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We study numerically the transport and storage of light in a 3D photonic bandgap crystal doped by a single embedded resonant cavity. The crystal has finitesupport since it is surrounded by vacuum, as in experiments. Therefore, weemploy the finite element method to model the diamond-like inverse woodpilecrystal that consists of two orthogonal arrays of pores in a high-indexdielectric such as silicon and that has experimentally been realized byCMOS-compatible methods. A point defect that functions as the resonant cavityis formed in the proximal region of two selected orthogonal pores with a radiussmaller than the ones in the bulk of the crystal. We present a field-fieldcross-correlation method to identify resonances in the finite-support crystalwith defect states that appear in the 3D photonic band gap of the infinitecrystal. Out of 5 observed angle-independent cavity resonances, one iss-polarized and 4 are p-polarized for light incident in the X or Z directions.It is remarkable that quality factors up to Q = 1000 appear in such thinstructures (3 unit cells). We find that the optical energy density isremarkably enhanced at the cavity resonances by up to 2400x the incident energydensity in vacuum or up to 1200x the energy density of the equivalent effectivemedium. We find that an inverse woodpile photonic band gap cavity with asuitably adapted lattice parameter reveals substantial absorption in thevisible range. Below the 3D photonic band gap, Fano resonances arise due tointerference between the discrete fundamental cavity mode and the continuumlight scattered by the photonic crystal. We argue that the five eigenstates ofour 3D photonic band gap cavity have quadrupolar symmetry, in analogy to d-likeorbitals of transition metals. We conclude that inverse woodpile cavities offerinteresting perspectives for applications in optical sensing and photovoltaics.

Three-dimensional photonic band gap cavity with finite support: enhanced energy density and optical absorption