From polarized gravitational waves to analytically solvable electromagnetic beams
Using the correspondence between solutions of gravitational and gauge theories (the so-called classical double copy conjecture) some analytically solvable electromagnetic fields with vortices are constructed. The starting point is a certain class of plane gravitational waves exhibiting the conformal symmetry. The notion of the Niederer transformation, crucial for the solvability, is analysed in the case of the Lorentz force equation on the curved spacetimes. Furthermore, the models discussed recently in the context of the intense laser beams are constructed from their gravitational counterparts, with the special emphasis put on the focusing property, and new solvable examples are presented.