Branch and bound (B&B) algorithms structure the search space as a tree and eliminate infeasible solutions early by pruning subtrees that cannot lead to a valid or optimal solution. Custom hardware designs significantly accelerate the execution of these algorithms. In this article, we demonstrate a high-performance B&B implementation on FPGAs. First, we identify general elements of B&B algorithms and describe their implementation as a finite state machine. Then, we introduce workers that autonomously cooperate using work stealing to allow parallel execution and full utilization of the target FPGA. Finally, we explore advantages of instance-specific designs that target a specific problem instance to improve performance. We evaluate our concepts by applying them to a branch and bound problem, the reconstruction of corrupted AES keys obtained from cold-boot attacks. The evaluation shows that our work stealing approach is scalable with the available resources and provides speedups proportional to the number of workers. Instance-specific designs allow us to achieve an overall speedup of 47 × compared to the fastest implementation of AES key reconstruction so far. Finally, we demonstrate how instance-specific designs can be generated just-in-time such that the provided speedups outweigh the additional time required for design synthesis.

The problem of light scattering by ice crystals of cirrus clouds is considered in the case of a hexagonal ice plate with different distributions over crystal orientations. The physical-optics approximation based on (E, M)-diffraction theory is compared with two exact numerical methods: the finite difference time domain (FDTD) and the discontinuous Galerkin time domain (DGTD) in order to estimate its accuracy and limits of applicability. It is shown that the accuracy of the physical-optics approximation is estimated as 95% for the averaged backscattering Mueller matrix for particles with size parameter more than 120. Furthermore, the simple expression that allows one to estimate the minimal number of particle orientations required for appropriate spatial averaging has been derived.

We simulate light scattering by random irregular particles that have dimensions much larger than the wavelength of incident light at the size parameter of 𝑋=200 using the discontinuous Galerkin time domain method. A comparison of the DGTD solution for smoothly faceted particles with that obtained with a geometric optics model shows good agreement for the scattering angle curves of intensity and polarization. If a wavelength-scale surface roughness is introduced, diffuse scattering at rough interface results in smooth and featureless curves for all scattering matrix elements which is consistent with the laboratory measurements of real samples.

The physical optics approximations are derived from the Maxwell equations. The scattered field equations by Kirchhoff, Stratton-Chu, Kottler and Franz are compared and discussed. It is shown that in the case of faceted particles, these equations reduce to a sum of the diffraction integrals, where every diffraction integral is associated with one plane–parallel optical beam leaving a particle facet. In the far zone, these diffraction integrals correspond to the Fraunhofer diffraction patterns. The paper discusses the E-, M- and (E, M)-diffraction theories as applied to ice crystals of cirrus clouds. The comparison to the exact solution obtained by the discontinuous Galerkin time domain method shows that the Kirchhoff diffraction theory is preferable.

We report on second harmonic generation spectroscopy on a series of rectangular arrays of split-ring resonators. Within the sample series, the lattice constants are varied, but the area of the unit cell is kept fixed. The SHG signal intensity of the different arrays upon resonant excitation of the fundamental plasmonic mode strongly depends on the respective arrangement of the split-ring resonators. This finding can be explained by variations of the electromagnetic interactions between the split-ring resonators in the different arrays. The experimental results are in agreement with numerical calculations based on the discontinuous Galerkin time-domain method. (PDF) The role of electromagnetic interactions.... Available from: https://www.researchgate.net/publication/297612326_The_role_of_electromagnetic_interactions_in_second_harmonic_generation_from_plasmonic_metamaterials [accessed Aug 13 2018].

Recently, the quantum harmonic oscillator model has been combined with maximally localized Wannier functions to account for long-range dispersion interactions in density functional theory calculations (Silvestrelli, J. Chem. Phys. 2013, 139, 054106). Here, we present a new, improved set of values for the three parameters involved in this scheme. To test the new parameter set we have computed the potential energy curves for various systems, including an isolated Ar2 dimer, two N2 dimers interacting within different configurations, and a water molecule physisorbed on pristine graphene. While the original set of parameters generally overestimates the interaction energies and underestimates the equilibrium distances, the new parameterization substantially improves the agreement with experimental and theoretical reference values. © 2016 Wiley Periodicals, Inc.

