  The structure of an optical waveguide determines the characteristics of its
guided modes, such as their spatial profile and group index. General features
are shared by modes regardless of the waveguiding structure; for example, modal
dispersion is inevitable in multimode waveguides, every mode experiences
group-velocity dispersion, and higher-order modes are usually slower than their
lower-order counterparts. We show here that such trends can be fundamentally
altered -- altogether severing the link between modal order and group index
hybrid and eliminating dispersion -- by exploiting hybrid guided space-time
modes in a planar multimode waveguide. Such modes are confined in one-dimension
by the waveguide and in the other by the spatio-temporal spectral structure of
the field itself. Direct measurements of the modal group delays confirm that
the group index for low-loss, dispersion-free, hybrid space-time modes can be
each tuned away from the group index of the conventional mode of same order,
and that the transverse size of these hybrid modes can be varied independently
of the modal order and group index. These findings are verified in a few-mode
planar waveguide consisting of a 25.5-mm-long, 4-$\mu$m-thick silica film
deposited on a MgF$_2$ substrate.
