  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.
