Fano resonance in 3-D compound spirals: Chiral quality, extraordinary transmission and polarization gap

A unique recipe of achieving compound spiral photonic crystals (CSPCs) in three dimensions by holography is proposed, which is composed of unit cells with double right-handed (RH) spirals of π phase shift. Interferences between side beams in the umbrella-type configurations are employed to generate CSPCs. Chirality is pronounced, and paradoxical high RH transmission peaks appear exactly in the RH polarization gap. Fano resonances, which stems from the mode interferences between left-handed propagating modes along spiral axis (direct pathway) and negative group velocity modes in the extended Brillouin zone (resonance-assisted indirect pathway), is revealed and discussed. By analyzing Fourier spectra and chirality of the photonic eigenmodes, intrinsic mechanism of such a paradox is well understood by the mode coupling theory.