The accuracy of water models derived from ab initio molecular dynamics simulations by means on an improved force-matching scheme is assessed for various thermodynamic, transport, and structural properties. It is found that although the resulting force-matched water models are typically less accurate than fully empirical force fields in predicting thermodynamic properties, they are nevertheless much more accurate than generally appreciated in reproducing the structure of liquid water and in fact superseding most of the commonly used empirical water models. This development demonstrates the feasibility to routinely parametrize computationally efficient yet predictive potential energy functions based on accurate ab initio molecular dynamics simulations for a large variety of different systems. © 2016 Wiley Periodicals, Inc.

The influence of electronic many-body interactions, spin-orbit coupling, and thermal lattice vibrations on the electronic structure of lithium niobate is calculated from first principles. Self-energy calculations in the GW approximation show that the inclusion of self-consistency in the Green function G and the screened Coulomb potential W opens the band gap far stronger than found in previous G0W0 calculations but slightly overestimates its actual value due to the neglect of excitonic effects in W. A realistic frozen-lattice band gap of about 5.9 eV is obtained by combining hybrid density functional theory with the QSGW0 scheme. The renormalization of the band gap due to electron-phonon coupling, derived here using molecular dynamics as well as density functional perturbation theory, reduces this value by about 0.5 eV at room temperature. Spin-orbit coupling does not noticeably modify the fundamental gap but gives rise to a Rashba-like spin texture in the conduction band.

The phonon dispersions of the ferro‐ and paraelectric phase of LiTaO3 are calculated within density‐functional perturbation theory. The longitudinal optical phonon modes are theoretically derived and compared with available experimental data. Our results confirm the recent phonon assignment proposed by Margueron et al. [J. Appl. Phys. 111, 104105 (2012)] on the basis of spectroscopical studies. A comparison with the phonon band structure of the related material LiNbO3 shows minor differences that can be traced to the atomic‐mass difference between Ta and Nb. The presence of phonons with imaginary frequencies for the paraelectric phase suggests that it does not correspond to a minimum energy structure, and is compatible with an order‐disorder type phase transition.

<p>We report a combined experiment-theory study on low energy vibrational modes in fluorescence spectra of perylene-3,4,9,10-tetracarboxylic acid dianhydride (PTCDA) molecules.</p>

We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.

A microscopic approach that is based on the multisubband semiconductor Bloch equations formulated in the basis of a 14-band k⋅p model is employed to compute the temporal dynamics of photocurrents in GaAs quantum wells following excitation with femtosecond laser pulses. This approach provides a transparent description of the interband, intersubband, and intraband excitations, fully includes all resonant as well as off-resonant excitations, and treats the light-matter interaction nonperturbatively. For linearly polarized excitations, the photocurrents contain contributions from shift and rectification currents. We numerically compute and analyze these currents generated by excitation with femtosecond laser pulses for [110]- and [111]-oriented GaAs quantum wells. It is shown that the often employed perturbative χ(2) approach breaks down for peak fields larger than about 10 kV/cm, and that nonperturbative effects lead to a reduction of the peak values of the shift and rectification currents and to temporal oscillations that originate from Rabi flopping. In particular, we find a complex oscillatory photon energy dependence of the magnitudes of the shift and rectification currents. Our simulations demonstrate that this dependence is the result of mixing between the heavy- and light-hole valence bands. This is a surprising finding since the band mixing has an even larger influence on the strength of the photocurrents than the absorption coefficient. For [110]-oriented GaAs quantum wells, the calculated photon energy dependence is compared to experimental results, and good agreement is obtained. This validates our theoretical approach.

We investigate the transient optical response in high-quality Cd0.88Zn0.12Te crystals in the regime of slow light propagation on the lower exciton-polariton branch. Femtosecond photoexcitation leads to very substantial transmission changes in a ∼10-meV broad spectral range within the transparency window of the unexcited semiconductor. These nonlinear optical signatures decay on picosecond time scales governed by carrier thermalization and recombination. The temporal and spectral dependence indicate the dynamical optical response as arising from excitation-induced dephasing and perturbed free induction decay. Model simulations for the optical response taking into account the actual exciton-polariton dispersion and excitation-induced dephasing of a nonlinearly driven two-level system support this interpretation.

The vibrational properties of stoichiometric LiNbO3 are analyzed within density-functional perturbation theory in order to obtain the complete phonon dispersion of the material. The phonon density of states of the ferroelectric (paraelectric) phase shows two (one) distinct band gaps separating the high-frequency (~800 cm−1) optical branches from the continuum of acoustic and lower optical phonon states. This result leads to specific heat capacites in close agreement with experimental measurements in the range 0–350 K and a Debye temperature of 574 K. The calculated zero-point renormalization of the electronic Kohn–Sham eigenvalues reveals a strong dependence on the phonon wave vectors, especially near Γ. Integrated over all phonon modes, our results indicate a vibrational correction of the electronic band gap of 0.41 eV at 0 K, which is in excellent agreement with the extrapolated temperature-dependent measurements.

