Radiation from a dipole embedded in a dielectric slab

A unified analytical treatment of the radiation from an electric dipole of arbitrary orientation embedded at an arbitrary location within a symmetrically clad dielectric slab is presented. Both the emission into three dimensional (3-D) radiation modes, corresponding to emission within the critical angle escape cone within the dielectric slab, and into the two-dimensional (2-D) waveguide modes are evaluated from a single calculation. The model is valid for arbitrary dielectric contrast between the slab and the cladding. The mathematical approach uses well-known complex analysis techniques: the 3-D radiation is described by a steepest descents integration around branch cuts while the 2-D waveguide modes correspond to simple poles. The division of the radiated power between the 3-D and 2-D modes is evaluated across the entire range from small dielectric contrast appropriate to diode lasers (less than or similar to1.1) to the very large dielectric contrast of free-standing semiconductor slabs (similar to 12-19). Both enhancement and suppression, depending on position, slab width, dielectric contrast, and wavelength, of the total radiated power in comparison with that in an unbounded dielectric medium are found for slab widths on the order of a wavelength with a maximum enhancement of similar to 30% for these one-dimensional Fabry-Perot structures. For thicker slabs, the total radiation is almost constant and equal to that in the unbounded medium for low dielectric contrast while still exhibiting some modulation as increasing thickness allows additional waveguide modes.