The nature of downward wave coupling between the stratosphere and troposphere in both hemispheres is analyzed using the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) dataset. Downward wave coupling occurs when planetary waves reflected in the stratosphere impact the troposphere, and it is distinct from zonal-mean coupling, which results from wave dissipation and its subsequent impact on the zonal-mean flow. Cross-spectral correlation analysis and wave geometry diagnostics reveal that downward wave-1 coupling occurs in the presence of both a vertical reflecting surface in the mid-to-upper stratosphere and a high-latitude meridional waveguide in the lower stratosphere. In the Southern Hemisphere, downward wave coupling occurs from September to December, whereas in the Northern Hemisphere it occurs from January to March. A vertical reflecting surface is also present in the stratosphere during early winter in both hemispheres; however, it forms at the poleward edge of the meridional waveguide, which is not confined to high latitudes. The absence of a high-latitude waveguide allows meridional wave propagation into the subtropics and decreases the likelihood of downward wave coupling. The results highlight the importance of distinguishing between wave reflection in general, which requires a vertical reflecting surface, and downward wave coupling between the stratosphere and troposphere, which requires both a vertical reflecting surface and a high-latitude meridional waveguide. The relative roles of downward wave and zonal-mean coupling in the Southern and Northern Hemispheres are subsequently compared. In the Southern Hemisphere, downward wave-1 coupling dominates, whereas in the Northern Hemisphere downward wave-1 coupling and zonal-mean coupling are found to be equally important from winter to early spring. The results suggest that an accurate representation of the seasonal cycle of the wave geometry is necessary for the proper representation of downward wave coupling between the stratosphere and troposphere.