Simulations of the Huygens, Fresnel, and Rayleigh–Sommerfeld I approximations in the case of free-space propagation of a Gaussian beam are compared with analytical solutions. The most accurate results were obtained by the Rayleigh–Sommerfeld I approximation. The study reveals that the approximations are not uniform throughout the propagation region. While the accuracies of the Huygens and Fresnel methods generally increase as the propagation distance increases, the accuracy of the Rayleigh–Sommerfeld I approximation at first starts to diminish and later recovers as the propagation distance is further increased.
© 2013 Optical Society of America
Diffraction and Gratings
Original Manuscript: January 17, 2013
Manuscript Accepted: February 2, 2013
Published: March 18, 2013
Seyed M. Azmayesh-Fard, "Gaussian beam propagation: comparison of the analytical closed-form Fresnel integral solution to the simulations of the Huygens, Fresnel, and Rayleigh–Sommerfeld I approximations," J. Opt. Soc. Am. A 30, 640-644 (2013)