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The single-photon scattering in a rectangular waveguide by a V-typethree-level emitter is studied for large range of input-photon energy beyondthe single-mode region. By using Lippmann-Schwinger formalism, the necessaryand sufficient conditions of complete transmission and complete reflection arederived analytically. In the single-mode region, the complete transmissioncaused by electromagnetically induced transparency (EIT) and the completereflection due to Fano resonance can both be achieved by adjusting theemitter's parameters. But in the multi-mode region, except that the input-stateis prepared in a coherent superposition state, the perfect reflection isabsent, and the photon inevitably enters other propagation modes due to theindirectly interaction between waveguide modes mediated by the emitter. Otherremarkable features in the photon transport induced by the finite cross sectionincludes the blueshift of the reflection resonance and the cutoff-frequencyeffect.

Controlling single-photon scattering in a rectangular waveguide by a V-type three-level emitter