Spontaneous emission of photons by an atom placed near a dielectric cylindr
ical waveguide at an arbitrary position is analyzed using global free elect
romagnetic modes, satisfying necessary continuity conditions at the slab bo
undaries. These modes include the modes extended over the whole space (trav
elling) and the modes trapped to a waveguide (waveguided). To describe angu
lar properties of the spontaneous emission, a parametrization of the travel
ling modes by the outgoing waves has been proposed. Angular characteristics
of the travelling photon emission, distributions of the trapped photon emi
ssion, as well as the global decay rates have been calculated using the qua
ntum approach and the standard perturbation theory. Difficulties due to the
presence of sharp resonances (whispering gallery modes) among the travelli
ng photons are pointed out.