Approximate analytic expressions for calculation of spontaneous emission spectra for a quantum well embedded in a planar microcavity

The control of spontaneous emission is one of important characteristics of a planar microcavity. The integrals in the spherical coordinate for TE and TM modes spontaneous emission spectra of a quantum well (QW) embedded in a planar microcavity are derived with new variables dependent on wavelength and Taylor series including the two polarizations of the vacuum field. The approximate expressions of spontaneous emission in QW planar microcavities are obtained. The approximate results show that spontaneous emission spectra agree well with that in the numerical integral for planar semiconductor microcavities, in which Fermi-Dirac distribution functions of electrons and holes are considered. The main contribution to the spontaneous emission, radiated into all direction, has been found.