99% beta factor and directional coupling of quantum dots to fast light in photonic crystal waveguides determined by hyperspectral imaging.

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.