Sjoberg, D., Gustafsson, M. and Seviour, Rebecca (2013) A sum rule and physical bound for electromagnetic band gap structures. In: International Conference on Electromagnetics in Advanced Applications. ICEAA 2013 . IEEE, Torino, Italy, pp. 1236-1239. ISBN 978-1-4673-5705-0

We give a physical bound on the product
of bandwidth and attenuation per unit length for
general electromagnetic band gap structures. The
analysis is based on the Kramers-Kronig relations
for the Bloch refractive index for a fixed direction of
propagation through the crystal. The bound is given
in terms of the low- and high-frequency asymptotes
of the refractive index, which can be given simple
estimates in terms of the volume fractions of the
component materials and their static permittivities