  The squeeze-out phenomenon of $K^+$ and $K^-$ mesons, i.e. the azimuthal
asymmetry of $K^+$ and $K^-$ mesons emitted at midrapidity in heavy ion
reactions, is investigated for beam energies of 1-2 A.GeV. It is found that the
squeeze-out signal is strongly affected by in-medium potentials of these
mesons. The repulsive $K^+$-nucleus potential gives rise to a pronounced
out-of-plane emission of $K^+$'s at midrapidity. With the $K^+$ potential we
reproduce well the experimental data of the $K^+$ azimuthal distribution. It is
found that the attractive $K^-$-nucleus potential cancels to a large extent the
influence of rescattering and reabsorption of the $K^-$ mesons on the
projectile and target residuals (i.e. shadowing). This results in an
azimuthally isotropic emission of the midrapidity $K^-$ mesons with transverse
momentum up to 0.8 GeV/c. Since it is well accepted that the shadowing alone
would lead to a significant out-of-plane preference of particle emission, in
particular at high transverse momenta, the disappearance of the out-of-plane
preference for the $K^-$ mesons can serve as an unambiguous signal of the
attractive $K^-$ potential. We also apply a covariant formalism of the kaon
dynamics to the squeeze-out phenomenon. Discrepancies between the theory and
the experiments and possible solutions are discussed.
