mode - spectrum in 2D), and an integral equation is enforced on the surface of the scatterers in each unit cell. In the FSS case, the unit cell is 2-dimensional and in the photonic crystal case, the unit cell is 3-dimensional. Field equations for 3D PEC photonic crystal structures The Bloch wave - MoM approach will be illustrated here for the case of perfectly electrically conducting (PEC) structures admitting only electric current sources, J. However, it can also be readily expanded to dielectric structures, using the well-known interior and exterior equivalent problems commonly employed in ordinary spatial domain method of moments formulations. In dielectric problems, there are twice as many unknowns - J & M - and also twice as many equations to enforce - continuity of tangential E & H - at the dielectric interfaces. For PEC structures, the electric field E is related to the vector magnetic potential A via the well-known relation: and the vector magnetic potential is in turn related to the source currents via: where Bloch wave expansion of the fields To solve equations () and () within the infinite periodic volume, we may assume a Bloch wave expansion for all currents, fields and potentials: where for simplicity, we assume an orthogonal lattice in which α only depends on m, β only depends on n and γ only depends on p. With this assumption, and, where lx, ly, lz are the unit cell dimensions in the x,y,z directions respectively, λ is the effective wavelength in the crystal and θ0, φ0 are the directions of propagation in spherical coordinates. The quantity k in equations () and () comes originally from the time derivative in Maxwell's equations and is the free space propagation constant (actually, the propagation constant of whatever dielectric medium the metallic scatterers are embedded in), proportional to frequency as in equation (). On the other hand, k0 in the equations above comes from the assumed Bloch wave solution given by equations () & (). As a result, it represents the propagation constant inside the periodic medium, inversely proportional to wavelength. These two k's, i.e. the free space propagation constant (proportional to frequency) and the propagation constant of the Bloch wave (inversely proportional to wavelength), are in general different thereby allowing for dispersion in the solution. The band diagram is essentially a plot of k as a function of k0. The Bloch wave expansions in