Gustafsson, Mats

Sjöberg, Daniel

Vakili, Iman

English

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Forward scattering experiments on periodic metamaterials in a parallel platewaveguideVakili, Iman; Gustafsson, Mats; Sjöberg, Daniel2012Link to publicationCitation for published version (APA):Vakili, I., Gustafsson, M., & Sjöberg, D. (2012). Forward scattering experiments on periodic metamaterials in aparallel plate waveguide. 1-1. Abstract from Antenn/EMB Symposium, 2012, Stockholm, Sweden.Total number of authors:3General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.Forward scattering experiments on periodic metamaterials in a parallelplate waveguideIman Vakili, Mats Gustafsson, and Daniel SjöbergDepartment of Electrical and Information Technology, Lund University, P.O.Box 118, S-221 00 Lund, Sweden, Iman.Vakili@eit.lth.seA forward scattering sum rule of periodic metamaterials is investigated. The sum rulerelates the total extincted power over a bandwidth to the static polarizability of a scatterer.This shows that the all spectrum interaction between the electromagnetic field and an objectis bounded by the sum of the electric and magnetic polarizability,γ. The sum rule was firstintroduced for dielectric spheroids by Purcell [1] and it was generalized to arbitrary objectsin [2, 3].The forward scattering sum rule, 1π2∫∞0 σext(λ) dλ = γ, where σext denotes the extinctioncross section and λ the wavelength in free space, is derived using the optical theorem. Thisversion of optical theorem is used to show that σext = Imh(k), where k is the wavenum-ber in free space, h(k) = i2(1 − T (k))A is a Herglotz function [4], A denotes the crosssection area of the unit cell and T the co-polarized part of the lowest order transmission co-efficient. Using the analytic properties of Herglotz function, the low-frequency asymptoticexpansion of h(k) is used to derive the forward scattering sum rule for an arbitrary periodicstructure [4, 5].A parallel plate waveguide measurement setup is used to verify the forward scattering sumrule for a set of Split Ring Resonators (SRR). Two TEM horn antennas are placed insidethe parallel plate waveguide as to be the transmitter and the receiver. They operate over thefrequency range [1− 20]GHz and generate a plane wave front at a close distance from theantennas. The measurement results are in good agreement with simulations and confirm thesum rule.References[1] E. M. Purcell. “On the absorption and emission of light by interstellar grains”. J.Astrophys., vol. 158, pp. 433–440, 1969.[2] M. Gustafsson. “Time-domain approach to the forward scattering sum rule”. Proc. R.Soc. A, vol. 466, pp. 3579–3592, 2010.[3] C. Sohl, M. Gustafsson, and G. Kristensson. “Physical limitations on broadband scat-tering by heterogeneous obstacles”. J. Phys. A: Math. Theor., vol. 40, pp. 11165–11182,2007.[4] A. Bernland, A. Luger, and M. Gustafsson. “Sum rules and constraints on passivesystems”. J. Phys. A: Math. Theor., vol. 44(14), pp. 145205, 2011.[5] M. Gustafsson, I. Vakili, S. E. Bayer, D. Sjöberg, and C. Larsson. “Optical theorem andforward scattering sum rule for periodic structures”. (LUTEDX/(TEAT-7213)/(2011)),2011.

Forward scattering experiments on periodic metamaterials in a parallel plate waveguide

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Forward scattering experiments on periodic metamaterials in a parallel plate waveguide

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