On Special Functions for Radiation From Sources Close to an Electrically Large Convex Surface

Several high frequency asymptotic methods in electromagnetics include Fock-type functions. Acoustic hard and soft Fock functions are used as special functions in asymptotic solutions for radiation from sources on an electrically large conducting convex surface. Formulations are available for accurate evaluation of these functions. Asymptotic solutions for radiation from sources close to an electrically large conducting convex surface include the derivatives of these Fock functions as well. However, the existing formulations for the functions do not yield accurate and continuous results for their derivatives. In this letter, the existing formulations are modified to adjust the boundaries between separate intervals for efficient and accurate evaluation of the Fock functions and their derivatives, and to assess continuity across the boundaries for different numbers of terms. The modified formulations are used in the extended uniform geometrical theory of diffraction solution to predict the radiation pattern of a quarter wavelength monopole antenna, which is validated in comparison with the results of the multilevel fast multipole method (MLFMM).