Computational Nanoplasmonics for Biosensing Applications: A Boundary Integral Implementation in the Quasistatic Limit.
Open Access DepositedLocalized surface plasmon resonance biosensors provide high sensitivity in detectingbiomolecules via shifts in the resonance frequency when targets are in the vicinity. The physics of this phenomenon is modeled with Maxwell’s equations, but in the long-wavelength limit, electrostatics serves as a good approximation. This work uses this approach, expanding the open-source PyGBe software to compute the extinction cross section of metallic and dielectric nanoparticles in the presence of biomolecules. PyGBe is a Python boundary integral research software for continuum electrostatics, where the computationally expensive parts are accelerated on GPU hardware. It is also algorithmically accelerated via a treecode that offers O(NlogN) computational complexity, allowing PyGBe to handle problems with over half a million boundary elements. These features enable PyGBe to represent the target molecule as a solvent excluded mesh based on the crystal structure and capture its complexity. Our results show grid convergence as 1/N, and accurate computation of the extinction cross-section as a function of wavelength. The computations are compared to the analytical solution for the case of an isolated nanoparticle, and compared to the Richardson extrapolation when we have the presence of an analyte. We demonstrate the suitability of PyGBe for computational nanoplasmonics for biosensing applications. We verified our solver against an analytical solution of the extinction cross section as a function of the wavelength for a silver nanosphere in a water medium. We present a sensitivity study for a biosensor model, where we computed the resonance frequency shift for different distances between two proteins located in the z-axis and the nanoparticle, and show that the shift decays from 0.75 nm to 0.25 nm as the proteins move away from the sensor from a distance of 0.5 nm to 2 nm. We also show that this behavior varies depending on the position of the proteins as we see no shift when the proteins are located at 1 nm on the x or y axis. Computational studies to date in the field of nanoplasmonic biosensing have used full Maxwell’s equations with simplified models of the sensor-analyte system. We show that reduced order models for the analyte are not sufficiently accurate compared to the full protein representation extracted from its crystal structure. Compared to the crystal structure model, the volume-equivalent model overestimates the shift by 50 % and the surface-equivalent by 400 %. Despite the overestimation of the shift, we show that ellipsoidal models capture orientation effects, while spherical models do not. We show that using the volume-equivalent is still valuable since it results in faster computations that we use to explore the multiple factors involved in the computational model of a biosensor. We replicated two studies in electromagnetic excitations on silicon carbide nanostructures, where the quantity of interest is the wavelength of the resonance peak. Despite the differences in our method, we replicated a result by Rockstuhl et al. [1] where they used a two-dimensional boundary element method on silicon carbide rectangular cylinders. The second replication case corresponds to a result in the work of Ellis et al. [2], where they looked at the aspect ratio effects on high-order modes of localized surface phonon-polariton nanostructures. We partially replicated the results since the wavenumber position of certain modes match while for others there is a discrepancy that cannot be explained without detailed information (not provided) of the original simulations. Finally, we validated PyGBe by comparing against experiments from the work of Ellis et al. [2] that measured the polarized reflectance of silicon carbide nanopillars. We perform a first order correction in our results, which leads to a match on the wavenumber for the dominant mode and two more, but with some differences in other minor modes. All the results in this work are reproducible, and all the materials needed to run the computations and re-create the figures are openly available in the form of reproducibility packages that include input files, scripts to run the simulations and process the results, and any additional data needed to reproduce the results.
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Clementi_gwu_0075A_15456.pdf | 2025-04-11 | Open Access |
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