Angle-dependent Andreev reflection at an interface with a polaritonic superfluid

We study analytically an analog of the Andreev reflection at a normal-superfluid interface. The polariton gapped superfluid region is achieved by quasiresonant optical pumping. The interacting polaritons are described with the driven-dissipative Gross-Pitaevskii equation. We find analytical formulas for the angles and amplitudes of the reflected and transmitted particles. There are limit angles and energies, above which Andreev reflection and transmission cannot be observed anymore and where the Andreev wave becomes a surface mode, exponentially localized on the interface. These properties are confirmed by solving numerically the Gross-Pitaevskii equation in simulations reproducing realistic experimental conditions.