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The quasiclassical theory in terms of equations for the Green's functions(Eilenberger equations) is generalized in order to allow for quantitativedescription of the magneto-electric effects and proximity-induced tripletcorrelations in the presence of spin-orbit coupling in hybrid superconductingsystems. The formalism is valid under the condition that the spin-orbitcoupling is weak with respect to the Fermi energy, but exceeds thesuperconducting energy scale considerably. On the basis of the derivedformalism it is shown that the triplet correlations in the spin-orbit couplednormal metal can be induced by proximity to a singlet superconductor withoutany exchange or external magnetic field. They contain an odd-frequencyeven-momentum component, which is stable against disorder. The value of theproximity-induced triplet correlations is of the order of$\Delta_{so}/\varepsilon_F$, that is absent in the framework of the standardquasiclassical approximation, but can be described by our theory. The spinpolarization, induced by the Josephson current flowing through thesuperconductor/Rashba metal/superconductor junction, is also calculated.

Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of the spin-orbit coupling