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

Dynamical theory of single photon transport in a one-dimensional waveguide coupled to identical and non-identical emitters