Definability by Horn Formulas and Linear Time on Cellular Automata

We establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d+1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time

Excited states of neutral donor bound excitons in GaN

We investigate the excited states of a neutral donor bound exciton (D0X) in bulk GaN by means of high-resolution, polychromatic photoluminescence excitation (PLE) spectroscopy. The optically most prominent donor in our sample is silicon accompanied by only a minor contribution of oxygen—the key for an unambiguous assignment of excited states. Consequently, we can observe a multitude of Si0X-related excitation channels with linewidths down to 200 μeV. Two groups of excitation channels are identified, belonging either to rotational-vibrational or electronic excited states of the hole in the Si0X complex. Such identification is achieved by modeling the excited states based on the equations of motion for a Kratzer potential, taking into account the particularly large anisotropy of effective hole masses in GaN. Furthermore, several ground- and excited states of the exciton-polaritons and the dominant bound exciton are observed in the photoluminescence (PL) and PLE spectra, facilitating an estimate of the associated complex binding energies. Our data clearly show that great care must be taken if only PL spectra of D0X centers in GaN are analyzed. Every PL feature we observe at higher emission energies with regard to the Si0X ground state corresponds to an excited state. Hence, any unambiguous peak identification renders PLE spectra highly valuable, as important spectral features are obscured in common PL spectra. Here, GaN represents a particular case among the wide-bandgap, wurtzite semiconductors, as comparably low localization energies for common D0X centers are usually paired with large emission linewidths and the prominent optical signature of exciton-polaritons, making the sole analysis of PL spectra a challenging task.EC/H2020/749565/EU/Heat Transport and its Effects on the Performance of Nanostructured, Photonic Materials/PhotoHeatEffectDFG, 43659573, SFB 787: Halbleiter - Nanophotonik: Materialien, Modelle, Bauelement

Intrinsic degradation mechanism of nearly lattice-matched InAlN layers grown on GaN substrates

Thanks to its high refractive index contrast, band gap and polarization mismatch compared to GaN, In0.17Al0.83N layers lattice-matched to GaN are an attractive solution for applications such as distributed Bragg reflectors, ultraviolet light-emitting diodes, or high electron mobility transistors. In order to study the structural degradation mechanism of InAlN layers with increasing thickness, we performed metalorganic vapor phase epitaxy of InAlN layers of thicknesses ranging from 2 to 500 nm, on free-standing (0001) GaN substrates with a low density of threading dislocations, for In compositions of 13.5% (layers under tensile strain), and 19.7% (layers under compressive strain). In both cases, a surface morphology with hillocks is initially observed, followed by the appearance of V-defects. We propose that those hillocks arise due to kinetic roughening, and that V-defects subsequently appear beyond a critical hillock size. It is seen that the critical thickness for the appearance of V-defects increases together with the surface diffusion length either by increasing the temperature or the In flux because of a surfactant effect. In thick InAlN layers, a better (worse) In incorporation occurring on the concave (convex) shape surfaces of the V-defects is observed leading to a top phase-separated InAlN layer lying on the initial homogeneous InAlN layer after V-defects coalescence. It is suggested that similar mechanisms could be responsible for the degradation of thick InGaN layers

Propagating Polaritons in III-Nitride Slab Waveguides

We report on III-nitride waveguides with c-plane GaN/AlGaN quantum wells in the strong light-matter coupling regime supporting propagating polaritons. They feature a normal mode splitting as large as 60 meV at low temperatures thanks to the large overlap between the optical mode and the active region, a polariton decay length up to 100 $\mu$m for photon-like polaritons and lifetime of 1-2 ps; with the latter values being essentially limited by residual absorption occurring in the waveguide. The fully lattice-matched nature of the structure allows for very low disorder and high in-plane homogeneity; an important asset for the realization of polaritonic integrated circuits that could support nonlinear polariton wavepackets up to room temperature thanks to the large exciton binding energy of 40 meV

Efficient continuous-wave nonlinear frequency conversion in high-Q Gallium Nitride photonic crystal cavities on Silicon

