The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated.
© 1999 Optical Society of America
Original Manuscript: January 13, 1999
Revised Manuscript: April 15, 1999
Manuscript Accepted: April 15, 1999
Published: October 1, 1999
Qing Cao, "Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media," J. Opt. Soc. Am. A 16, 2494-2499 (1999)