We show that, in low-dimensional photonic bandgaps, wave diffraction resulting from localization in the translational-invariant directions is strongly influenced by the photonic band structure of the periodic crystal, leading to new kinds of wave localization. In particular, for a periodic layered structure we show that, close to a bandgap edge, diffraction is enhanced, with a transition from a parabolic diffraction curve—typical of isotropic media and supporting Gaussian beams—to hyperbolic or elliptic diffraction curves. In the last two cases localization in the form of stationary X-shaped or sinc-shaped waves is possible.
© 2004 Optical Society of America
Stefano Longhi and Davide Janner, "Diffraction and localization in low-dimensional photonic bandgaps," Opt. Lett. 29, 2653-2655 (2004)