Frequency dependent hyperpolarizability and two photon excitations in hydrogen atom confined under classical plasma environment

•Frequency dependent hyperpolarizability of atomic systems surrounded by Debye plasma is reported taking H atom as a prototype.•Time dependent variation perturbation theory with Slater basis is used to study nonlinear response of plasma embedded H atom.•Two photon absorption in such systems is observed as an outcome of the present calculation.•The accidental degeneracy of H atom is systematically removed in presence of plasma.