Recently, it was suggested that the polarization dependence of light absorption to a single-walled carbon nanotube is altered by carrier doping. We specify theoretically the doping level at which the polarization anisotropy is reversed by plasmon excitation. The plasmon energy is mainly determined by the diameter of a nanotube, because pseudospin makes the energy independent of the details of the band structure. We find that the effect of doping on the Coulomb interaction appears through the screened exchange energy, which can be observed as changes in the absorption peak positions. Our results strongly suggest the possibility that oriented nanotubes function as a polarization switch.
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