Abstract
The discrete sources method is adapted to the study of surface quantum effects based on mesoscopic boundary conditions with Feibelman parameters. A comparative analysis of the influence of bulk nonlocal effects and surface effects on optical characteristics of gold and silver nanoparticles is carried out using the generalized nonlocal optical response model. It is established that allowance for the nonlocal effect in the noble metals always leads to a reduced amplitude of the surface plasmon resonance (SPR) and its blue shift, while the surface effect depends substantially on the geometry of the particles. To a large degree, the mesoscopic boundary conditions recover the SPR amplitude as compared with the bulk nonlocal effect. This difference is especially noticeable in the field enhancement factor on the surface of the particles. Additionally, substantial differences in the SPR behavior for gold and silver particles are found in the case of mesoscopic boundary conditions.
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REFERENCES
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
J. W. M. Chon and K. Iniewski, Nanoplasmonics: Advanced Device Applications (CRC, Boca Raton, FL, 2018).
H. Shi, X. Zhu, S. Zhang, et al., “Plasmonic metal nanostructures with extremely small features: New effects, fabrication and applications,” Nanoscale Adv. 3, 4349 (2021).
C. David and F. J. Garcìa de Abajo, “Surface plasmon dependence on the electron density profile at metal surfaces,” ACS Nano 8 (9), 9558 (2014).
W. Zhu, R. Esteban, A. G. Borisov, et al., “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
C. A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications (Oxford Univ. Press, Oxford, 2011).
R. Sinha-Roy, P. Garcìa-Gonźlez, H.-C. Weissker, et al., “Classical and ab initio plasmonics meet at sub-nanometric noble metal rods,” ACS Photonics 4 (6), 1484 (2017).
G. Toscano, J. Straubel, A. Kwiatkowski, et al., “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6 (1), 7132 (2015).
N. A. Mortensen, S. Raza, M. Wubs, et al., “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
M. Kupresak, X. Zheng, V. Gae, and V. V. Moshchalkov, “Appropriate nonlocal hydrodynamic models for the characterization of deep-nanometer scale plasmonic scatterers,” Adv. Theory Simul. 3, 1900172 (2019).
P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287 (1982).
H.-Y. Deng, “A theory of electrodynamic response for bounded metals: Surface capacitive effects,” Ann. Phys. 418, 168204 (2020).
Y. Yang, D. Zhu, W. Yan, et al., “A general theoretical and experimental framework for nanoscale electromagnetism,” Nature (London) 576, 248 (2019).
P. A. D. Gonçalves, T. Christensen, N. Rivera, et al., “Plasmon–emitter interactions at the nanoscale,” Nat. Commun. 11, 366 (2020).
P. E. Stamatopoulou and C. Tserkezis, “Finite-size and quantum effects in plasmonics: Manifestations and theoretical modelling [invited],” Opt. Mater. Express 12 (5), 1869 (2022).
N. A. Mortensen, “Mesoscopic electrodynamics at metal surfaces (review),” Nanophotonics 10 (10), 2563 (2021).
F. Yang and K. Ding, “Transformation optics approach to mesoscopic plasmonics,” Phys. Rev. B 105, L121410 (2022).
N. A. Mortensen, P. A. D. Gonçalves, F. A. Shuklin, et al., “Surface-response functions obtained from equilibrium electron-density profiles,” Nanophotonics 10 (14), 3647 (2021).
Yu. A. Eremin and A. G. Sveshnikov, “Mathematical model taking into account nonlocal effects of plasmonic structures on the basis of the discrete source method,” Comput. Math. Math. Phys. 58 (4), 572 (2018).
Yu. A. Eremin and A. G. Sveshnikov, “Semi-classical models of quantum nanoplasmonics based on the discrete source method (review),” Comput. Math. Math. Phys. 61 (4), 564 (2021).
A. Doicu, Yu. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, San Diego, 2000).
Yu. A. Eremin and A. G. Sveshnikov, “Mathematical models in nanooptics and biophotonics problems based on the discrete sources method,” Comput. Math. Math. Phys. 47 (2), 262 (2007).
N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, Ordinary Differential Equations (Nauka, Moscow, 1975; Mir, Moscow, 1977).
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).
Yu. A. Eremin and E. V. Zakharov, “Analytical representation of the integral scattering cross-section in the integrofunctional discrete source method,” Differ. Equations 58 (8), 1064 (2022).
M. K. Svendsen, C. Wolff, A.-P. Jauho, et al., “Role of diffusive surface scattering in nonlocal plasmonics,” J. Phys.: Condens. Matter 32, 395702 (2020).
R. A. Echarri, P. A. D. Gonçalves, C. Tserkezis, et al., “Optical response of noble metal nanostructures: Quantum surface effects in crystallographic facets,” Optica 8 (5), 710 (2021).
Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation and within the program of the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2022-284).
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Translated by I. Ruzanova
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Eremin, Y.A., Lopushenko, V.V. Analysis of the Influence of Quantum Effects on Optical Characteristics of Plasmonic Nanoparticles Based on the Discrete Sources Method. Comput. Math. and Math. Phys. 63, 2139–2149 (2023). https://doi.org/10.1134/S0965542523110088
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DOI: https://doi.org/10.1134/S0965542523110088