  A quantum dot spin LED provides a test of carrier spin injection into a
qubit, as well as a means of analyzing carrier spin injection in general and
local spin polarization. The polarization of the observed light is, however,
significantly influenced by the dot geometry so the spin may be more polarized
than the emitted light would naively suggest. We have calculated carrier
polarization-dependent optical matrix elements using 8-band strain-dependent
k.p theory for InAs/GaAs self-assembled quantum dots (SAQDs) for electron and
hole spin injection into a range of quantum dot sizes and shapes, and for
arbitrary emission directions. The observed circular polarization does not
depend on whether the injected spin-polarized carriers are electrons or holes,
but is strongly influenced by the SAQD geometry and emission direction.
Calculations for typical SAQD geometries with emission along [110] show light
that is only ~5% circularly polarized for spin states that are 100% polarized
along [110]. Therefore observed polarizations [Chye et al. PRB 66, 201301(R)]
of ~1% imply a spin polarization within the dot of ~20%. We also find that
measuring along the growth direction gives near unity conversion of spin to
photon polarization, and is the least sensitive to uncertainties in SAQD
geometry.
