  We present a complete set of analytical and invariant expressions for the
steady-state density matrix of atoms in a resonant radiation field with
arbitrary intensity and polarization. The field drives the closed dipole
transition with arbitrary values of the angular momenta $J_{g}$ and $J_{e}$ of
the ground and excited state. The steady-state density matrix is expressed in
terms of spherical harmonics of a complex direction given by the field
polarization vector. The generalization to the case of broad-band radiation is
given. We indicate various applications of these results.
