We theoretically present a flexible method to obtain dual-channel optical bistability (OB) in a coupled system consisting of a metallic nanoshell (MNS) and a carbon nanotube (CNT) nanomechanical resonator (NR) beyond the dipole approximation. The MNS is made of a metallic core and a dielectric shell. The results show that, the four-wave mixing signal is suppressed significantly due to multipole polarizations in comparison to that in the dipole approximation. Also, the four-wave mixing signal can be enhanced greatly with the exciton-phonon coupling strength g increasing. Especially, bistability...
