Achievable Transverse Cylindrical Electromagnetic Mode
  The system of Maxwell equations with an initial condition in a vacuum is solved in a cylindrical coordinate system. It derives the cylindrical transverse electromagnetic wave mode in which the electric field and magnetic field are not in phase. Such electromagnetic wave can generate and exist in actual application, and there is no violation of the law of conservation of energy during the electromagnetic field interchanges. 
R. Chen and X. Li
physics.gen-ph