  We report on the development of a high-resolution and highly efficient
beamline for soft-X-ray resonant inelastic X-ray scattering (RIXS) located at
Taiwan Photon Source. This beamline adopts an optical design that uses an
active grating monochromator (AGM) and an active grating spectrometer (AGS) to
implement the energy compensation principle of grating dispersion. Active
gratings are utilized to diminish defocus, coma and higher-order aberrations as
well as to decrease the slope errors caused by thermal deformation and optical
polishing. The AGS is mounted on a rotatable granite platform to enable
momentum-resolved RIXS measurements with scattering angle over a wide range.
Several high-precision instruments developed in house for this beamline are
briefly described. The best energy resolution obtained from this AGM-AGS
beamline was 12.4 meV at 530 eV, achieving a resolving power 42,000, while the
bandwidth of the incident soft X-rays was kept at 0.5 eV. To demonstrate the
scientific impacts of high-resolution RIXS, we present an example of
momentum-resolved RIXS measurements on a high-temperature superconducting
cuprate, La$_{2-x}$Sr$_x$CuO$_4$. The measurements reveal the A$_{1g}$ apical
oxygen phonons in superconducting cuprates, opening a new opportunity to
investigate the coupling between these phonons and charge density waves.
