ABSTRACT
The selection rules of the optical transition can be derived by taking into
account the conservation of the orbital angular momentum and the decom-
position of the linear polarization into the circular polarization:
xˆ cosωt = 1
2 (xˆ+ iyˆ) cosωt+
2 (xˆ− iyˆ) cosωt , (8.5)
yˆ cosωt = 1
2i (xˆ+ iyˆ) cosωt− 1
2i (xˆ− iyˆ) cosωt , (8.6)
where xˆ(yˆ) denotes the unit vector in the x(y)-direction. Assuming |`h1〉 to be the ground hole state (namely, g`h > 0), we have the optical selection
rules:
|`h〉1 −→ 1√ 2 (|c ↑〉 − |c ↓〉) = − |e1〉 (8.7)
for the x−polarized light and
|`h〉1 −→ −i√ 2 (|c ↑〉+ |c ↓〉) = −i |e2〉 (8.8)
for the y−polarized light, respectively, where |e1〉(|e2〉) is the conduction band electron state with the spin in the −x(x) direction. The schematic energy levels are plotted in Fig. 8.1.
