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

Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5 K into nonguided and guided modes is determined by direct spectral 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 40 meV in the fast light regime, reaching a maximum of (99 +/- 1)%. We measure the directional emission of the circularly polarized transitions in a magnetic field into counterpropagating 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.