Browsing by Author "Silva-Oelker, Gerardo"

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    Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings
    (2020) Aylwin, Ruben; Silva-Oelker, Gerardo; Jerez-Hanckes, Carlos; Fay, Patrick
    This work presents the implementation, numerical examples, and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape derivatives, the profile of a grating is optimized such that it maximizes the diffraction efficiency for given diffraction modes for transverse electric polarization. We provide a thorough comparison of three different optimization methods: a first-order method (gradient descent); a second-order approach based on a Newton iteration, where the usual Newton step is replaced by taking the absolute value of the eigenvalues given by the spectral decomposition of the Hessian matrix to deal with non-convexity; and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, a quasi-Newton method. Numerical examples are provided to validate our claims. Moreover, two grating profiles are designed for high efficiency in the Littrow configuration and then compared to a high efficiency commercial grating. Conclusions and recommendations, derived from the numerical experiments, are provided as well as future research avenues. (C) 2020 Optical Society of America
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    Tuning the Electronic Bandgap of Penta-Graphene from Insulator to Metal Through Functionalization: A First-Principles Calculation
    (2024) Morales-Ferreiro, J. O.; Silva-Oelker, Gerardo; Kumar, Chandra; Zambra, Carlos; Liu, Zeyu; Diaz-Droguett, Donovan E.; Celentano, Diego
    We performed first-principles density functional theory (DFT) calculations to numerically investigate the electronic band structures of penta-graphene (PG), a novel two-dimensional carbon material with a pentagonal lattice structure, and its chemically functionalized forms. Specifically, we studied hydrogenated PG (h-PG), fluorinated PG (f-PG), and chlorinated PG (Cl-PG). We used the generalized gradient approximation (GGA) and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functional in the DFT-based software VASP to capture electronic properties accurately. Our results indicate that hydrogenation and fluorination increased the indirect bandgap of PG from 3.05 eV to 4.97 eV and 4.81 eV, respectively, thereby effectively transforming PG from a semiconductor to an insulator. In contrast, we found that chlorination closed the bandgap, thus indicating the metallic behavior of Cl-PG. These results highlight the feasibility of tuning the electronic properties of PG through functionalization, offering insight into designing new materials for nanoelectronic applications.