  The band structure of photons in cholesteric liquid crystals (CLCs) is
investigated in the shortwave approximation. The bound states or narrow
resonances of photons in the CLC are formed by the extraordinary waves. The
explicit expressions for the spectrum bands and the dispersion laws of photons
in these bands are obtained. It is shown that these states describe photons
propagating almost perpendicular to the CLC axis. The density of photon states
acquires a sharp peak due to the presence of bound states. Near this peak, in
the particular case of plasma permittivity, the photons posses a linear or
quadratic dispersion relations in the directions perpendicular to the CLC axis
depending on the sign of the anisotropy of the CLC permittivity tensor. The
resonances in the CLC plate are also described.
