  In this paper, we develop a quantum transport theory to describe photonic
transport in photonic networks. The photonic networks concerned in the paper
consist of all-optical circuits incorporating photonic bandgap waveguides and
driven resonators. The photonic transport flowing through waveguides are
entirely determined from the exact master equation of the driven resonators.
The master equation of the driven resonators is obtained by explicitly
eliminating all the waveguide degrees of freedom while the back-reactions
between resonators and waveguides are fully taken into account. The relations
between the driven photonic dynamics and photocurrents are obtained. The
non-Markovian memory structure and quantum coherence and decoherence effects in
photonic transport are also fully included. This quantum transport theory
unifies two fundamental nonequilibrium approaches, the Keldysh's nonequilibrium
Green function technique and the Feynman-Vernon influence functional approach,
together to make the investigation of the transient quantum photonic transport
become more powerful. As an illustration, the theory is applied to the
transport phenomena of a driven nanocavity coupled to two waveguides in
photonic crystals. The controllability of photonic transport through the driven
resonator is demonstrated.
