Cavity quantum electrodynamics with three-dimensional photonic bandgap crystals

This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate all known photonic crystal structures with a demonstrated 3D band gap.Comment: 21 pages, 6 figures, 2 tables, Chapter 8 in "Light Localisation and Lasing: Random and Pseudorandom Photonic Structures", Eds. M. Ghulinyan and L. Pavesi (Cambridge University Press, Cambridge, 2015, ISBN 978-1-107-03877-6

Design of a 3D photonic band gap cavity in a diamond-like inverse woodpile photonic crystal

We theoretically investigate the design of cavities in a three-dimensional (3D) inverse woodpile photonic crystal. This class of cubic diamond-like crystals has a very broad photonic band gap and consists of two perpendicular arrays of pores with a rectangular structure. The point defect that acts as a cavity is centred on the intersection of two intersecting perpendicular pores with a radius that differs from the ones in the bulk of the crystal. We have performed supercell bandstructure calculations with up to $5 \times 5 \times 5$ unit cells. We find that up to five isolated and dispersionless bands appear within the 3D photonic band gap. For each isolated band, the electric-field energy is localized in a volume centred on the point defect, hence the point defect acts as a 3D photonic band gap cavity. The mode volume of the cavities resonances is as small as 0.8 $\lambda^{3}$ (resonance wavelength cubed), indicating a strong confinement of the light. By varying the radius of the defect pores we found that only donor-like resonances appear for smaller defect radius, whereas no acceptor-like resonances appear for greater defect radius. From a 3D plot of the distribution of the electric-field energy density we conclude that peaks of energy found in sharp edges situated at the point defect, similar to how electrons collect at such features. This is different from what is observed for cavities in non-inverted woodpile structures. Since inverse woodpile crystals can be fabricated from silicon by CMOS-compatible means, we project that single cavities and even cavity arrays can be realized, for wavelength ranges compatible with telecommunication windows in the near infrared.Comment: 11 figure

Method to make a single-step etch mask for 3D monolithic nanostructures

Current nanostructure fabrication by etching is usually limited to planar structures as they are defined by a planar mask. The realisation of three-dimensional (3D) nanostructures by etching requires technologies beyond planar masks. We present a method to fabricate a 3D mask that allows to etch three-dimensional monolithic nanostructures by using only CMOS-compatible processes. The mask is written in a hard-mask layer that is deposited on two adjacent inclined surfaces of a Si wafer. By projecting in single step two different 2D patterns within one 3D mask on the two inclined surfaces, the mutual alignment between the patterns is ensured. Thereby after the mask pattern is defined, the etching of deep pores in two oblique directions yields a three-dimensional structure in Si. As a proof of concept we demonstrate 3D mask fabrication for three-dimensional diamond-like photonic band gap crystals in silicon. The fabricated crystals reveal a broad stop gap in optical reflectivity measurements. We propose how 3D nanostructures with five different Bravais lattices can be realised, namely cubic, tetragonal, orthorhombic, monoclinic, and hexagonal, and demonstrate a mask for a 3D hexagonal crystal. We also demonstrate the mask for a diamond-structure crystal with a 3D array of cavities. In general, the 2D patterns for the different surfaces can be completely independent and still be in perfect mutual alignment. Indeed, we observe an alignment accuracy of better than 3.0 nm between the 2D mask patterns on the inclined surfaces, which permits one to etch well-defined monolithic 3D nanostructures.Comment: 18 pages, 10 figure

Signature of a three-dimensional photonic band gap observed on silicon inverse woodpile photonic crystals

We have studied the reflectivity of CMOS-compatible three-dimensional silicon inverse woodpile photonic crystals at near-infrared frequencies. Polarization-resolved reflectivity spectra were obtained from two orthogonal crystal surfaces corresponding to 1.88 pi sr solid angle. The spectra reveal broad peaks with high reflectivity up to 67 % that are independent of the spatial position on the crystals. The spectrally overlapping reflectivity peaks for all directions and polarizations form the signature of a broad photonic band gap with a relative bandwidth up to 16 %. This signature is supported with stopgaps in plane wave bandstructure calculations and with the frequency region of the expected band gap.Comment: 9 pages, 5 figure

Observation of sub-Bragg diffraction of waves in crystals

We investigate the diffraction conditions and associated formation of stopgaps for waves in crystals with different Bravais lattices. We identify a prominent stopgap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centred rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg condition. These results have implications for wave propagation in 2 of the 5 two-dimensional Bravais lattices and 7 out of 14 three-dimensional Bravais lattices, such as centred rectangular, triangular, hexagonal and body-centred cubic

ANALISIS BANJIR RANCANGAN DENGAN METODE HSS NAKAYASU PADA BENDUNGAN GINTUNG

Jebolnya Situ Gintung merupakan akibat dari perubahan debit banjir yang terus bertambah. Hal tersebut perlu diana/isis terhadap debit banjir rancangan yang selanjutnya dapat digunakan untuk merencanakan Bendungan Gintung yang baru. Berdasarkan permasalahan di atas, maka perlu dikembangkan perhitungan banjir rancangan dengan metode HSS Nakayasu. Perhitungan dengan menggunaan data hujan. Pada penelitian ini digunakan 18 Pos stasiun penangkar hujan yang diseleksi menurut kelayakan data menjadi 9 pos stasiun hujan dengan memasukan nilai hujan harian maksimum tahunan. Data curah hujan yang disaring memilki tingkat kepercayaan yang rendah, namun masih masuk ke dalam data aman. Dalam penentuan debit banjir rencana terlebih dahulu dilakukan ana/isa frekuensi dan penetapan sebaran data curah hujan kemudian diuji dengan chi-kuadrat. Distribusi yang sesuai adalah distribusi Log Pearson Type III. Dari hasil ana/isa debit banjir rancangan, untuk merencanakan bendungan digunakan debit banjir kala ulang Ql000 = 289,348 m3/dt

The role of fabrication deviations on the photonic band gap of 3D inverse woodpile nanostructures

In this report the effects of unintended deviations from ideal inverse woodpile photonic crystals on the band gap are discussed. These deviations occur during the nanofabrication of the crystal. By computational analyses it is shown that the band gap of this type of crystal is robust to most types of deviations that relate to the radii, position and angular alignment of the pores. However, the photonic band gap is very sensitive to tapering of the pores, i.e., conically shaped pores instead of cylindrical pores. To obtain three-dimensional inverse woodpile photonic crystals with a large volume, our work shows that with modern fabrication performances, tapering contributes most significantly to a reduction in the photonic strength of inverse woodpile photonic crystals.Comment: 36 pages, 15 figure

Angular redistribution of near-infrared emission from quantum dots in 3D photonic crystals

We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal photonic crystals. Strong deviations from the Lambertian emission profile are observed. An attenuation of 60 % is observed in the angle dependent radiant flux emitted from the samples due to photonic stop bands. At angles that correspond to the edges of the stop band the emitted flux is increased by up to 34 %. This increase is explained by the redistribution of Bragg-diffracted light over the available escape angles. The results are quantitatively explained by an expanded escape-function model. This model is based on diffusion theory and adapted to photonic crystals using band structure calculations. Our results are the first angular redistributions and escape functions measured at near-infrared, including telecom, wavelengths. In addition, this is the first time for this model to be applied to describe emission from samples that are optically thick for the excitation light and relatively thin for the photoluminesence light.Comment: 24 pages, 8 figures (current format = single column, double spaced