The plane wave expansion method can be used to calculate the band structure using an eigen formulation of the Maxwell's equations, and thus solving for the eigen frequencies for each of the propagation directions, of the wave vectors. It directly solves for the dispersion diagram. Electric field strength values can also be calculated over the spatial domain of the problem using the eigen vectors of the same problem. For the picture shown to the right, corresponds to the band-structure of a 1D distributed Bragg reflector (DBR) with air-core interleaved with a dielectric material of relative permittivity 12.25, and a lattice period to air-core thickness ratio (d/a) of 0.8, is solved using 101 planewaves over the first irreducible Brillouin zone. The Inverse dispersion method also exploited plane wave expansion but formulates Maxwell's equation as an eigenproblem for the wave vector k while the frequency ω ω is considered as a parameter. Thus, it solves the dispersion relation k ( ω ω ) instead of ω ω ( k ) , which plane wave method does. The inverse dispersion method makes it possible to find complex value of the wave vector e.g. in the bandgap, which allows one to distinguish photonic crystals from metamaterial. Besides, the method is ready for the frequency dispersion of the permittivity to be taken into account.