  We consider the problem of broadcasting arbitrary states of radiation modes
from N to M>N copies by a map that preserves the average value of the field and
optimally reduces the total noise in conjugate variables. For N>=2 the
broadcasting can be achieved perfectly, and for sufficiently noisy input states
one can even purify the state while broadcasting--the so-called
superbroadcasting. For purification (i.e. M<=N), the reduction of noise is
independent of M. Similar results are proved for broadcasting with
phase-conjugation. All the optimal maps can be implemented by linear optics and
linear amplification.
