Atomic radiation rates in photonic crystals

Abstract

A photonic crystal, defined as a periodic dielectric structure, can influence the radiation rate of an embedded dipolar emitter. A theory of this effect is developed and the efficiency of a dipolar photonic source is calculated for a realistic three-dimensional crystal. Taking as a starting point the photonic band structure and its associated eigenfields, it is shown that the emission rate is strongly correlated with the density of modes, but also that the density of modes alone cannot explain all features found in the emission spectrum. For an infinite crystal, the computation of the field propagator confirms that the emission rate falls to zero in the frequency range defined by the photonic band gap. The emitter lifetime changes with the dipole location and orientation, leading to a radiation rate enhancement or inhibition according to the direction of the emission. These results may open routes to photonic sources with very high quantum efficiency. One of the early motivations for the study of photonic crystals ~PC’s ! has been their potential for the control of electromagnetic radiation from quantized sources. The pioneering work of Yablonovitch 1 suggested that optical bandgap materials could inhibit spontaneous emission. Thus, for instance, a spatial modulation of the refractive index in semiconductors could prevent the direct-gap electron-hole radiative recombination if the radiation frequency happened to lie in the range of the photonic gap. The control of the random spontaneous emission could also have important consequences on the reduction of noise in optoelectronic devices. Beyond the simple control of spontaneous emission, photonic crystals could provide paths to photon sources engineering. Being able to modify radiation rates in specific directions could have far-reaching consequences on the physics of light sources. It is currently thought, for instance, that obliterating the junction emission of a light-emitting diode in directions where total reflection on the packaging case would preclude photon escape, while enhancing the emission rate in more favorable directions, could lead to a dramatic improvement of the overall quantum efficiency of the device. Near-perfect light-generating systems which could follow may have as large an impact as Edison’s invention of incandescence light. Surprisingly, few experiments have been performed on molecular lifetime changes in PC. 2‐5 Preparation difficulties of a well-defined system, particularly the embedding of dye molecules inside the PC, conduct to different interpretations, subject to controversy. 6,7 However, these experiments have first been concerned with dye molecules embedded in Bravais fcc structures of dielectric spheres. It appears that the modification of the spontaneous emission is found to be weak due to the absence of a complete band gap with such structures. Recently, an inverse opal, that is an actual photonic band-gap material, has been used. It unambiguously shows the important expected changes. 5