Controlling single-photon transport in waveguides with finite cross-section

TL;DR

This paper investigates how the finite transverse size of a rectangular waveguide influences single-photon scattering, revealing mode involvement, photon loss, and multiple resonance phenomena that lead to complete photon reflection.

Contribution

It introduces a detailed analysis of transverse size effects on single-photon transport, including mode coupling and resonance phenomena, expanding understanding of waveguide quantum optics.

Findings

Transverse size larger than critical involves higher transverse modes.

Photon loss occurs into other channels when energy exceeds bound-state energy.

Resonances cause complete photon reflection at specific conditions.

Abstract

We study the transverse-size effect of a quasi-one-dimensional rectangular waveguide on the single-photon scattering on a two-level system. We calculate the transmission and reflection coefficients for single incident photons using the scattering formalism based on the Lippmann-Schwinger equation. When the transverse size of the waveguide is larger than a critical size, we find that the transverse mode will be involved in the single-photon scattering. Including the coupling to a higher traverse mode, we find that the photon in the lowest channel will be lost into the other channel, corresponding to the other transverse modes, when the input energy is larger than the maximum bound-state energy. Three kinds of resonance phenomena are predicted: single-photon resonance, photonic Feshbach resonance, and cutoff (minimum) frequency resonance. At these resonances, the input photon is completely reflected.