Optics of photonic crystals

In this article, a general theoretical framework to describe and analyze th e optical properties of photonic crystals is presented. In addition to the analytical treatment of their optical response based on the method of Green 's function, numerical tools to calculate the dispersion relations and the eigenfunctions of the radiation held, transmission spectra, localized midga p modes, and lasing threshold are introduced and applied to some typical ex amples. Group theory to analyze the symmetry of the eigenmodes is also intr oduced, and the existence of uncoupled modes that cannot be excited by exte rnal plane waves is shown. The presence of the enhancement effect of nonlin ear optical processes and stimulated emission due to the small group veloci ty which is easily realized in the photonic crystals is pointed out, and th e possibility of low-threshold lasing in the photonic crystals is discussed .