The reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the MoM solution of the volume integral equation. The asymptotic waveform evaluation (AWE) technique is utilized to obtain a Pade approximation of the solution in terms of a parameter such as frequency or incident angle. The use of AWE technique enables a fast sweep with respect to the approximation parameter. Moreover, a robust method for extracting the dispersion characteristics of periodic structures via Pade approximation is proposed. The AWE procedure requires the calculation of high order derivatives of the complicated kernel function that consists of Green's functions for stratified medium. These derivatives are calculated by employing the Automatic Differentiation Theory. The reflection coefficient, propagation constant and band diagram of the structure are obtained both via point-by-point simulations and through the use of AWE technique. It is observed that AWE technique increases the computational efficiency without losing accuracy.