Eigenfunctions and eigenvalues in superradiance with x-y translational symmetry

The Lienard-Wiechert potential is the kernel of the integral equation describing superradiance from N two-level atoms, one atom being initially excited. In 1-d geometry, an eigenmode with definite parity is, in general, dominant for a specific slab thickness. The shapes of these eigenmodes are similar to those obtained in numerical solutions of the coupled Maxwell-Bloch equations