Wave diffraction by a half-plane for grazing incidence

The diffracted wave, related with a half-plane on which the total field satisfies the Dirichlet boundary condition, becomes zero when the angle of incidence of the incident wave is equal to zero according to the solution of Sommerfeld. However, this behaviour of the solution causes some physical inconsistencies. The letter proposes a new approach for the elimination of the mentioned defect. The results are supported by some simulations.