Spontaneous emission rates of a single-impurity molecule in birefringent host crystals for electric quadrupole transitions

In a birefringent host crystal, the spontaneous emission rate of zero-phonon line of a single-impurity molecule depends on the angles between the transition dipole moment and the principal axes of the dielectric (permittivity) tensor and also on the main dielectric constants of a host crystal. In this paper, the spontaneous emission rate of the electric quadrupole transition of a single-impurity molecule is calculated for uniaxial host crystals with the ordinary reflective indices n_o=1.5, 2, 3 and a variable extraordinary reflective index, and for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl). For the above-mentioned biaxial crystals, differences in the values of spontaneous emission rate of the quadrupole transition in the same host crystal are up to 11%.