  We report the existence and properties of localized modes described by
nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential
well. Exact analytical expressions of the localized modes are found in both one
dimensional and two-dimensional geometry with self-focusing and self-defocusing
Kerr nonlinearity. Linear stability analysis reveals that these localized modes
are unstable for all real values of the potential parameters although
corresponding linear Schroedinger eigenvalue problem possesses unbroken
PT-symmetry. This result has been verified by the direct numerical simulation
of the governing equation. The transverse power flow density associated with
these localized modes has also been examined.
