The explicit dispersion relation for one-dimensional photonic crystals consisting of alternative layers of indefinite metamaterial and ordinary positive-index material is obtained and analyzed in detail. It is shown that such a photonic crystal possesses an omnidirectional zero-averaged refractive-index gap when the indefinite metamaterial is a cutoff or anticutoff medium, yet it possesses an omnidirectional zero-effective phase gap when the photonic crystal contains two different always-cutoff media. The appearance of these two omnidirectional gaps does not require that all tensor elements of permittivity and permeability have negative values, quite different from that for the photonic crystal containing isotropic negative-index or single-negative material. Moreover, the new zero-averaged refractive-index gap and zero-effective phase gap are also insensitive to the incident angle and polarization of light and are invariant upon the change of scale length. These properties provide more degrees of freedom to design new types of optical devices.
© 2007 Optical Society of America
Original Manuscript: October 31, 2006
Revised Manuscript: March 11, 2007
Manuscript Accepted: May 16, 2007
Published: July 13, 2007
Yuanjiang Xiang, Xiaoyu Dai, and Shuangchun Wen, "Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials," J. Opt. Soc. Am. B 24, 2033-2039 (2007)