On the basis of the vectorial Rayleigh–Sommerfeld formulas and by means of the relation between Hermite and Laguerre polynomials, the analytical expressions for the propagation of the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams beyond the paraxial approximation are derived, with the corresponding far-field propagation expressions and that for the Gaussian beams being given as special cases of the results. Some detailed comparisons of our results with the expansion series and paraxial expressions are made, which show the advantages of our results over the expansion series. With the results obtained, some typical intensity patterns of nonparaxial HG and LG beams are shown.
© 2005 Optical Society of America
Original Manuscript: December 23, 2004
Manuscript Accepted: March 8, 2005
Published: September 1, 2005
Kailiang Duan, Baida Lü, and Beizhan Wang, "Propagation of Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A 22, 1976-1980 (2005)