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1. A 1D Gaussian Function for Efficient Generation of Plane Waves in 1D, 2D, and 3D FDTD

   https://doi.org/10.1109/IEEECONF35879.2020.9329878  

   Guiana, Brian; Zadehgol, Ata (February 2021, 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting)

   null (Ed.)

   A 1D Gaussian expression is derived and used as the 1D E/H incident field in the TF/SF formulation to efficiently generate plane waves in 1D, 2D, and 3D FDTD simulations. The analytic expression is simple, and it eliminates the need for computational resources to store and compute the E/H-field incident arrays and their associated absorbing boundaries. FDTD simulation results at the magic time-step in 1D, 2D, and 3D FDTD show good correlation between plane waves generated by the 1D analytic Gaussian function vs. those generated by 1D FDTD incident arrays. 

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2. Characterizing THz Scattering Loss in Nano-Scale SOI Waveguides Exhibiting Stochastic Surface Roughness with Exponential Autocorrelation

   https://doi.org/10.3390/electronics11030307  

   Guiana, Brian; Zadehgol, Ata (February 2022, Electronics)

   Electromagnetic (EM) scattering may be a significant source of degradation in signal and power integrity of high-contrast silicon-on-insulator (SOI) nano-scale interconnects, such as opto-electronic or optical interconnects operating at 100 s of THz where two-dimensional (2D) analytical models of dielectric slab waveguides are often used to approximate scattering loss. In this work, a formulation is presented to relate the scattering (propagation) loss to the scattering parameters (S-parameters) for the smooth waveguide; the results are correlated with results from the finite-difference time-domain (FDTD) method in 2D space. We propose a normalization factor to the previous 2D analytical formulation for the stochastic scattering loss based on physical parameters of waveguides exhibiting random surface roughness under the exponential autocorrelation function (ACF), and validate the results by comparing against numerical experiments via the 2D FDTD method, through simulation of hundreds of rough waveguides; additionally, results are compared to other 2D analytical and previous 3D experimental results. The FDTD environment is described and validated by comparing results of the smooth waveguide against analytical solutions for wave impedance, propagation constant, and S-parameters. Results show that the FDTD model is in agreement with the analytical solution for the smooth waveguide and is a reasonable approximation of the stochastic scattering loss for the rough waveguide. 

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3. Geometrically Tunable Beamed Light Emission from a Quantum‐Dot Ensemble Near a Gradient Metasurface

   https://doi.org/10.1002/adom.201901951  

   Wang, Xiaowei; Li, Yuyu; Toufanian, Reyhaneh; Kogos, Leonard_C; Dennis, Allison_M; Paiella, Roberto (February 2020, Advanced Optical Materials)

   Abstract Optical metasurfaces have been widely investigated in recent years as a means to tailor the wavefronts of externally incident light for passive device applications. At the same time, their use in active optoelectronic devices such as light emitters is far less established. This work explores their ability to control the radiation properties of a nearby continuous ensemble of randomly oriented incoherent dipole sources via near‐field interactions. Specifically, a film of colloidal quantum dots is deposited on a plasmonic metasurface consisting of a 1D array of metallic nanoantennas on a metal film. The array is designed to introduce a linear phase profile upon reflection, and a bi‐periodic nanoparticle arrangement is introduced to ensure adequate sampling of the desired phase gradient. Highly directional radiation patterns are correspondingly obtained from the quantum dots at an enhanced emission rate. The underlying radiation mechanism involves the near‐field excitation of surface plasmon polaritons at the metal film, and their selective diffractive scattering by the metasurface into well‐collimated beams along predetermined geometrically tunable directions. These results underscore the distinctive ability of metasurfaces to control radiation properties directly at the source level, which is technologically significant for the continued miniaturization and large‐scale integration of optoelectronic devices. 

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4. Learning domain-independent Green’s function for elliptic partial differential equations

   https://doi.org/10.1016/j.cma.2024.116779  

   Negi, Pawan; Cheng, Maggie; Krishnamurthy, Mahesh; Ying, Wenjun; Li, Shuwang (March 2024, Computer Methods in Applied Mechanics and Engineering)

   Lorenzis, Laura (Ed.)

   Green’s function characterizes a partial differential equation (PDE) and maps its solution in the entire domain as integrals. Finding the analytical form of Green’s function is a non-trivial exercise, especially for a PDE defined on a complex domain or a PDE with variable coefficients. In this paper, we propose a novel boundary integral network to learn the domain independent Green’s function, referred to as BIN-G. We evaluate the Green’s function in the BIN-G using a radial basis function (RBF) kernel-based neural network. We train the BIN-G by minimizing the residual of the PDE and the mean squared errors of the solutions to the boundary integral equations for prescribed test functions. By leveraging the symmetry of the Green’s function and controlling refinements of the RBF kernel near the singularity of the Green function, we demonstrate that our numerical scheme enables fast training and accurate evaluation of the Green’s function for PDEs with variable coefficients. The learned Green’s function is independent of the domain geometries, forcing terms, and boundary conditions in the boundary integral formulation. Numerical experiments verify the desired properties of the method and the expected accuracy for the two-dimensional Poisson and Helmholtz equations with variable coefficients. 

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5. Efficient classical simulation of noisy random quantum circuits in one dimension

   https://doi.org/10.22331/q-2020-09-11-318  

   Noh, Kyungjoo; Jiang, Liang; Fefferman, Bill (September 2020, Quantum)

   Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers. 

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