  We introduce a new platform for realizing on-chip quantum electrodynamics
using photonic crystal waveguide structures comprised of periodic nanowire
arrays with embedded semiconductor quantum dots to act as quantum light
sources. These nanowire-based structures, which can now be fabricated with
excellent precision, are found to produce waveguide Purcell factors exceeding
100 and on-chip beta factors up to 99%. We investigate the fundamental optical
properties of photonic crystal waveguides and finite-size structures using both
photonic band structure calculations and rigorous Green function computations
which allows us to obtain the modal properties and the local density of photon
states. A comparison with slab-based photonic crystals is also made and we a
highlight key advantages in the nanowire system, including the potential to
minimize extrinsic scattering losses and produce high theoretical Purcell
factors and beta-factors on-chip. We also demonstrate that these structures
exhibit rich photonic Lamb shifts over broadband frequencies.
