  We develop a general dynamical theory for studying a single photon transport
in a one-dimensional (1D) waveguide coupled to multiple emitters which can be
either identical or non-identical. In this theory, both the effects of the
waveguide and non-waveguide vacuum modes are included. This theory enables us
to investigate the propagation of an emitter excitation or an arbitrary single
photon pulse along an array of emitters coupled to a 1D waveguide. The
dipole-dipole interaction induced by the non-waveguide modes, which is usually
neglected in the literatures, can significantly modify the dynamics of the
emitter system as well as the characteristics of output field if the emitter
separation is much smaller than the resonance wavelength. Non-identical
emitters can also strongly couple to each other if their energy difference is
smaller than or of the order of the dipole-dipole energy shift. Interestingly,
if their energy difference is close but non-zero, a very narrow transparency
window around the resonance frequency can appear which does not occur for
identical emitters. This phenomenon may find important applications in quantum
waveguide devices such as optical switch and ultra narrow single photon
frequency comb generator.
