The theory of launching lower hybrid waves in fusion-oriented plasmas using waveguide arrays (the 'grill') is generalized to allow for the excitation of the fast wave in the outer layers of the plasma. It is found that the reflection coefficient of the antenna and the fraction of power radiated in the 'inaccessible' portion of the parallel-wavenumber spectrum remain essentially the same as those predicted by the simplified theory considering only the slow plasma wave. The most important new feature is that the power radiated in this part of the spectrum is mainly coupled to discrete waveguide-like eigenmodes confined to the outer layers of the plasma, which guide the power away from the antenna in the direction parallel to the wall of the chamber. This fraction of the power is likely to be lost from the point of view of the heating efficiency; therefore, one should make it as small as possible by using arrays of four guides or more.