[en] In DIII-D and other machines, a low edge density often exists at the scrape-off layer during H-mode discharges. Sometimes these densities can be low enough that a lower hybrid resonance layer can be present at the edge. The coupling of the antenna to the slow and fast branches in such a plasma is different from that in a plasma with a higher density pedestal. In this paper, ICRF coupling at low edge densities is studied using a cold plasma model. The singularity near the lower hybrid resonance is analyzed. A numerical code is developed, and coupling to the fast and slow branches is studied for different antenna configurations. The results are discussed and compared with experimental results from DIII-D. The possible effects of septum partitions on the launched spectrum are discussed. 2 refs