Propagation of ultrashort electromagnetic wave packets in free space   beyond the paraxial and slowly-varying-envelope approximations : a   time-domain approach
  A time-domain approach is proposed for the propagation of ultrashort electro- magnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the wave equation in free space without resorting to Fourier trans- forms. An exact solution is obtained in terms of successive temporal and spatial derivatives of a monochromatic paraxial beam. The special case of a radially polarized transverse magnetic wave packet is discussed. 
Charles Varin and Michel Pich\'e