A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.
© 2006 Optical Society of America
Diffraction and Gratings
Original Manuscript: July 14, 2005
Revised Manuscript: October 12, 2005
Manuscript Accepted: October 14, 2005
Xueen Wang, Zhaozhong Fan, and Tiantong Tang, "Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials. I. General theory," J. Opt. Soc. Am. A 23, 872-877 (2006)