Abstract

The higher-order correction terms of the electric field vector of a Gaussian beam are derived explicitly from the magnetic vector potential that is assumed to be Gaussian and linearly polarized at the $z=0$ plane. The correction terms are proved to satisfy exactly Lax’s recurrence equations [Phys. Rev. A 11, 1365 (1975)]. The electric field vector with correction terms of orders up to 3 is compared with the exact electric field vector of an integral form that is also derived from the magnetic vector potential.

© 1999 Optical Society of America

Corrections to the paraxial approximation of an arbitrary free-propagation beam

Qing Cao and Ximing Deng
J. Opt. Soc. Am. A 15(5) 1144-1148 (1998)

Electromagnetic Gaussian beams beyond the paraxial approximation

C. J. R. Sheppard and S. Saghafi
J. Opt. Soc. Am. A 16(6) 1381-1386 (1999)

Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space

Dongmei Deng, Qi Guo, Sheng Lan, and Xiangbo Yang
J. Opt. Soc. Am. A 24(10) 3317-3325 (2007)

Weakly diverging to tightly focused Gaussian beams: a single set of analytic expressions

Uri Levy and Yaron Silberberg
J. Opt. Soc. Am. A 33(10) 1999-2009 (2016)

Propagation of light beams beyond the paraxial approximation

Takashi Takenaka, Mitsuhiro Yokota, and Otozo Fukumitsu
J. Opt. Soc. Am. A 2(6) 826-829 (1985)