Analysis of periodic arrays of waveguide apertures on conducting cylinders covered by dielectric

The analysis of infinite arrays of waveguide apertures on cylinders covered by a dielectric is approached by enforcing the continuity of the EM fields at the air-dielectric and at the dielectric-cylinder interfaces. The continuity of the EM fields at the first interface is enforced by representing the fields in the air and in the dielectric by an orthonormal set of modes LSE and LSM with respect to the radial direction. The matching of the fields at the second interface is performed by resorting to the "eigenexcitation" method [1]. The fields external to the cylinder are represented by a set of space harmonics matching the symmetry of the excitation of the array and the fields in the waveguides by a superposition of normal waveguide modes. The continuity of the fields is approximately enforced by using Galerkin's method. The rigorous analysis of these structures leads to rather involved expressions for the element driving point admittance and for the far fields. An approximate analysis is introduced to simplify the design of these structures for cylinders of large radius. Numerical examples illustrate the good approximation given by the simplified analysis. Numerical results are presented for the case of an array on a cylinder with radius approximately100lambda. The array element pattern shows the presence of resonance dips much more pronounced than the notches due to grating lobe phenomena.