Decay rate and level shift in a circular dielectric waveguide

Using a Green tensor formalism, we perform a comprehensive investigation into the spontaneous emission decay rate and energy-level shift in a circular dielectric waveguide. The two-dimensional (2D) Green tensor for an embedded line source and 3D Green tensor for a point source are obtained by a combination of Fourier integral and multipole methods. We fully characterize resonant states, which include whispering gallery modes, and examine the associated cavitylike effects. The quality factor of resonant states increases with frequency, resulting in a strongly enhanced decay rate and a large anomalous level shift in both the 2D and 3D cases.