Recently, a new class of nonlinear systems was introduced, in which the self-trapping of fundamental and vortical localized modes in space of dimension D is supported by cubic self-repulsion with a strength growing as a function of the distance from the center, r, at any rate faster that rD. These systems support robust 2D and 3D modes which either do not exist or are unstable in other nonlinear systems. Here we demonstrate a possibility to create solitary vortices in this setting by applying a phase-imprinting torque to the ground state. Initially, a strong torque completely destroys the ground state. However, contrary to usual systems, where the destruction is irreversible, the present ones demonstrate a rapid restabilization and the creation of one or several shifted vortices orbiting the center. For the sake of comparison, we show analytically that, in the linear system with a 3D trapping potential, the action of a torque on the ground state is inefficient and creates only even-vorticity states with a small probability.

The Kane–Mele model was previously used to describe effective spin–orbit couplings (SOCs) in graphene. Here we extend this model and also incorporate curvature effects to analyze the combined influence of SOC and curvature on the band structure of carbon nanotubes (CNTs). The extended model then reproduces the chirality-dependent asymmetric electron-hole splitting for semiconducting CNTs and in the band structure for metallic CNTs shows an opening of the band gap and a change of the Fermi wave vector with spin. For chiral semiconducting CNTs with large chiral angle we show that the spin-splitting configuration of bands near the Fermi energy depends on the value of $\text{mod}(2n+m,3)$ .

The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.

The dynamics of two component-coupled vectorial Airy beams is investigated. In the linear propagation regime, a complete analytic solution describes the breather-like propagation of two components that feature nondiffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility of designing more complex nondiffracting propagation scenarios. In the strongly nonlinear regime, the dynamics remain qualitatively robust as is revealed by direct numerical simulations. Because of the Kerr effect, the two beams emit solitonic breathers whose coupling period is compatible with the remaining Airy-like beams. The results of this study are relevant for the description of photonic and plasmonic beams that propagate in coupled planar waveguides, as well as for birefrigent or multiwavelength beams.

Starting from the extended Su-Schrieffer-Heeger model, multiband semiconductor Bloch equations are formulated in momentum space and applied to the analysis of the linear optical response of semiconducting carbon nanotubes (SCNTs). This formalism includes the coupling of electron-hole pair excitations between different valence and conduction bands, originating from the electron-hole Coulomb attraction. The influence of these couplings, which are referred to as nondiagonal interband Coulomb interaction (NDI-CI), on the linear excitonic absorption spectra is investigated and discussed for light fields polarized parallel to the tube direction. The results show that the intervalley NDI-CI leads to a significant increase of the band gap and a decrease of the exciton binding energy that results in a blueshift of the lowest-frequency excitonic absorption peak. The strength of these effects depends on the symmetry of the SCNT. Furthermore, for zigzag SCNTs with higher symmetry other nonintervalley NDI-CI terms also affect the spectral positions of excitonic absorption peaks.

Dispersion management of periodically alternating fiber sections with opposite signs of two leading dispersion terms is applied for the regeneration of self-accelerating truncated Airy pulses. It is demonstrated that for such a dispersion management scheme, the direction of the acceleration of the pulse is reversed twice within each period. In this scheme the system features light hot spots in the center of each fiber section, where the energy of the light pulse is tightly focused in a short temporal slot. Comprehensive numerical studies demonstrate a long-lasting propagation also under the influence of a strong fiber Kerr nonlinearity.

The frequency-dependent dielectric function and the second-order polarizability tensor of ferroelectric LiNbO3 are calculated from first principles. The calculations are based on the electronic structure obtained from density-functional theory. The subsequent application of the GW approximation to account for quasiparticle effects and the solution of the Bethe-Salpeter equation for the stoichiometric material yield a dielectric function that slightly overestimates the absorption onset and the oscillator strength in comparison with experimental measurements. Calculations at the level of the independent-particle approximation indicate that these deficiencies are, at least, partially related to the neglect of intrinsic defects typical for the congruent material. The second-order polarizability calculated within the independent-particle approximation predicts strong nonlinear coefficients for photon energies above 1.5 eV. The comparison with measured data suggests that the inclusion of self-energy effects in the nonlinear optical response leads to a better agreement with experiments. The intrinsic defects of congruent samples reduce the optical nonlinearities, in particular, for the 21 and 31 tensor components, further improving the agreement between experiments and theory.

