  In a unified approach, we study the transport properties of
periodic-on-average bi-layered photonic crystals, metamaterials and electron
superlattices. Our consideration is based on the analytical expression for the
localization length derived for the case of weakly fluctuating widths of
layers, that also takes into account possible correlations in disorder. We
analyze how the correlations lead to anomalous properties of transport. In
particular, we show that for quarter stack layered media specific correlations
can result in a $\omega^2$-dependence of the Lyapunov exponent in all spectral
bands.
