Dipole radiation in a one-dimensional photonic crystal: TE polarization

We study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac delta functions (Dirac comb SL). The radiation is permitted to propagate in all directions in space; however, it is restricted to the transverse electric (TE) polarization mode. The calculation is based on a classical theory of radiation in nonuniform dielectric media by Dowling and Bowden [Phys. Rev. A 46, 612 (1992)]. The emitted power is derived in terms of a single integral, with no approximations. A SL has no omnidirectional photonic band gaps, and therefore the power is always finite. The power spectrum exhibits slope discontinuities, which occur at the band edges for on-axis propagation. It also depends strongly on the dipole's position in the SL and on the grating strength that characterizes the Dirac comb model. The power peaks for low frequencies, and there can be large enhancement of emission as compared to free space. The closer the dipole is to a barrier (Dirac delta) and the greater the grating strength, the stronger the enhancement is. These conclusions are expected to be relevant for a real SL.