  We present a theoretical analysis and optimisation of the properties and
performance of mid-infrared semiconductor lasers based on the dilute bismide
alloy In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$, grown on conventional (001) InP
substrates. The ability to independently vary the epitaxial strain and emission
wavelength in this quaternary alloy provides significant scope for band
structure engineering. Our calculations demonstrate that structures based on
compressively strained In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$ quantum wells (QWs)
can readily achieve emission wavelengths in the 3 -- 5 $\mu$m range, and that
these QWs have large type-I band offsets. As such, these structures have the
potential to overcome a number of limitations commonly associated with this
application-rich but technologically challenging wavelength range. By
considering structures having (i) fixed QW thickness and variable strain, and
(ii) fixed strain and variable QW thickness, we quantify key trends in the
properties and performance as functions of the alloy composition, structural
properties, and emission wavelength, and on this basis identify routes towards
the realisation of optimised devices for practical applications. Our analysis
suggests that simple laser structures -- incorporating
In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$ QWs and unstrained ternary
In$_{0.53}$Ga$_{0.47}$As barriers -- which are compatible with established
epitaxial growth, provide a route to realising InP-based mid-infrared diode
lasers.
