Toroidal Resonators for Electromagnetic Waves

The solution of Maxwell's equations for toroidal systems has been reduced to the solution of the scalar Helmholtz equation. The eigenfunctions and the corresponding electromagnetic fields have been calculated analytically. The dispersion relation was formulated. Three different types of eigenmodes were obtained for each frequency. The structure of the electromagnetic field of the m= 0,1,2, and 3 modes is analyzed.