Ca. Kyriazidou et al., Artificial versus natural crystals: Effective wave impedance of printed photonic bandgap materials, IEEE ANTENN, 48(1), 2000, pp. 95-106
Printed metallo-dielectric photonic bandgap (PBG) materials are analyzed us
ing an analytical approach based on multipole expansions for the scattered
fields off individual scatterers and a transfer-matrix method for reconstru
cting the total scattered fields created by successive lattice planes of th
e artificial crystal. An effective description of the PEG medium is derived
and its correspondence with natural crystals is further advanced through a
n analysis based on Lorentzian response functions, which characterize natur
al crystals. The effective wave impedance and bulk reflection coefficient o
f the medium are provided and their properties inside and outside the bandg
aps are examined. The presented treatment for these effective response func
tions extends far beyond the traditional effective medium theory (EMT) limi
ts.