basis function (i.e., dotting from the left and integrating over the domain of the i-th current basis function, thereby completing the quadratic form) produces the i-th row of the matrix eigenvalue equation for a 3-dimensional array of PEC scatterers as: As in all MoM formulations, the reaction concept in electromagnetics was used in obtaining this equation. The electric field boundary/continuity conditions are "tested" (or enforced) by being integrated against electric current basis functions (for dielectric structures, the magnetic field continuity conditions are additionally tested by being integrated against magnetic current basis functions), and this is how the electric (and magnetic) field boundary conditions are converted into a matrix equation via the method of moments. This process is wholly analogous to that used to decompose a periodic function into its Fourier sine & cosine components, the only difference being that in this case the basis functions are not necessarily orthogonal, merely linearly independent. This matrix equation is easy to implement and requires only that the 3D Fourier transform (FT) of the basis functions be computed, preferably in closed form. In fact, computing bands of a 3D photonic crystal with this method is no more difficult than computing reflection and transmission from a 2D periodic surface using the spectral domain method. This is because equation () is identical to the basic EFIE for a freestanding PEC FSS (see Frequency selective surface eq. ), the only difference being the stronger singularity in 3D which significantly accelerates convergence of the triple sums, and of course the fact that the vectors are now 3-dimensional. As a result, an ordinary PC is sufficient to compute bands of many types of photonic crystals. It's evident from () that the EFIE could become singular whenever the free space wavenumber is exactly equal to one of the wave numbers in any of the 3 periodic coordinate directions. This can happen for example when the free space wavelength exactly equals the lattice spacing. This is a statistically rare occurrence in computational practice and corresponds to a propagation anomaly similar to a Wood's reflection anomaly for gratings. Computing bands To compute bands of the crystal (i.e. k-k0 diagrams), successive values of frequency (k) are tried - in conjunction with pre-selected values of propagation constant (k0) and propagation direction (θ0 & φ0) - until a combination is found which drives the determinant of the matrix to zero. Equation () has been used