated physical bounds are reviewed and it is shown that integral identities for Herglotz functions offer a unified approach in deriving them.


8. 
 Gustafsson, Mats, et al.
(författare)

Sum rules and physical bounds on passive metamaterials
 2010

Ingår i: New Journal of Physics. ; 12, s. 043046

Tidskriftsartikel (refereegranskat)abstract
 Frequency dependence of the permittivity and permeability is inevitable in metamaterial applications such as cloaking and perfect lenses. In this paper, Herglotz functions are used as a tool to construct sum rules from which we derive physical bounds suited for metamaterial applications, where the material parameters are often designed to be negative or near zero in the frequency band of interest. Several sum rules are presented that relate the temporal dispersion of the material parameters with the difference between the static and instantaneous parameter values, which are used to give upper bounds on the bandwidth of the application. This substantially advances the understanding of the behavior of metamaterials with extraordinary material parameters, and reveals a beautiful connection between properties in the design band (finite frequencies) and the low and highfrequency limits.


9. 
 Gustafsson, Mats, et al.
(författare)

Sum rules and physical bounds on passive metamaterials
 2010

Rapport (övrigt vetenskapligt)abstract
 Frequency dependence of the permittivity and permeability is inevitable in metamaterial applications such as cloaking and perfect lenses. In this paper, Herglotz functions are used as a tool to construct sum rules from which we derive physical bounds suited for metamaterial applications, where the material parameters are often designed to be negative or near zero in the frequency band of interest. Several sum rules are presented that relate the temporal dispersion of the material parameters with the difference between the static and instantaneous parameter values, which are used to give upper bounds on the bandwidth of the application. This substantially advances the understanding of the behavior of metamaterials with extraordinary material parameters, and reveals a beautiful connection between properties in the design band (finite frequencies) and the low and highfrequency limit.


10. 
 Gustafsson, Mats, et al.
(författare)

Sum rules and physical limitations for passive metamaterials
 2011

Konferensbidrag (refereegranskat)abstract
 Bandwidth is an important parameter in many metamaterial applications. It has been shown that Herglotz functions and sum rules offer a powerful methodology to analyze the tradeoff between bandwidth and design parameters. Here, this approach is described for the temporal dispersion of constitutive relations and highimpedance surfaces.

