Since the advent of quantum mechanics and the clear demonstration of the existence of 'matter waves', physicists have never failed to take advantage of concepts and theoretical methods developed in the fields of optics and electromagnetism. Thus, a number of phenomena in solid state physics are commonly interpreted by analysing electronic excitations in terms of electronic waves. By contrast, the opposite situation has rarely occurred, and only on a few occasions have optics and electromagnetism borrowed concepts and theoretical methods from solid state physics. From this point of view, the emergence of photonic bandgap materials and photonic crystals at the end of the 1980s can be seen as a revenge to the benefit this time of optics and electromagnetism. In the same way as the periodicity of solid state crystals determines the energy bands and the conduction properties of electrons, the periodical structuring of optical materials at wavelength scales has turned out to be one the most viable approaches towards the control of the energies and of the fluxes of photons occurring in these materials. The analogy between electronic waves and electromagnetic waves is a mere consequence of the formal relation between the Schrödinger's equation for electronic wavefunctions and Maxwell’s equations for electromagnetic waves. Indeed, leaving aside the spins of the particles, a harmonic electromagnetic wave in a dielectric lossless medium satisfies Eq. 1a, which formally is analogous to the equation ruling the wave function for an electron with mass m in a potential V (Eq. 1b):