  Photonic band gaps for the soft x-rays, formed in the periodic structures of
solids or dense plasmas, are theoretically investigated. Optical manipulation
mechanisms for the soft x-rays, which are based on these band gaps, are
computationally demonstrated. The reflection and amplification of the soft
x-rays, and the compression and stretching of chirped soft x-ray pulses are
discussed. A scheme for lasing with atoms with two energy levels, utilizing the
band gap, is also studied.