We report on nonlinear frequency conversion from the telecom range via second harmonic generation (SHG) and third harmonic generation (THG) in suspended gallium nitride slab photonic crystal (PhC) cavities on silicon, under continuous-wave resonant excitation. Optimized two-dimensional PhC cavities with augmented far-field coupling have been characterized with quality factors as high as 4.4$\times10^{4}$, approaching the computed theoretical values. The strong enhancement in light confinement has enabled efficient SHG, achieving normalized conversion efficiency of 2.4$\times10^{-3}$ $W^{-1}$, as well as simultaneous THG. SHG emission power of up to 0.74 nW has been detected without saturation. The results herein validate the suitability of gallium nitride for integrated nonlinear optical processing.Comment: 5 pages, 5 figure

Prediction of changes in landslide rates induced by rainfall

National audienceThis work focuses on the use of a combined statistical-mechanical approach to predict changes in landslide displacement rates from observed changes in rainfall amounts. The forecasting tool associates a statistical impulse response (IR) model to simulate the changes in landslide rates by computing a transfer function between the input signal (e.g. rainfall) and the output signal (e.g. displacements) and a simple 1D mechanical (MA) model (e.g. visco-plastic rheology) to take into account changes in pore water pressures. The models have been applied to forecast the displacement rates at the Super-Sauze landslide (South East France), one of the most active and instrumented clayey landslide in the European Alps. Results indicate that the three models are able to reproduce the displacement pattern in the general kinematic regime with very good accuracy (succession of acceleration and deceleration phases); at the contrary, extreme kinematic regimes such as fluidization of part of the landslide mass are not being reproduced: this statement, quantitatively characterised by the Root Mean Square Error between the model and the observations, constitutes however a robust approach to predict changes in displacement rates from rainfall or groundwater time series, several days before it happens. The variability of the results, depending in particular on the fluidization events and on the location of displacement data is discussed

Exact determination of electrical properties of wurtzite Al1−xInxN/(AlN)/GaN heterostructures (0.07≤x≤0.21) by means of a detailed charge balance equation

This paper discusses the determination of key electrical parameters of AlInN/(AlN)/GaN heterostructures from capacitance-voltage (CV) measurements. These heterostructures gained recently importance since they allow for high electron mobility transistor (HEMT) devices with several remarkable records: densities of the 2D electron gas (2DEG) of 2.6×1013 cm−2 for lattice-matched (LM) heterostructures and barrier thickness of 14nm, beyond 2 A/mm saturation currents, above 100GHz operation for heterostructures grown on Si (111) with gate length of 0.1µm. Despite these striking experimental results, a consistent determination of the most important electrical parameters, namely polarization sheet charge density, surface potential, and dielectric constant of the alloy are still missing. By setting up the correct charge balance equation, these parameters can unambiguously be determined. For instance, in the case of nearly LM Al0.85In0.15N these parameters amount to σAl0.85In0.15N/GaN~3.7×1017 m−2, eΦS~3 eV and Al0.85In0.15N ~11.2, for the charge density, the surface barrier potential, and the dielectric constant, respectivel

Doubly resonant second-harmonic generation of a vortex beam from a bound state in the continuum

Second harmonic generation in nonlinear materials can be greatly enhanced by realizing doubly-resonant cavities with high quality factors. However, fulfilling such doubly resonant condition in photonic crystal (PhC) cavities is a long-standing challenge, because of the difficulty in engineering photonic bandgaps around both frequencies. Here, by implementing a second-harmonic bound state in the continuum (BIC) and confining it with a heterostructure design, we show the first doubly-resonant PhC slab cavity with $2.4\times10^{-2}$ W$^{-1}$ conversion efficiency under continuous wave excitation. We also report the confirmation of highly normal-direction concentrated far-field emission pattern with radial polarization at the second harmonic frequency. These results represent a solid verification of previous theoretical predictions and a cornerstone achievement, not only for nonlinear frequency conversion but also for vortex beam generation and prospective nonclassical sources of radiation.Comment: revtex4-2, 7 pages, 5 figures, conference CLE