  Incorporation of bismuth (Bi) in dilute quantities in (In)GaAs has been shown
to lead to unique electronic properties that can in principle be exploited for
the design of high efficiency telecomm lasers. This motivates the development
of simple models of the electronic structure of these dilute bismide alloys,
which can be used to evaluate their potential as a candidate material system
for optical applications. Here, we begin by using detailed calculations based
on an $sp^{3}s^{*}$ tight-binding model of (In)GaBi$_{x}$As$_{1-x}$ to verify
the presence of a valence band-anticrossing interaction in these alloys. Based
on the tight-binding model the derivation of a 12-band
$\textbf{k}\cdot\textbf{p}$ Hamiltonian for dilute bismide alloys is outlined.
We show that the band structure obtained from the 12-band model is in excellent
agreement with full tight-binding supercell calculations. Finally, we apply the
12-band model to In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$ and compare the
calculated variation of the band gap and spin-orbit-splitting to a variety of
spectroscopic measurements performed on a series of MBE-grown
In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$/InP layers.
