  The problem of optical radiation produced by a bunch of relativistic
positrons channeled to a crystalline undulator (CU) is considered. Taking into
account the polarization of the crystal medium, an energy threshold takes place
to form the radiation. If the energy of the bunch is above the threshold, the
radiation is created in a limited frequency range. Both soft and hard boundary
photons exist and are emitted at zero angle due to the polarization of the
medium. In the case where the ratio between bunch's and threshold energies is
much greater than unity, the energy of the boundary soft photons depends only
on the characteristic parameters (spatial period, amplitude) of the crystalline
sinusoidal undulator and can be tuned to the optical range. It is shown that it
is possible to obtain a directed optical beam in the "water window" range. Such
photon beams have important applications in medicine and biological research.
