Nonparaxial Lorentz and Lorentz–Gauss beams

The Lorentz and Lorentz–Gauss beams are extended to the nonparaxial regime. Analytical propagation expressions of nonparaxial Lorentz and Lorentz–Gauss beams in free space are derived, and the propagation of paraxial Lorentz and Lorentz–Gauss beams is treated as a special case of our general results. The propagation properties of Lorentz and Lorentz–Gauss beams are illustrated and compared with numerical examples.