We describe a simple process for the fabrication of ultrathin, transparent, optically homogeneous, electrically conducting films of pure single-walled carbon nanotubes and the transfer of those films to various substrates. For equivalent sheet resistance, the films exhibit optical transmittance comparable to that of commercial indium tin oxide in the visible spectrum, but far superior transmittance in the technologically relevant 2- to 5-micrometer infrared spectral band. These characteristics indicate broad applicability of the films for electrical coupling in photonic devices. In an example application, the films are used to construct an electric field-activated optical modulator, which constitutes an optical analog to the nanotube-based field effect transistor.