Waves in Layered Medium and Photonic Crystals

There are several examples of waves in periodic media  

Light waves in the natural media such as opal, mother-of-pearl, beetle shells, etc. 

Light waves interacting with artificial diffraction gratings, one or two dimensional and three dimensional photonic bandgap crystals, in particular, artificial opals 

Acoustic waves between periodically arranged columns in a theatre 

A common feamre of all these media is a spatial periodicity with a period comparable to that of the external wave of any sort. In the three dimensional case, the diffraction may result in light localisation and trapping like electrons may be completely localised in a disordered metal (metal-insulator transition). 

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