Purcell effect in two-dimensional photonic crystal slabs with triangular lattice

We present the results of theoretical studies of the Purcell effect in infinite photonic crystal slabs without defects or cavities. First, we describe a theoretical model for calculating total and external Purcell factors in two-dimensional photonic crystal slabs in terms of dipole's emissivity to the near field and the far field. Then we apply this theory to silicon photonic crystal slabs with triangular lattice on silica substrate and study how the Purcell factor depends on the wavelength and the dipole's position. We show that by placing the dipoles in the hot spots of modes with the zero group velocity, one can greatly enhance the Purcell factor in comparison to a homogeneous silicon slab. We demonstrate that this effect is associated with Van Hove singularities. We also calculate partial contributions to the total Purcell factor from different energy dissipation channels.