Relationship between the source excitation, electromagnetic field solutions and the resonance of modes in material structures

In this paper, a case of a simple antenna represented by a spherical dipole, coated by dual layers of homogeneous material, is considered and solved analytically using the spherical harmonics. The excitation is assumed to be due to a constant gap voltage. It is shown that in the works of Shafai and Kehn (2008, 2009), the classical boundary value problem solution results in unrealistic power radiations, especially when certain modes become resonant in the coating structure. The problem is further investigated here by studying the determinant of the coefficient matrix of the selected solution. It is found that, at the mode resonances the determinant of the coefficient matrix becomes vanishingly small, causing the computed field vectors and subsequently the radiated power, to approach infinity. Further investigation of the problem reveals that in correct and physical excitation source the voltage is variable and is inversely proportional to coefficient matrix determinant. In addition, at the mode resonances, nearly the entire input power is transferred to the single excited mode. In such cases then, one need not solve the boundary value problem for all the modes, and the field vectors can simply be represented by a single resonant mode. The difficulty of the infinite radiated power resolves automatically, as the coefficient of the excited mode is determined directly from the input power.