Optical field properties in micro- and nano-structures

We present an envelope formalism describing nonlinear phenomena in photonic crystals by casting the Maxwell equations as a linear Hermitian eigenvalue problem in close analogy with the Schrodinger equation of quantum mechanics. From this formulation, applied to one dimensional photonic crystal, comes a variety of useful properties, including the density of modes and second harmonic generation. The mutual control of radiation field and matter defined by the control of photon modes by nonlinear photonic crystals-mode shapes, dispersion relations, optical solitons- is a key technology for future photonic devices.