  We calculate the electronic and optical properties of
InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattices within relativistic density
functional theory. To have a good description of the electronic and optical
properties, the modified Becke-Johnson exchange-correlation functional is
pondered to correctly approximate the band gap. First, we analyze electronic
and optical characteristics of bulk InAs and InSb, and then we investigate the
InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattice. The optical gaps deduced from the
imaginary part of the dielectric function are associated with the
characteristic interband transitions. We investigate the electronic and optical
properties of the InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattice with three
lattice constants of the bulk InAs, GaSb and AlSb, respectively. It is observed
that the electronic and optical properties strongly depend on the lattice
constant. Our results support the presence of two heavy-hole bands with
increasing in-plane effective mass as we go far from the Fermi level. We notice
a considerable decrease in the energy gaps and the effective masses of the
heavy-holes in the k$_x$-k$_y$ plane compared to the bulk phases of the parent
compounds. We demonstrate that the electrons are s-orbitals delocalized in the
entire superlattice, while the holes have mainly 5p-Sb character localized in
the In(As,Sb) side of the superlattice. In the superlattice, the low-frequency
absorption spectra greatly increase when the electric field is polarized
orthogonal to the growth axis allowing the applicability of III-V compounds for
the long-wavelength infrared detectors.
