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The characteristics of photon and phonon standing waves in a periodic medium

The main characteristics of the spatial variation of the photon and phonon wave fields at the band gap boundaries are analysed for a one-dimensional medium with periodic optical or acoustic parameters. The derivations are based on symmetry considerations and on analytical results derived from the basic differential equation for the wave field. A simple relation is derived between the band gap width and the derivative of the field intensity at the interface between the regions of high and low wave velocity. The general field characteristics are derived for some examples. Using the analysis a remarkable asymmetric behaviour of the wave absorption near the Brillouin zone boundaries can be explained in a straightforward way.