Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case

In paraxial optics, the spatial and angular localization of a beam are usually characterized through second moments in intensity. For these measures, Gaussian beams have the property of achieving a minimum angular spread for a given spatial spread (or beam waist). For wide-angle fields, however, the standard measures of spatial and angular localization become inappropriate, and new definitions must be used. Previously proposed definitions [J. Opt. Soc. Am. A 17, 2391 (2000)] are adopted, and the scalar monochromatic wave fields that achieve a minimum angular spread for a given spatial spread are found. (C) 2006 Optical Society of America