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

## TL;DR

This paper analyzes how a V-type three-level emitter controls single-photon scattering in a rectangular waveguide, revealing conditions for perfect transmission or reflection across multiple modes and identifying unique transport features.

## Contribution

It provides analytical conditions for complete transmission and reflection in multi-mode waveguides, extending understanding beyond the single-mode regime with new insights into photon transport features.

## Key findings

- Complete transmission via EIT in single-mode region
- Complete reflection via Fano resonance in single-mode region
- Absence of perfect reflection in multi-mode region unless in a superposition state

## Abstract

The single-photon scattering in a rectangular waveguide by a V-type three-level emitter is studied for large range of input-photon energy beyond the single-mode region. By using Lippmann-Schwinger formalism, the necessary and sufficient conditions of complete transmission and complete reflection are derived analytically. In the single-mode region, the complete transmission caused by electromagnetically induced transparency (EIT) and the complete reflection due to Fano resonance can both be achieved by adjusting the emitter's parameters. But in the multi-mode region, except that the input-state is prepared in a coherent superposition state, the perfect reflection is absent, and the photon inevitably enters other propagation modes due to the indirectly interaction between waveguide modes mediated by the emitter. Other remarkable features in the photon transport induced by the finite cross section includes the blueshift of the reflection resonance and the cutoff-frequency effect.