  We calculate the response of a vortex core in a layered superconductor to
{\em ac} electromagnetic fields with frequencies $\omega\lsim 2\Delta/\hbar$.
In this frequency range the response is dominated by order parameter collective
modes which are coupled to the vortex-core bound states of Caroli, de Gennes
and Matricon. Our calculations show that a vortex core has a more complex and
richer dynamics than predicted by previous theories. The {\em ac} field drives
an oscillating, nearly homogeneous supercurrent in the direction of the
electric field, superimposed with a dissipative current flow which has a
dipolar spatial structure. The order parameter response at low frequencies is
an approximately rigid collective motion of the vortex structure perpendicular
to the external field. This structure becomes strongly deformed at frequencies
of order $\omega\gsim 0.5 \Delta /\hbar $. Coupling of the vortex-core bound
states to collective modes of the order parameter at low frequencies leads to
substantial enhancement of the dissipation near the vortex-center well above
that of the normal-state.