We derive a transparent and easy-to-use analytic expression for the selection rules and the optical dipole matrix elements for carbon nanotubes of arbitrary chirality in the presence of axial magnetic fields using a single-orbital π-electron tight-binding model. From this, we calculate the linear absorption spectrum for arbitrary polarization directions of the incident light, providing insight into all optically allowed transition. We show that the transverse absorption peaks can be selectively excited with circularly polarized light and spectrally resolved in an axial magnetic field.

We study the quantum properties and statistics of photons emitted by a quantum-dot biexciton inside a cavity. In the biexciton-exciton cascade, fine-structure splitting between exciton levels degrades polarization-entanglement for the emitted pair of photons. However, here we show that the polarization-entanglement can be preserved in such a system through simultaneous emission of two degenerate photons into cavity modes tuned to half the biexciton energy. Based on detailed theoretical calculations for realistic quantum-dot and cavity parameters, we quantify the degree of achievable entanglement.

The generation of specific high harmonics for an optical two-level system is elucidated. The desired emitted radiation can be induced by a carefully designed excitation pulse, which is found by a multiparameter optimization procedure. The presented mechanism can also be applied to semiconductor structures for which the calculations result in much higher emission frequencies. The optimization procedure is either performed using a genetic algorithm or a rigorous mathematical optimization technique.

The vibrational properties of the LiNbO3 (0001) surfaces have been investigated both from first principles and with Raman spectroscopy measurements. Firstly, the phonon modes of bulk and of the (0001) surface are calculated by means of the density functional theory. Our calculations reveal the existence of localised vibrational modes both at the positive and at the negative surface. The surface vibrations are found at energies above and within the bulk bands. Phonon modes localised at the positive and at the negative surface differ substantially. In a second step, the Raman spectra of LiNbO3 bulk and of the two surfaces have been measured. Raman spectroscopy is shown to be sensitive to differences between bulk and surface and between positive and negative surface. The calculated and measured frequencies are in agreement within the error of the method.

Given the vast range of lithium niobate (LiNbO3) applications, the knowledge about its electronic and optical properties is surprisingly limited. The direct band gap of 3.7 eV for the ferroelectric phase – frequently cited in the literature – is concluded from optical experiments. Recent theoretical investigations show that the electronic band‐structure and optical properties are very sensitive to quasiparticle and electron‐hole attraction effects, which were included using the GW approximation for the electron self‐energy and the Bethe‐Salpeter equation respectively, both based on a model screening function. The calculated fundamental gap was found to be at least 1 eV larger than the experimental value. To resolve this discrepancy we performed first‐principles GW calculations for lithium niobate using the full‐potential linearized augmented plane‐wave (FLAPW) method. Thereby we use the parameter‐free random phase approximation for a realistic description of the nonlocal and energydependent screening. This leads to a band gap of about 4.7 (4.2) eV for ferro(para)‐electric lithium niobate.

It is demonstrated that valence-band mixing in GaAs quantum wells tremendously modifies electronic transport. A coherent control scheme in which ultrafast currents are optically injected into undoped GaAs quantum wells upon excitation with femtosecond laser pulses is employed. An oscillatory dependence of the injection current amplitude and direction on the excitation photon energy is observed. A microscopic theoretical analysis shows that this current reversal is caused by the coupling of the light- and heavy-hole bands and that the hole currents dominate the overall current response. These surprising consequences of band mixing illuminate fundamental physics as they are unique for experiments which are able to monitor electronic transport resulting from carriers with relatively large momenta.

Microdisks made from GaAs with embedded InAs quantum dots are immersed in the liquid crystal 4-cyano-4’-pentylbiphenyl (5CB). The quantum dots serve as emitters feeding the optical modes of the photonic cavity. By changing temperature, the liquid crystal undergoes a phase transition from the isotropic to the nematic state, which can be used as an effective tuning mechanism of the photonic modes of the cavity. In the nematic state, the uniaxial electrical anisotropy of the liquid crystal molecules can be exploited for orienting the material in an electric field, thus externally controlling the birefringence of the material. Using this effect, an electric field induced tuning of the modes is achieved. Numerical simulations using the finite-differences time-domain (FDTD) technique employing an anisotropic dielectric medium allow to understand the alignment of the liquid crystal molecules on the surface of the microdisk resonator.