An efficient modal solution for scattering by an arbitrary isosceles triangular groove (ITG) in an infinite ground plane is suggested. The procedure consists of expanding the fields in two distinct regions and three different cylindrical coordinate systems, employing Graf’s addition theorem for convenience in imposing boundary conditions on an arc-shaped boundary, and determining the field expansion coefficients by solving a system of linear equations. The method is in good agreement with the time-consuming methods such as the finite-element method (FEM) and the method of moment (MoM) while it has an appropriate computational efficiency especially when the width of a groove increases. This method is utilized to investigate the effects of the problem parameters such as the size of ITG, the wave polarization, and the incidence angle on the scattering signature.
