Computing parametrized solutions for plasmonic nanogap structures

The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the confinement of light to small regions, typically several orders of magnitude smaller than the incident wavelength. The accurate prediction of these resonances entails several challenges. Small geometric variations in the plasmonic structure may lead to large variations in the electromagnetic field responses. Furthermore, the material parameters that characterize the optical behavior of metals at the nanoscale need to be determined experimentally and are consequently subject to measurement errors. It then becomes essential that any predictive tool for the simulation and design of plasmonic structures accounts for fabrication tolerances and measurement uncertainties. In this paper, we develop a reduced order modeling framework that is capable of real-time accurate electromagnetic responses of plasmonic nanogap structures for a wide range of geometry and material parameters. The main ingredients of the proposed method are: (i) the hybridizable discontinuous Galerkin method to numerically solve the equations governing electromagnetic wave propagation in dielectric and metallic media, (ii) a reference domain formulation of the time-harmonic Maxwell's equations to account for geometry variations; and (iii) proper orthogonal decomposition and empirical interpolation techniques to construct an efficient reduced model. To demonstrate effectiveness of the models developed, we analyze geometry sensitivities and explore optimal designs of a 3D periodic annular nanogap structure.Comment: 28 pages, 9 figures, 4 tables, 2 appendice

A reduced-basis method for input-output uncertainty propagation in stochastic PDEs

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 123-132).Recently there has been a growing interest in quantifying the effects of random inputs in the solution of partial differential equations that arise in a number of areas, including fluid mechanics, elasticity, and wave theory to describe phenomena such as turbulence, random vibrations, flow through porous media, and wave propagation through random media. Monte-Carlo based sampling methods, generalized polynomial chaos and stochastic collocation methods are some of the popular approaches that have been used in the analysis of such problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable evaluation of the statistics of linear functionals of stochastic PDEs. Our approach is based on constructing a reduced-basis model for the quantity of interest that enables to solve the full problem very efficiently. In particular, we apply a reduced-basis technique to the Hybridizable Discontinuous Galerkin (HDG) approximation of the underlying PDE, which allows for a rapid and accurate evaluation of the input-output relationship represented by a functional of the solution of the PDE. The method has been devised for problems where an affine parametrization of the PDE in terms of the uncertain input parameters may be obtained. This particular structure enables us to seek an offline-online computational strategy to economize the output evaluation. Indeed, the offline stage (performed once) is computationally intensive since its computational complexity depends on the dimension of the underlying high-order discontinuous finite element space. The online stage (performed many times) provides rapid output evaluation with a computational cost which is several orders of magnitude smaller than the computational cost of the HDG approximation. In addition, we incorporate two ingredients to the reduced-basis method. First, we employ the greedy algorithm to drive the sampling in the parameter space, by computing inexpensive bounds of the error in the output on the online stage. These error bounds allow us to detect which samples contribute most to the error, thereby enriching the reduced basis with high-quality basis functions. Furthermore, we develop the reduced basis for not only the primal problem, but also the adjoint problem. This allows us to compute an improved reduced basis output that is crucial in reducing the number of basis functions needed to achieve a prescribed error tolerance. Once the reduced bases have been constructed, we employ Monte-Carlo based sampling methods to perform the uncertainty propagation. The main achievement is that the forward evaluations needed for each Monte-Carlo sample are inexpensive, and therefore statistics of the output can be computed very efficiently. This combined technique renders an uncertainty propagation method that requires a small number of full forward model evaluations and thus greatly reduces the computational burden. We apply our approach to study the heat conduction of the thermal fin under uncertainty from the diffusivity coefficient and the wave propagation generated by a Gaussian source under uncertainty from the propagation medium. We shall also compare our approach to stochastic collocation methods and Monte-Carlo methods to assess the reliability of the computations.by Ferran Vidal-Codina.S.M

Optimal collapse simulator for three-dimensional structures

In this project limit analysis for 3D structures is studied. The goal is to obtain for a certain structure the load factor that applied to the external loads induces collapse to the structure. The static theorem of limit analysis is the theoretical basis for the Structural Collapse Simulator (SCS), that is nding a stress distribution in equilibrium that does not violate yield criteria anywhere. This theorem is employed combined with linear programming techniques. Thereby a tutorial on LP problems is presented rst. Then a brief summary of the progresses in study of limit analysis for structures is o ered, being a useful introduction for understanding the very nature of SCS functioning. Moreover, limit analysis is developed and written as a LP problem, which consists of the maximization of the collapse load factor subject to equilibrium and yield criteria. Two major contributions are presented for nding the collapse load. Firstly, the yield curve of standard 2D beam cross sections is adaptively approximated with inscribed and circumscribed polygons that yield to lower and upper bounds of respectively. Secondly, an interesting approach for accounting with uniform distributed loads is shown, producing bounding of the load factor. Combining these two techniques the bound gap can be reduced arbitrarily, observing convergence of the upper and the lower bounds to the exact load factor. A tutorial for using SCS and computing structures is provided, and numerical examples are thoroughly studied in order to illustrate the functioning of the program and the limits of the method. Finally, recent developments and future branches of research are detailed in order to widen the applicability range of SCS, the most important being the adaptive approximation of the yield surface for 3D beams

