  Quantum teleportation of an unknown broadband electromagnetic field is
investigated. The continuous-variable teleportation protocol by Braunstein and
Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum
state of a single mode of the electromagnetic field is generalized for the case
of a multimode field with finite bandwith. We discuss criteria for
continuous-variable teleportation with various sets of input states and apply
them to the teleportation of broadband fields. We first consider as a set of
input fields (from which an independent state preparer draws the inputs to be
teleported) arbitrary pure Gaussian states with unknown coherent amplitude
(squeezed or coherent states). This set of input states, further restricted to
an alphabet of coherent states, was used in the experiment by Furusawa {\it et
al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for
optimizing the teleportation fidelity. In our broadband scheme, the excess
noise added through unit-gain teleportation due to the finite degree of the
squeezed-state entanglement is just twice the (entanglement) source's squeezing
spectrum for its ``quiet quadrature.'' The teleportation of one half of an
entangled state (two-mode squeezed vacuum state), i.e., ``entanglement
swapping,'' and its verification are optimized under a certain nonunit gain
condition. We will also give a broadband description of this
continuous-variable entanglement swapping based on the single-mode scheme by
van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]
