  We study the effects of periodic matter in kaon regeneration, motivated by
the possibility of parametric resonance in neutrino oscillations. The large
imaginary parts of the forward kaon-nucleon scattering amplitudes and the decay
width difference $\Delta\Gamma$ prevent a sizable enhancement of the $K_L\to
K_S$ transition probability. However, some interesting effects can be produced
using regenerators made of alternating layers of two different materials.
Despite the fact that the regenerator has a fixed length one can obtain
different values for the probability distribution of the $K_L$ decay into a
final state. Using a two-arm regenerator set up it is possible to measure the
imaginary parts of the $K^0(\bar{K}^0)$-nucleon scattering amplitudes in the
correlated decays of the $\phi$-resonance. Combining the data of the single-arm
regenerator experiments with direct and reverse orders of the matter layers in
the regenerator one can independently measure the CP violating parameter
$\delta$.
