Singular Locally Propagating Azimuthal Electromagnetic Fields

We investigate locally propagating azimuthal electromagnetic waves where the ‘propagation’ constant m, which controls the angular variation e^imΦ, is continuous instead of assuming only integer values. An interesting outcome of this study is that in circular waveguides, the transverse components of the electromagnetic field become singular at the centre (ρ=0) but remain square integrable for all values of 0<m<1. The lowest TE branch starts from a resonance at m=0 where the energy is logarithmically singular. The singular nature of these local fields is an intrinsic property that is not imposed by the boundary conditions of the waveguide. It is due to the cylindrical symmetry instead. Similar local singularities appear in spherical electromagnetic waves. Resonant structures exhibiting these singular solutions are presented. It is suggested that naturally occurring energetic phenomena might involve these singular electromagnetic waves.