  The linear combination of bulk bands method recently introduced by Wang,
Franceschetti and Zunger [Phys. Rev. Lett.78, 2819 (1997)] is applied to a
calculation of energy bands and optical constants of (GaAs)$_n$/(AlAs)$_n$ and
(GaAs)$_n$/(vacuum)$_n$ (001) superlattices with n ranging from 4 to 20.
Empirical pseudopotentials are used for the calculation of the bulk energy
bands. Quantum-confined induced shifts of critical point energies are
calculated and are found to be larger for the GaAs/vacuum system. The $E_1$
peak in the absorption spectra has a blue shift and splits into two peaks for
decreasing superlattice period; the $E_2$ transition instead is found to be
split for large-period GaAs/AlAs superlattices. The band contribution to linear
birefringence of GaAs/AlAs superlattices is calculated and compared with recent
experimental results of Sirenko et al. [Phys. Rev. B 60, 8253 (1999)]. The
frequency-dependent part reproduces the observed increase with decreasing
superlattice period, while the calculated zero-frequency birefringence does not
account for the experimental results and points to the importance of
local-field effects.
