A simple but exact treatment of spatiotemporal behavior of ultrawideband pulses under an arbitrarily tight focusing is developed. The model makes use of the oblate spheroidal coordinate system to represent free scalar field as if generated by a point-like source-and-sink pair placed at a complex location. The results, illustrated by animated 3D plots, demonstrate characteristic temporal reshaping of the pulses in the course of propagation through the focus, which is a spectacular manifestation of the Gouy phase shift. It is shown that the salient features of the reshaping, which were recently established for the paraxial limit, remain valid beyond it. The treatment is particularly applicable to an ultrawideband isodiffracting ultrashort terahertz-domain or light pulses in high-aperture resonators, such as microcavities, and it is usable in femto- and attosecond optics in general.
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