Spherical symmetry breaking in electric, magnetic and toroidal multipole moment radiations in spherical toroidal resonant cavities and optimum-efficiency antennas

This Letter reports the breaking of spherical symmetry in complete electromagnetic multipole expansion when its sources are distributed on toroidal surfaces, identifying specic geometrical and physical changes fromthe familiar case a surface. In fact, for toroids dened by concentric rings symmetric conical rings, boundary conditions at latter not compatible general with integer values orbital angular momentum label moments: polar angle eigenfunctions become Legendre functions order λ associativity m represented as innite series denite parity, their complementary associated radial Bessel same λ. Consequently, corresponding electric, magnetic moments connections identied within Debye formalism, theappropriate outgoing wave Green constructed new basis Helmholtz equation. Our familiarity exact solutions, cases sphere cylindrical toroids, allow us to give preliminary account elds via integration function resonant cavities optimum effciency antennas.