We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap, with the aim to interpret recent experiments. We employ the finite element method to study crystals with the cubic diamond-like inverse woodpile structure. The high-index backbone has a dielectric function similar to silicon. We study crystals with a range of thicknesses up to ten unit cells (L ≤ 10c). The crystals are surrounded by vacuum, and have a finite support as in experiments. The polarization-resolved reflectivity spectra reveal Fabry-Pérot fringes related to standing waves in the finite crystal, as well as broad stop bands with nearly 100 % reflectivity, even for thin crystals. From the strong reflectivity peaks, it is inferred that the maximum reflectivity observed in experiments is not limited by finite size. The frequency ranges of the stop bands are in excellent agreement with stop gaps in the photonic band structure, that pertain to infinite and perfect crystals. The frequency ranges of the observed stop bands hardly change with angle of incidence, which is plausible since the stop bands are part of the 3D band gap. Moreover, this result supports the previous assertion that intense reflection peaks measured with a large numerical aperture provide a faithful signature of the 3D photonic band gap. The Bragg attenuation lengths LB exceed the earlier estimates based on the width of the stop band by a factor 6 to 9. Hence crystals with a thickness of 12 unit cells studied in experiments are in the thick crystal limit (L >> LB). In our calculations for p-polarized waves, we also observe an intriguing hybridization of the zero reflection of Fabry-Pérot fringes and the Brewster angle, which has not yet been observed in experiments.

We study numerically the transport and storage of light in a three-dimensional (3D) photonic band gap crystal doped by a single embedded resonant cavity. The crystal has finite support since it is surrounded by vacuum, as in experiments. Therefore, we employ the finite element method to model the diamond-like inverse woodpile crystal that consists of two orthogonal arrays of pores in a high-index dielectric such as silicon and that has experimentally been realized by CMOS-compatible methods. A point defect that functions as the resonant cavity is formed in the proximal region of two selected orthogonal pores with a radius smaller than the ones in the bulk of the crystal. We present a field-field cross-correlation method to identify resonances in the finite-support crystal with defect states that appear in the 3D photonic band gap of the infinite crystal. Out of five observed angle-independent cavity resonances, one is s-polarized and four 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 thin structures (only three unit cells), which is attributed to the relatively small Bragg length of the perfect crystal. We find that the optical energy density is remarkably enhanced at the cavity resonances by up to 2400× the incident energy density in vacuum or up to 1200× the energy density of the equivalent effective medium. We find that an inverse woodpile photonic band gap cavity with a suitably adapted lattice parameter reveals substantial absorption in the visible range. Below the 3D photonic band gap, Fano resonances arise due to interference between the discrete fundamental cavity mode and the continuum light scattered by the photonic crystal. We argue that the five eigenstates of our 3D photonic band gap cavity have quadrupolar symmetry, in analogy to d-like orbitals of transition metals. We conclude that inverse woodpile cavities offer interesting perspectives for applications in optical sensing and photovoltaics. arXiv:1808.05607v1 [physics.optics]

To investigate the performance of three-dimensional (3D) nanostructures, it is vital to study their internal structure with a methodology that keeps the device fully functional and ready for further integration. To this aim, we introduce here traceless X-ray tomography (TXT) that combines synchrotron X-ray holographic tomography with high X-ray photon energies (17 keV) in order to study nanostructures “as is” on massive silicon substrates. The combined strengths of TXT are a large total sample size to field-of-view ratio and a large penetration depth. We study exemplary 3D photonic band gap crystals made by CMOS-compatible means and obtain real space 3D density distributions with 55 nm spatial resolution. TXT identifies why nanostructures that look similar in electron microscopy have vastly different nanophotonic functionality: one “good” crystal with a broad photonic gap reveals 3D periodicity as designed; a second “bad” structure without a gap reveals a buried void, and a third “ugly” one without gap is shallow due to fabrication errors. Thus, TXT serves to nondestructively differentiate between the possible reasons of not finding the designed and expected performance and is therefore a powerful tool to critically assess 3D functional nanostructures.

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Devashish3D periodic photonic nanostructures with disrupted symmetries 3D periodieke fotonische nanostructuren met verstoorde symmetrieën Cover Schematic illustration of the 2 × 2 × 2 supercell of a 3D inverse woodpile photonic crystal, which is a 3D periodic photonic nanostructure with disrupted symmetry. The cover is designed by Devashish.