  We show that the periodic array of left-handed cylinders possesses a rich
spectrum of guided modes when the negative permeability of cylinders equals
exactly to minus value of permeability of embedding media. These resonances
strongly influences propagation of electromagnetic waves through photonic
structures made from left-handed materials. A series of Fano resonances excited
by incident wave destroys the band frequency spectrum of square array of
left-handed cylinders and increases considerably the absorption of transmitted
waves.
