The validity of the paraxial approximation for laser beams in free space is studied via an integral criterion based on the propagation invariants of Helmholtz and paraxial wave equations. This approach allows one to determine the paraxial limit for beams with nondefined spot size and for beams described by more parameters in addition to typical longitudinal wavelength and transverse waist. As examples, the paraxiality of higher-order Hermite, Laguerre, and Bessel–Gaussian beams was completely determined. This method could be extended to nonlinear optics and Bose condensates.
© 2007 Optical Society of America
Lasers and Laser Optics
Original Manuscript: October 19, 2006
Revised Manuscript: January 2, 2007
Manuscript Accepted: January 8, 2007
Published: March 19, 2007
Pablo Vaveliuk, Beatriz Ruiz, and Alberto Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007)