  Weber-type parabolic beams have a transverse intensity profile, which is
parabolically-shaped and can be flexibly controlled. On the other hand, this
type of beams belongs to the family of the so-called nondiffracting beams and
have properties, promising for applications where the shape of the beam is of
an importance. Vector electromagnetic theory has to be introduced in order to
fully describe optical beams inside a high numerical aperture system, where the
angles of the spatial spectra are large. We introduce here parabolic vector
focus wave modes (FWM), which are both resistant to diffraction and to material
dispersion. We employ here a spectral approach and investigate durations of
parabolic vector FWMs in the femtosecond region. Two cases of transverse
electric and transverse magnetic modes are introduced and both standing and
traveling types of waves are considered. We demonstrate how the angular
dispersion affects the pulse shape and its properties. Parabolic vector FWMs
are studied in a transparent dielectric media (sapphire), which is widely used
as laser processed material.
