Mutual coupling analysis of arrays of apertures on cones

The analysis of the element pattern in an array of waveguide elements on a cone is approached by systematically exploiting the geometrical symmetry of the structure. The method consists of decomposing the arbitrary array excitation into fundamental excitations (eigenexcitations) for which the solution of the electromagnetic problem is simpler than in the general case. Following Bailin and Silver, the fields external to the cone are represented as a superposition of modes TE and TM to the radial direction. For each eigenexcitation the fields in the waveguide elements are represented as a superposition of normal waveguide modes. The enforcement of the continuity of the electromagnetic fields at the conical interface provides complete information about the radiation from the elements and the reflection coefficients of the modes in the waveguide. The array element pattern is obtained by the superposition, with suitable weights, of the patterns of the eigenexcitations. The communication presents the computational procedures followed to evaluate with high speed and precision the roots of the Legendre functions necessary to represent the fields external to the conical structure. Numerical results for the realized element patterns of a particular conical array are presented in the final section.