  We give an example of a scalar second order differential operator in the
plane with double periodic coefficients and describe its modification, which
causes an additional spectral band in the essential spectrum. The modified
operator is obtained by applying to the coefficients a mirror reflection with
respect to a vertical or horizontal line. This change gives rise to Rayleigh
type waves localized near the line. The results are proven using asymptotic
analysis, and they are based on high contrast of the coefficient functions.
