Vertical beaming of wavelength-scale photonic crystal resonators

We report that $> 80%$ of the photons generated inside a photonic crystal slab resonator can be funneled within a small divergence angle of $\pm 30^\circ$. The far-field radiation properties of a photonic crystal slab resonant mode are modified by tuning the cavity geometry and by placing a reflector below the cavity. The former method directly shapes the near-field distribution so as to achieve directional and linearly-polarized far-field patterns. The latter modification takes advantage of the interference effect between the original waves and the reflected waves to enhance the energy-directionality. We find that, regardless of the slab thickness, the optimum distance between the slab and the reflector closely equals one wavelength of the resonance under consideration. We have also discussed an efficient far-field simulation algorithm based on the finite-difference time-domain method and the near- to far-field transformation.Comment: 14 pages, 15 figures, submitted to Phys. Rev.