Analytic Study of Optical, Electro-optical and Magnetooptical Properties of Cabon Nanotubes

Multi-wall and single-wall carbon nanotubes (SWCNs) have attracted considerable amount
of attention in nanoscience due to their unique physical properties and great potential for
nanotechnology applications. The SWCNs are more fundamental and had been the basis
for a large body of theoretical studies and predictions that preceded the experimental
observation of SWCNs. In this thesis, we have used a tight binding model with nearest
neighbor interactions to investigate the electric dipole matrix elements and subsequently the
linear susceptibility as a function of optical frequency for SWCNs. We have derived an
analytic expression for the linear optical susceptibility of single wall zigzag CNs for light
polarized parallel to the nanotube axis. For light polarized perpendicular to the nanotube
axis, a closed-form expression for the electric dipole matrix element has been obtained.
Hence, numerical evaluation of the perpendicular susceptibility has been greatly simplified.
By simplifying the long-axis linear susceptibility, analytic expression for the quadratic
electro-optic effect in semiconducting zigzag CNs including the transitions between all pairs
of valence and conduction bands has been obtained. We further have derived closed-form
expressions for the dipole matrix elements for both parallel and perpendicular polarizations
and hence general expressions for diagonal and off-diagonal elements of the optical
susceptibility for zigzag CNs in the presence of an axial static magnetic field. The offdiagonal
elements have been applied to calculate the interband Faraday rotation and the
Verdet constant. Finally, we have derived a universal analytic expression for the long-axis
linear susceptibility of SWCNs near the Fermi level, valid for arbitrary diameter and chirality
and hence an analytic expression for the quadratic electro-optic effect has been derived for
arbitrary semiconducting SWCNs.