  We consider a microcavity made by a graded-index (GRIN) glass, doped by dye
molecules, placed within two planar mirrors and study Bose-Einstein
condensation (BEC) of photons. The presence of the mirrors leads to an
effective photon mass, and the index grading provides an effective trapping
frequency; the photon gas becomes formally equivalent to a two dimensional Bose
gas trapped in an isotropic harmonic potential. The inclusion of nonlinear
effects provides an effective interaction between photons. We discuss, in
particular, thermal lensing effects and nonlocal nonlinearity, and
quantitatively compare our results with the reported experimental data.
