Approximate Asymptotic Expressions for the Electromagnetic Field and the Mutual Admittance of Slоts in a Conducting Convex Surface of Rotation in the Form of Series of Azimuthal Harmonics

In this paper, we obtain approximate asymptotic expressions for the electromagnetic field and the self and mutual admittances of "single-mode" slots in a smooth convex surface of rotation of large sizes in the form of a series of azimuthal harmonics. The coefficients of the series are expressed as integrals over the wave spectrum and can be calculated numerically or as a sum series of deductions (for mutual admittances). The expressions for the coefficients are uniformly valid in the boundary surface layer, except for the vicinity of the poles of the surface of rotation, and do not have discontinuities on the caustics of the surface rays. The resulting expressions can be directly used to calculate the fields and the self and mutual admittances of annular slots. In contrast to the eigenfunction method, asymptotic expressions allow us to cover the case of an arbitrary-shaped surface and avoid summing slowly converging double series. A comparison of the results of calculating the admittances of annular slots in a conducting spherical surface obtained by the proposed method and the method of eigenfunctions was executed, and their good agreement shown even for a small radius of the sphere equal to 3λ.