Abstract: A photonic crystal, an analog of a semiconductor for light waves, is a material in which propagation of certain photon wavelengths is forbidden. It appeared first as a theoretical proposal about 10 years ago, but rapid progress in manufacturing such newly-engineered materials at microwave and then optical wavelengths, has involved the development of new fundamental physical concepts and ideas. We provide a simple introduction into the field and overview the recent progress, emphasizing our results on nonlinear photonic crystals and also making an effort to oversee some future developments.

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