A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures

In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with the hydrodynamic model for the conduction-band electrons in metals. By means of a static condensation to eliminate the degrees of freedom of the approximate solution defined in the elements, the HDG method yields a linear system in terms of the degrees of freedom of the approximate trace defined on the element boundaries. Furthermore, we propose to reorder these degrees of freedom so that the linear system accommodates a second static condensation to eliminate a large portion of the degrees of freedom of the approximate trace, thereby yielding a much smaller linear system. For the particular metallic structures considered in this paper, the resulting linear system obtained by means of nested static condensations is a block tridiagonal system, which can be solved efficiently. We apply the nested HDG method to compute the second harmonic generation (SHG) on a triangular coaxial periodic nanogap structure. This nonlinear optics phenomenon features rapid field variations and extreme boundary-layer structures that span multiple length scales. Numerical results show that the ability to identify structures which exhibit resonances at $\omega$ and $2\omega$ is paramount to excite the second harmonic response.Comment: 31 pages, 7 figure

Impact of surface roughness in nanogap plasmonic systems

Recent results have shown unprecedented control over separation distances between two metallic elements hundreds of nanometers in size, underlying the effects of free-electron nonlocal response also at mid-infrared wavelengths. Most of metallic systems however, still suffer from some degree of inhomogeneity due to fabrication-induced surface roughness. Nanoscale roughness in such systems might hinder the understanding of the role of microscopic interactions. Here we investigate the effect of surface roughness in coaxial nanoapertures resonating at mid-infrared frequencies. We show that although random roughness shifts the resonances in an unpredictable way, the impact of nonlocal effects can still be clearly observed. Roughness-induced perturbation on the peak resonance of the system shows a strong correlation with the effective gap size of the individual samples. Fluctuations due to fabrication imperfections then can be suppressed by performing measurements on structure ensembles in which averaging over a large number of samples provides a precise measure of the ideal system's optical properties

An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations

We present an empirical interpolation and model-variance reduction method for the fast and reliable computation of statistical outputs of parametrized stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the real-time computation of reduced basis (RB) outputs approximating high-fidelity outputs computed with the hybridizable discontinuous Galerkin (HDG) discretization; (2) the empirical interpolation for an efficient offline-online decoupling of the parametric and stochastic inuence; and (3) a multilevel variance reduction method that exploits the statistical correlation between the low-fidelity approximations and the high-fidelity HDG dis- cretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the RB approximations. Fur- thermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the RB approximations and the size of Monte Carlo samples to achieve a given error tolerance. In addition, we extend the method to compute estimates for the gradients of the statistical out- puts. The proposed method is particularly useful for stochastic optimization problems where many evaluations of the objective function and its gradient are required

Optimal collapse simulator for three-dimensional frames

In this work a limit analysis for 3D structures software package is presented. The goal is to obtain for a certain structure the load factor λ that applied to the external loads induces collapse to the structure. The static theorem of limit analysis is the theoretical basis for the Structural Collapse Simulator (SCS), that is finding a stress distribution in equilibrium that does not violate yield criteria anywhere. The limit analysis is developed and written as a Linear Programming Problem, which consists of the maximization of the collapse load factor subject to equilibrium and yield criteria. The Structural Collapse Simulator has been applied to several types of structures to assess its capabilities on world applications

Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. The plasmonic response in these extreme-scale gaps is significantly affected by nonlocal electrodynamics, quenching field enhancement and blue-shifting the resonance with respect to a purely local behavior. The extreme mismatch in lengthscales, ranging from millimeter-long wavelengths to atomic-scale charge distributions, poses a daunting computational challenge. In this paper, we perform computations of a single nanoslit using the hybridizable discontinuous Galerkin method to solve Maxwell’s equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of the slit while accounting for the nonlocal interactions between electrons and the incident light. We study the impact of gap width, film thickness and electron motion model on the plasmon resonances of the slit for two different frequency regimes: (1) terahertz frequencies, which lead to 1000-fold field amplitude enhancements that saturate as the gap shrinks; and (2) the near- and mid-infrared regime, where we show that narrow gaps and thick films cluster Fabry-Pérot (FP) resonances towards lower frequencies, derive a dispersion relation for the first FP resonance, in addition to observing that nonlocality boosts transmittance and reduces enhancement

