Published in Journal of the Optical Society of America B: Optical Physics, Volume 24, Issue 1, January 1, 2007, pages 1-8.
NOTE: At the time of publication, the author Glen Gillen was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1364/JOSAB.24.000001.
Focusing of light by a curved surface is described using the vector Kirchhoff diffraction theory. The electromagnetic fields of a light beam incident as a plane wave on a curved surface separating two transparent media having different refractive indices are expressed as dimensionless double integrals. The integrals are evaluated for a few specific cases, and the three-dimensional distribution of irradiance near the focus is determined. The role of aberration in limiting the maximum achievable irradiance is studied. The distribution of the longitudinal components of the electric field in the focal region is also studied, and the region where the longitudinal fields maximize is determined.
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