### Abstract

An experimental approach to investigate the forward scattering sum rule for periodic structures is presented. This approach allows an upper bound on the total cross section integrated over a bandwidth from a simple static problem to be found. Based on energy conservation, the optical theorem is used to construct a relation between the total cross section and the forward scattering of periodic structures as well as single scatterers inside a parallel-plate waveguide. Dynamic measurements are performed using a parallel-plate waveguide and a parallel-plate capacitor is utilized to find the static polarizability. Convex optimization is introduced to identify the total cross section in the dynamic measurements and estimate an optimal lower bound on the polarizability for objects. The results show that the interactions between the electromagnetic field and an object over all wavelengths are given by the static polarizability of the object.

Original language | English |
---|---|

Article number | 6905863 |

Pages (from-to) | 2574-2582 |

Number of pages | 9 |

Journal | IEEE Transactions on Microwave Theory and Techniques |

Volume | 62 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Nov 2014 |

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### Cite this

*IEEE Transactions on Microwave Theory and Techniques*,

*62*(11), 2574-2582. [6905863]. https://doi.org/10.1109/TMTT.2014.2354592

}

*IEEE Transactions on Microwave Theory and Techniques*, vol. 62, no. 11, 6905863, pp. 2574-2582. https://doi.org/10.1109/TMTT.2014.2354592

**Sum Rules for parallel-plate waveguides : Experimental results and theory.** / Vakili, Iman; Gustafsson, Mats; Sjoberg, Daniel; Seviour, Rebecca; Nilsson, Martin; Nordebo, Sven.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sum Rules for parallel-plate waveguides

T2 - Experimental results and theory

AU - Vakili, Iman

AU - Gustafsson, Mats

AU - Sjoberg, Daniel

AU - Seviour, Rebecca

AU - Nilsson, Martin

AU - Nordebo, Sven

PY - 2014/11/1

Y1 - 2014/11/1

N2 - An experimental approach to investigate the forward scattering sum rule for periodic structures is presented. This approach allows an upper bound on the total cross section integrated over a bandwidth from a simple static problem to be found. Based on energy conservation, the optical theorem is used to construct a relation between the total cross section and the forward scattering of periodic structures as well as single scatterers inside a parallel-plate waveguide. Dynamic measurements are performed using a parallel-plate waveguide and a parallel-plate capacitor is utilized to find the static polarizability. Convex optimization is introduced to identify the total cross section in the dynamic measurements and estimate an optimal lower bound on the polarizability for objects. The results show that the interactions between the electromagnetic field and an object over all wavelengths are given by the static polarizability of the object.

AB - An experimental approach to investigate the forward scattering sum rule for periodic structures is presented. This approach allows an upper bound on the total cross section integrated over a bandwidth from a simple static problem to be found. Based on energy conservation, the optical theorem is used to construct a relation between the total cross section and the forward scattering of periodic structures as well as single scatterers inside a parallel-plate waveguide. Dynamic measurements are performed using a parallel-plate waveguide and a parallel-plate capacitor is utilized to find the static polarizability. Convex optimization is introduced to identify the total cross section in the dynamic measurements and estimate an optimal lower bound on the polarizability for objects. The results show that the interactions between the electromagnetic field and an object over all wavelengths are given by the static polarizability of the object.

KW - Convex optimization

KW - forward scattering

KW - metamaterials

KW - optical theorem

KW - parallel-plate waveguide

KW - periodic structure

KW - positive real (PR) functions

KW - sum rule

UR - http://www.scopus.com/inward/record.url?scp=84910057995&partnerID=8YFLogxK

U2 - 10.1109/TMTT.2014.2354592

DO - 10.1109/TMTT.2014.2354592

M3 - Article

AN - SCOPUS:84910057995

VL - 62

SP - 2574

EP - 2582

JO - IEEE Transactions on Microwave Theory and Techniques

JF - IEEE Transactions on Microwave Theory and Techniques

SN - 0018-9480

IS - 11

M1 - 6905863

ER -