Inter-band transition probabilities and photon momentum

The theory of inter-band transitions is re-examined in the case of finite photon momentumq. New expressions for the joint density of states near critical points are derived. They give Van Hove’s expressions in both the limits of long and short wavelengths. The dispersion relation for the transverse dielectric functionɛ 2T due to inter-band processes is given explicitly and it is compared to that of the longitudinal dielectric functionɛ 2L . It is shown that in the limitq = 0ɛ 2T equalsɛ 2L even for anisotropic media. The possibility of an experimental evidence of the effects caused by a finite photon momentum on the shape of the optical absorption is discussed.