The author shall study the excitation of Surface Plasmon and Phonon on cylindrical polar semiconducting material. The possibility of their interaction has been discussed with the help of dispersion relation for the dual mode of CNT by using inherent properties of the dielectric interface in dual mode. The phonon dispersion relation of the CNT is calculated by large supercells containing an isolated nanotube, Density functional Theory, and plane wave basis sets. Achieving multimode or dual-mode coupling in nanoscale material is challenging due to the large damping rate. Here, we study an effective way to achieve multi-mode plasmonic in a hybrid system that has greater modulation and greater energy dissipation. The strong coupling between modes has not been reported yet at short wavelengths and high-frequency ranges. We used a K-basis point set to describe the Fermi energy and electronic states we found that on reducing the K-points the particular mode coupling is strong at the Fermi energy level. The main work of this research is that allow the tuning of Surface Plasmon and surface Phonon Polaritons interaction with CNT in the high frequencies infrared regime. It indicates a strong coupling of phono vibrations and free charge carriers at the surface. The charge carrier distribution may not be affected by IR radiation and it is not uniform near the interface Moreover, the phonon may decay which is slower than incoming radiation. We found some resonant frequencies the possibility of surface waves at infrared frequencies increased the propagation length of the surface waves. This research helps make waveguide designs and optic-based inherent properties of semiconducting nanomaterial.
