  We report an inelastic light scattering study of single-crystalline
NaCu$_2$O$_2$, a spin-chain compound known to exhibit a phase with helical
magnetic order at low temperatures. Phonon excitations were studied as a
function of temperature and light polarization, and the phonon frequencies are
compared to the results of ab-initio lattice dynamical calculations, which are
also reported here. The good agreement between the observed and calculated
modes allows an assignment of the phonon eigenvectors. Two distinct high-energy
two-magnon features as well as a sharp low-energy one-magnon peak were also
observed. These features are discussed in terms of the magnon modes expected in
a helically ordered state. Their polarization dependence provides evidence of
substantial exchange interactions between two closely spaced spin chains within
a unit cell. At high temperatures, the spectral features attributable to
magnetic excitations are replaced by a broad, quasielastic mode due to
overdamped spin excitations.
