Quantum mechanical treatment of light inside dielectric media is important to understand the behavior of an optical system. In this paper, a two-level atom embedded in a rectangular waveguide surrounded by a perfect electric conductor is considered.
Spontaneous emission, propagation, and detection of a photon are described by the second quantization formalism. The quantized modes for light are divided into two types: photonic propagating modes and localized modes with exponential decay along the direction of waveguide. Though spontaneous emission depends on all possible modes including the localized modes, detection far from the source only depends on the propagating modes. This discrepancy of dynamical behaviors gives two different decay rates along space and time in the correlation function of the photon detection.