Prospective individual patient data meta-analysis of two randomized trials on convalescent plasma for COVID-19 outpatients

Data on convalescent plasma (CP) treatment in COVID-19 outpatients are scarce. We aimed to assess whether CP administered during the first week of symptoms reduced the disease progression or risk of hospitalization of outpatients. Two multicenter, double-blind randomized trials (NCT04621123, NCT04589949) were merged with data pooling starting when = 50 years and symptomatic for <= 7days were included. The intervention consisted of 200-300mL of CP with a predefined minimum level of antibodies. Primary endpoints were a 5-point disease severity scale and a composite of hospitalization or death by 28 days. Amongst the 797 patients included, 390 received CP and 392 placebo; they had a median age of 58 years, 1 comorbidity, 5 days symptoms and 93% had negative IgG antibody-test. Seventy-four patients were hospitalized, 6 required mechanical ventilation and 3 died. The odds ratio (OR) of CP for improved disease severity scale was 0.936 (credible interval (CI) 0.667-1.311); OR for hospitalization or death was 0.919 (CI 0.592-1.416). CP effect on hospital admission or death was largest in patients with <= 5 days of symptoms (OR 0.658, 95%CI 0.394-1.085). CP did not decrease the time to full symptom resolution

High-titre methylene blue-treated convalescent plasma as an early treatment for outpatients with COVID-19: a randomised, placebo-controlled trial.

BACKGROUND: Convalescent plasma has been proposed as an early treatment to interrupt the progression of early COVID-19 to severe disease, but there is little definitive evidence. We aimed to assess whether early treatment with convalescent plasma reduces the risk of hospitalisation and reduces SARS-CoV-2 viral load among outpatients with COVID-19. METHODS: We did a multicentre, double-blind, randomised, placebo-controlled trial in four health-care centres in Catalonia, Spain. Adult outpatients aged 50 years or older with the onset of mild COVID-19 symptoms 7 days or less before randomisation were eligible for enrolment. Participants were randomly assigned (1:1) to receive one intravenous infusion of either 250-300 mL of ABO-compatible high anti-SARS-CoV-2 IgG titres (EUROIMMUN ratio ≥6) methylene blue-treated convalescent plasma (experimental group) or 250 mL of sterile 0·9% saline solution (control). Randomisation was done with the use of a central web-based system with concealment of the trial group assignment and no stratification. To preserve masking, we used opaque tubular bags that covered the investigational product and the infusion catheter. The coprimary endpoints were the incidence of hospitalisation within 28 days from baseline and the mean change in viral load (in log10 copies per mL) in nasopharyngeal swabs from baseline to day 7. The trial was stopped early following a data safety monitoring board recommendation because more than 85% of the target population had received a COVID-19 vaccine. Primary efficacy analyses were done in the intention-to-treat population, safety was assessed in all patients who received the investigational product. This study is registered with ClinicalTrials.gov, NCT04621123. FINDINGS: Between Nov 10, 2020, and July 28, 2021, we assessed 909 patients with confirmed COVID-19 for inclusion in the trial, 376 of whom were eligible and were randomly assigned to treatment (convalescent plasma n=188 [serum antibody-negative n=160]; placebo n=188 [serum antibody-negative n=166]). Median age was 56 years (IQR 52-62) and the mean symptom duration was 4·4 days (SD 1·4) before random assignment. In the intention-to-treat population, hospitalisation within 28 days from baseline occurred in 22 (12%) participants who received convalescent plasma versus 21 (11%) who received placebo (relative risk 1·05 [95% CI 0·78 to 1·41]). The mean change in viral load from baseline to day 7 was -2·41 log10 copies per mL (SD 1·32) with convalescent plasma and -2·32 log10 copies per mL (1·43) with placebo (crude difference -0·10 log10 copies per mL [95% CI -0·35 to 0·15]). One participant with mild COVID-19 developed a thromboembolic event 7 days after convalescent plasma infusion, which was reported as a serious adverse event possibly related to COVID-19 or to the experimental intervention. INTERPRETATION: Methylene blue-treated convalescent plasma did not prevent progression from mild to severe illness and did not reduce viral load in outpatients with COVID-19. Therefore, formal recommendations to support the use of convalescent plasma in outpatients with COVID-19 cannot be concluded. FUNDING: Grifols, Crowdfunding campaign YoMeCorono