  Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots
embedded in photonic crystal waveguides at 5K into non-guided and guided modes
is determined by direct hyperspectral imaging. This enables measurement of the
absolute coupling efficiency into the guided modes, the beta-factor, directly,
without assumptions on decay rates used previously. Notably, we found
beta-factors above 90% over a wide spectral range of 40meV in the fast light
regime, reaching a maximum of (99 $\pm$ 1)%. We measure the directional
emission of the circularly polarized transitions in a magnetic field into
counter-propagating guided modes, to deduce the mode circularity at the quantum
dot sites. We find that points of high directionality, up to 97%, correlate
with a reduced beta-factor, consistent with their positions away from the mode
field antinode. By comparison with calibrated finite-difference time-domain
simulations, we use the emission energy, mode circularity and beta-factor to
estimate the quantum dot position inside the photonic crystal waveguide unit
cell.
