By using local theory and taking into account retardation, we investig
ate the plasmon-polariton modes of a finite Canter-type heterostructur
es which are composed of two alternating materials with their thicknes
ses following Canter sequence. The effects of an external magnetic fie
ld applied parallel to the interfaces are considered. We find that the
modes have fractal structure due to the special geometry of the syste
m, and the dispersion relations of the modes are strikingly modified b
q the external magnetic field. Some new modes appear because of the ap
plication of the field. By plotting the profiles of the amplitudes of
the electric field, we also investigate the localization properties of
the modes.