Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, an analytical propagation equation of vectorial, nonparaxial, elliptical Gaussian beams through a rectangular aperture is derived. Unlike in previous work, the aperture effect and nonrotational symmetry of the beam and aperture are considered in our theoretical model. The results of the far-field and paraxial approximation for the apertured case are treated as special cases of our general expression. It is found that two <i>f</i> parameters f<sub>x</sub>, f<sub>y</sub> and two truncation parameters δ<sub>x</sub>, δ<sub>y</sub> in the <i>x</i> and <i>y</i> directions, respectively, have to be introduced that affect the beam nonparaxial evolution behavior in both the near field and the far field.
© 2004 Optical Society of America
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(140.0140) Lasers and laser optics : Lasers and laser optics
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation
Kailiang Duan and Baida Lü, "Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture," J. Opt. Soc. Am. A 21, 1613-1620 (2004)