**8. Acknowledgment**

Priscilla Simonis, on leave from the University of Namur, Belgium, acknowledges the hospitality of the "Institut des Nanosciences de Paris", Université Pierre et Marie Curie – Paris 6, where this work was carried out.

How Nature Produces Blue Color 23

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ISBN 0-691-12453-1


**2** 

*Germany* 

Andriy E. Serebryannikov

*Hamburg University of Technology, E-3* 

**Basics of the Photonic Crystal Gratings** 

More than twenty years have passed since that time when the analogy between solid-state physics and optics led to the concept of photonic crystals (PCs) (Yablonovitch, 1987). Fast progress in theory and applications of PCs has been stimulated to a large extent by their unique properties that allow increasing the potential of light controlling. Slabs of PC have mainly been studied in case of linear virtual interfaces and a noncurvilinear lattice. A rich variety of the fascinating physical phenomena has been demonstrated for these structures, which include superprism, subwavelength imaging, focusing, collimation, and negative refraction with and without left-handed behaviour (Inoue&Ohtaka, 2004; Luo, 2002). They all appear while using only conventional linear isotropic metals and dielectrics due to the specific dispersion of Floquet-Bloch waves in PCs, which is not obtainable for solid pieces of the same materials. Breaking of periodicity in PCs results in the appearance of defect modes, which manifest themselves in the transmission and waveguide regimes (Joannopoulos, 1995). On the other hand, PCs with curvilinear virtual interfaces but still linear lattice have been investigated in the context of such applications as planoconcave lenses (Gralak, 2000; Vodo, 2005), mirrors (Saado, 2005), and splitters (Wu, 2005). PCs having both curvilinear interfaces and lattice, e.g., coaxial PCs (Schleuer&Yariv, 2004) and atoll resonators (Nojima,

New operation regimes can be obtained due to *merging* effects of dispersion and diffraction, e.g., in two-dimensional PCs. In the mid 2000's, PCs with the corrugated interfaces have been proposed to redirect the reflected waves to the side directions (Collardey, 2005), obtain unusual order of the cutoff wavelengths for higher diffraction orders (Serebryannikov, 2006), and realize a new mechanism of negative refraction due to the umklapp refracted beams (Lu, 2007). Later, PCs with the corrugated interfaces have been called *photonic crystal gratings* (PCGs) (Serebryannikov, 2009). Strong asymmetry in transmission has been demonstrated in dielectric two-dimensional PCGs theoretically (Serebryannikov, 2009) and in the microwave experiment (Cakmak, 2010). Recently, a similar effect has been studied in the two-dimensional sonic crystals (Li, 2011). The structures with a corrugated interface and a defect-mode waveguide, which is perpendicular to the interface, have been used for obtaining of the beaming, that is connected with the excitation of surface waves due to corrugations (Caglayan, 2008; Smigaj, 2007). A structure that is excited by a defect-mode waveguide located along the virtual interfaces of the corresponding noncorrugated PC has been suggested (Le Thomas, 2007), where the corrugations provide coupling of an otherwise

**1. Introduction** 

2007) are also known.

uncoupled defect mode to an outgoing wave in air.

