We study the linear and nonlinear pulse propagation models whose dispersion relations presents bands of forbidden frequencies or forbidden wave numbers. These bands are due to the interplay between dispersion and longitudinal and transverse diffractions as a result of abandoning the paraxial approximation. We observe that as a result of these band gaps, narrow pulses radiate in some peculiar way. The role of each parameter on the band gap also has been studied. © 2018 Author(s).