Quasimonochromatic exact solutions to Maxwell’s equations with finite total energy and arbitrary frequencies in the vacuum

摘要

We analyze a family of exact finite energy solutions to Maxwell’s equations. These solutions are a subset of the modified-power-spectrum solutions found by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. There are three characteristic parameters in the solutions: q_1,q_2, and k_(0. q1) and q_2 are related to the frequency bandwidth of the solution. In the parameter space of k_(0q1)? 1 and k_(0q2) ? 1, they represent quasimonochromatic continuous wave fields with the main angular frequency k_0c and energy localized in the transverse directions. Under the restriction of q_1 ? q_2, the beam propagates mainly in the +z direction with velocity c and limited diffraction.