Radiation from a dipole embedded in a multilayer slab.

An analytical solution for the radiation emitted from a dipole embedded in an arbitrary, planar dielectric film stack is presented. The calculation uses a rigorous Hertz-vector formalism to treat the electromagnetic boundary conditions. The radiation fields are then evaluated in a far-field approximation to get the radiated fields far from the dipole. Both two-dimensional (2D) emission into bound modes of the dielectric stack and three-dimensional (3D) emission into radiation fields above and below the stack are evaluated. These solutions are explored for two simple cases: a InGaAs slab symmetrically clad with up to four high-contrast (Al 2 O 3 /GaAs) Bragg mirror pairs and semi-infinite air spaces, and a similar asymmetric structure with a GaAs substrate on one side. The symmetric structure supports both 2D bound and 3D radiation fields. The asymmetric structure only supports 3D radiation fields since there are no strictly bound modes, but "leaky" modes appear that are very similar to the bound modes in the symmetric structure except that the radiated power ultimately is transmitted into the substrate in a very highly directional beam. This calculation is applicable to a wide range of solid-state photonic devices, including vertical-cavity and edge-emitting lasers, spontaneous light-emitting diodes, and photodetectors.