Qc. Cao et Xm. Deng, CORRECTIONS TO THE PARAXIAL APPROXIMATION OF AN ARBITRARY FREE-PROPAGATION BEAM, Journal of the Optical Society of America. A, Optics, image science,and vision., 15(5), 1998, pp. 1144-1148
A relatively simple transform from an arbitrary solution of the paraxi
al wave equation to the corresponding exact solution of the Helmholtz
wave equation is derived in the condition that the evanescent waves ar
e ignored and is used to study the corrections to the paraxial approxi
mation of an arbitrary free-propagation beam. Specifically, the genera
l lowest-order correction field is given in a very simple form and is
proved to be exactly consistent with the perturbation method developed
by Lax et nl. [Phys. Rev. A 11, 1365 (1975)]. Some special examples,
such as the lowest-order correction to the paraxial approximation of a
fundamental Gaussian beam whose waist plane has a parallel shin from
the z = 0 plane, are presented. (C) 1998 Optical Society of America.