Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation

We study the effects of a truncated band structure on the linear and nonlinear optical response of crystals using four methods. These are constructed by (i) choosing either length or velocity gauge for the perturbation and (ii) computing the current density either directly or via the time-derivative of the polarization density. In the infinite band limit, the results of all four methods are identical, but basis truncation breaks their equivalence. In particular, certain response functions vanish identically and unphysical low-frequency divergences are observed for few-band models in the velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study, we analyze the problems associated with all methods and identify the optimal one. Our results show that the length gauge calculations provide the fastest convergence rates as well as the most accurate spectra for any basis size and, moreover, that low-frequency divergences are eliminated.Comment: 11 pages, 7 figure

Plasmons in ultra-thin gold slabs with quantum spill-out:Fourier modal method, perturbative approach, and analytical model

We numerically study the effect of the quantum spill-out (QSO) on the plasmon mode indices of an ultra-thin metallic slab, using the Fourier modal method (FMM). To improve the convergence of the FMM results, a novel nonlinear coordinate transformation is suggested and employed. Furthermore, we present a perturbative approach for incorporating the effects of QSO on the plasmon mode indices, which agrees very well with the full numerical results. The perturbative approach also provides additional physical insight, and is used to derive analytical expressions for the mode indices using a simple model for the dielectric function. The analytical expressions reproduce the results obtained from the numerically-challenging spill-out problem with much less effort and may be used for understanding the effects of QSO on other plasmonic structures.Comment: 11 pages, 4 figure

Gauge invariance of excitonic linear and nonlinear optical response

We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e. length and velocity gauges, and two ways of computing the current density, i.e. direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.Comment: 11 pages, 3 figure

Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides

Monolayer transition metal dichalcogenides (TMDs) are characterized by strong light-matter interactions due to enhanced excitonic effects, which make them exciting materials for fundamental physics and optoelectronics applications. Moreover, the valley-dependent chirality of the band structure in TMDs significantly modifies the optical selection rules for single- and multiphoton processes. Here, we propose an analytical approach for calculating the linear and nonlinear optical (NLO) responses of monolayer TMDs, including excitonic effects at low photon energies. Based on this approach, we provide an informative diagram which encompasses all excitonic selection rules. The diagram enables us to identify main transitions for the first-, second-, and third-order optical responses. As a case study, we calculate the optical conductivity and second-/third-harmonic generation responses of monolayer MoS2 and demonstrate that the analytical approach accurately reproduces the spectra obtained using the Bethe-Salpeter equation (BSE). Moreover, the analytical approach enables us to obtain valuable physical insight into the fundamental transitions responsible for individual resonances, which is not straightforward in the full BSE method. Our analytical approach can readily be extended to higher-order nonlinearities and, hence, provides a simple but accurate tool for analyzing experimental NLO spectra of monolayer TMDs.</p

Effect of Three Light Curing Protocols and Load Cycling on Microleakage of Class V Composite Restorations

Objective: Different methods have been suggested to overcome the polymerization shrinkage of composite restorations. Changing the light curing protocol to improve polymerization by using new light curing units is among these methods. The new devices are more efficient, portable and durable and produce less heat. This study aimed to assess the marginal microleakage of class V composite restorations subjected to three different light curing protocols and mechanical cycles.Methods: This was an in-vitro experimental study. Class V cavities measuring 2x3x1.5 mm were prepared on the buccal and lingual surfaces of 90 extracted human premolar teeth 1.5 mm above and below the cement enamel junction (CEJ). The samples were selected using convenience sampling and divided into 9 experimental groups of 10 each by using the Table of Random Numbers to  control for the bias. The cavities were restored with packable composite resin along with Tetric-N- Bond and cured using three light curing protocols of conventional (680 mW/cm2 for 30s), soft-start (380 mW/cm2 for 10s followed by 680 mW/cm2 for 20s) and pulse (680 mW/cm2 for 30s,1s interval and 1s of lighting). The teeth were then subjected to mechanical cycles of 0, 500,000 and 1,000,000 and immersed in 2% Fuchsin for 24h. The teeth were then sectioned in half from the middle of the restoration buccolingually and the degree of microleakage was evaluated under a stereomicroscope (Zeiss, Germany) with 40X magnification. Data were analyzed using the Kruskal Wallis and the Mann-Whitney tests.Results: Despite the structural differences between the enamel and dentin margins, no significant difference was found in the degree of microleakage between the enamel (occlusal wall, p&gt;0.05) and dentin (gingival wall, p&gt;0.05) margins among the understudy groups.Conclusion: The degree of marginal microleakage in soft-start (SS) polymerization was not significantly different from that in conventional and pulse polymerizations of class V composite restoration

Nonlinear optical response of doped mono- and bilayer graphene: length gauge tight-binding model

We compute the nonlinear optical response of doped mono- and bilayer graphene using the full dispersion based on tight-binding models. The response is derived with the density matrix formalism using the length gauge and is valid for any periodic system, with arbitrary doping. By collecting terms that define effective nonlinear response tensors, we identify all nonlinear Drude-like terms (up to third-order) and show that all additional spurious divergences present in the induced current vanish. The nonlinear response of graphene comprises a large Drude-like divergence and three resonances that are tightly connected with transitions occurring in the vicinity of the Fermi level. The analytic solution derived using the Dirac approximation captures accurately the first- and third-order responses in graphene, even at very high doping levels. The quadratic response of gapped graphene is also strongly enhanced by doping, even for systems with small gaps such as commensurate structures of graphene on SiC. The nonlinear response of bilayer graphene is significantly richer, combining the resonances that stem from doping with its intrinsic strong low-energy resonances.Comment: Revised manuscript 18 pages, 6 figure

ENPP: Extended Non-preemptive PP-aware Scheduling for Real-time Cloud Services

By increasing the use of cloud services and the number of requests to processing tasks with minimum time and costs, the resource allocation and scheduling, especially in real-time applications become more challenging. The problem of resource scheduling, is one of the most important scheduling problems in the area of NP-hard problems. In this paper, we propose an efficient algorithm is proposed to schedule real-time cloud services by considering the resource constraints. The simulation results show that the proposed algorithm shorten the processing time of tasks and decrease the number of canceled tasks