Theoretical investigations on the use of an advanced launcher to couple lower hybrid waves to a plasma, for current drive in tokamaks, have been developed. A study of the coupling has been carried out in a rigorous way, through the solution of the scattering by an array of cylinders with parallel axes in the presence of a plane of discontinuity for the electromagnetic constants. The general features of the proposed method are presented together with results on the launched spectra and coupled power. The numerical results of this work are relevant to the optimization of the single layer quasi-optical grill launching RF power towards a constant density plasma: it is shown that the power coupled in the plasma can reach values of about 25-30% in the -1 diffracted order and about 40% in all other orders. As a consequence it is expected that the coupling values for a suitable double layer configuration should approach those for total transmission