  We introduce a photonic crystal waveguide-cavity system for controlling
single photon cavity-QED processes. Exploiting Bloch mode analysis, and
medium-dependent Green function techniques, we demonstrate that the propagation
of single photons can be accurately described analytically, for integrated
periodic waveguides with little more than four unit cells, including an output
coupler. We verify our analytical approach by comparing to rigorous numerical
calculations for a range of photonic crystal waveguide lengths. This allows one
to nano-engineer various regimes of cavity-QED with unprecedented control. We
demonstrate Purcell factors of greater than 1000 and on-chip single photon beta
factors of about 80% efficiency. Both weak and strong coupling regimes are
investigated, and the important role of waveguide length on the output emission
spectra is shown, for vertically emitted emission and output waveguide
emission.
