We theoretically study the mechanism of excitation energy transfer (EET) between two ring-shaped aggregates of pigments. Dynamics of the pigment system and the light field are described by a Markovian quantum master equation and the Maxwell's equations, respectively. Self-consistently solving these equations, we investigate the interplay between light and aggregates of pigments. From our calculation, it is revealed that the isotropic property gives two coupling constants, which prevents the deterioration of the EET rate between anisotropic dipoles. The distance dependence of the coupling strengths is also calculated for all excited states of the aggregate, which shows that each excited state has a different distance dependence of the coupling strength.