It is shown in an earlier paper dealing with flat-topped light beams [Opt. Lett.27, 1007 (2002)] that the profile of flat-topped beams can be expressed in the form 1−[1−exp(−xi<sup>2</sup>)]<sup>M</sup>, where xi is a dimensionless parameter and M is a nonnegative number. The expansion of the proposed expression is a finite series containing only the lowest-order Gaussian modes. This situation provides the possibility of reformulating the scalar theory of diffraction at an aperture in an opaque screen if the Gaussian mode expansion is employed to describe the boundary values of the light incident on the screen. As an example of this effort, an asymptotic model is established for three-dimensional irradiance distributions near the focus in systems of different Fresnel numbers. The proposed expansions contain only elementary functions and permit all elementary operations; therefore no special functions or special algorithms are needed in the evaluation of either irradiance distributions or the integrated energy in a focused field.
© 2006 Optical Society of America
Original Manuscript: June 29, 2005
Manuscript Accepted: August 10, 2005
Yajun Li, "Expansions for irradiance distribution near the focus in systems of different Fresnel numbers," J. Opt. Soc. Am. A 23, 730-740 (2006)