Validity limits of the paraxial approximation in laser beams

VAVELIUK, P.; RUIZ, B.; LENCINA, A.

OPTICS LETTERS

Año: 2006

0146-9592

This letter studies the validity of the paraxial approximation for laser beams in free-space via an integral criterion based on the propagation invariants of Helmholtz and paraxial wave equations. This approach allows to determine the paraxial validity limits for beams whose spot size is not well-de¯ned and also for beams described by more parameters in addition to typical longitudinal wavelength and transversal waist. As examples, the paraxiality of higher-order Hermite, Laguerre and Bessel-Gaussian beams was completely determined in the whole space. This method can be extended to nonlinear optics and Bose condensates.