We present experimental and theoretical results on the absorption and dispersion of a single-walled carbon nanotube (SWNT) with and without fluorine (F) doping in the frequency range of 0.2-3 THz. Under the doping conditions, the power absorption, index of refraction, and the real and imaginary parts of the conductivity are decreased compared to those for pure SWNTs because the charge transfer to the F-2 molecule will be increased. Our measurement of pure SWNT agrees well with the Maxwell-Garnett and Drude models. However, the F-doped SWNT requires adding a Lorentz oscillator term for good agreement between theory and measurement. (c) 2005 American Institute of Physics.