ABSTRACT
H (1.42) According to the wave functions defined in the Section 1.3.1, the momentum matrix elements for the case of parallel polarization are , , 1,2,3, , | | , , Re( )iq zi iJ iz J J q q iiq J C p q J v e ed dfd d a - -¢¢ =¢ ¢ = Â (1.43)where dzi and dfi denote the axial and azimuthal coordinate differences between the positions of nearest-neighbor atoms. ai is a coefficient related to spatial dependence of the atomic orbitals. In order to obtain Equation (1.43), we only consider the momentum matrix elements between the nearest-neighbor atoms. Equation 1.43 suggests the momentum (q = q¢) and energy (J = J¢) are conserved in the parallel polarization optical transition. Figure 1.12a shows the first two allowed band-to-band transitions for parallel polarization, i.e., E11 and E22 transitions. The calculation of the matrix elements in the case of perpendicular polarization is particularly simple. Under the effect of the angular momentum operator, the quantum number J is changed by one unit:, , 1, , | | , , , , | , 1, q q J Jq J c p q J v q J c q J vf d d ¢±¢¢ ¢ µ ¢ ¢ ± = (1.44)
