×

Semi-classical models of quantum nanoplasmonics based on the discrete source method (review). (English. Russian original) Zbl 1466.78010

Comput. Math. Math. Phys. 61, No. 4, 564-590 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 4, 580-607 (2021).
Summary: Works concerning the quantum effect of nonlocal screening on field characteristics in the problem of scattering a plane wave by nanoscale structures, including ones located near a transparent substrate, are reviewed. Efficient computer models for analyzing such structures are constructed by applying the discrete source method. The nonlocality effect is studied using the generalized nonlocal optical response model. The field characteristics of nonspherical layered nanoparticles deposited in an active medium or on the surface of a transparent substrate are considered. It is shown that nonlocality has a large effect on the optical characteristics in the far- and near-field regions. It is established that the nonlocality effect leads to a decrease in the intensity of surface plasmon resonance by up to 2.5 times under a small shift toward short wavelengths. In the presence of a substrate, the excitation of particles by a propagating or an evanescent wave is considered. It is shown that the largest effect is exhibited for nonspherical layered particles located in the evanescent wave region.

MSC:

78A40 Waves and radiation in optics and electromagnetic theory
78A48 Composite media; random media in optics and electromagnetic theory
78A35 Motion of charged particles
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory

Software:

COMSOL
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Klimov, V. V., Nanoplasmonics (2009), Moscow: Fizmatlit, Moscow
[2] Pelton, M.; Bryant, G., Introduction to Metal-Nanoparticle Plasmonics (2013), New York: Wiley, New York
[3] Stockman, M. I., Nanoplasmonic sensing and detection, Science, 348, 287-288 (2015) · doi:10.1126/science.aaa6805
[4] Oulton, R. F.; Sorger, V. J.; Zentgraf, T., Plasmon lasers at deep subwavelength scale, Nature, 461, 629 (2009) · doi:10.1038/nature08364
[5] Ding, S. Y.; Yi, J.; Li, J. F., Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis materials, Nat. Rev. Mater., 1, 16021 (2016) · doi:10.1038/natrevmats.2016.21
[6] Jeong, Y.; Kook, Y.-M.; Lee, K.; Koh, W.-G., Metal enhanced fluorescence (MEF) for biosensors: General approaches and a review of recent developments, Biosensors Bioelectron., 111, 102-116 (2018) · doi:10.1016/j.bios.2018.04.007
[7] Eremina, E.; Eremin, Yu.; Wriedt, T., Computational nano-optic technology based on discrete sources method (review), J. Mod. Opt., 58, 384 (2011) · Zbl 1218.78036 · doi:10.1080/09500340.2010.515751
[8] Xu, D.; Xiong, X.; Wu, L., Quantum plasmonics: New opportunity in fundamental and applied photonics. Review, Adv. Opt. Photonics, 10, 703-756 (2018) · doi:10.1364/AOP.10.000703
[9] Oldenburg, S. J.; Averitt, R. D.; Westcott, S. L.; Halas, N. J., Nanoengineering of optical resonances, Chem. Phys. Lett., 288, 243 (1998) · doi:10.1016/S0009-2614(98)00277-2
[10] Khlebtsov, N. G.; Khlebtsov, B. N., Optimal design of gold nanomatryoshkas with embedded Raman reporters, J. Quant. Spectrosc. Radiat. Transfer, 190, 89 (2017) · doi:10.1016/j.jqsrt.2017.01.027
[11] Gawande, M. B.; Goswami, A.; Asefa, T., Core-shell nanoparticles: synthesis and applications in catalysis and electrocatalysis, Chemic. Soc. Rev., 44, 7540 (2015) · doi:10.1039/C5CS00343A
[12] Frost, R.; Wadell, C.; Hellman, A., Core-shell nanoplasmonic sensing for characterization of biocorona formation and nanoparticle surface interactions, ACS Sensors, 1, 798 (2016) · doi:10.1021/acssensors.6b00156
[13] Phan, A. D.; Nga, D. T.; Viet, N. A., Theoretical model for plasmonic photothermal response of gold nanostructures solutions, Opt. Commun., 410, 108 (2018) · doi:10.1016/j.optcom.2017.10.008
[14] Zhang, W.; Saliba, M.; Stranks, S. D., Enhancement of perovskite-based solar cells employing core-shell metal nanoparticles, Nano Lett., 13, 4505 (2013) · doi:10.1021/nl4024287
[15] Xu, L.; Li, F.; Liu, Y.; Yao, F.; Liu, S., Surface plasmon nanolaser: Principle, structure, characteristics, and applications, Appl. Sci., 9, 861 (2019) · doi:10.3390/app9050861
[16] Premaratne, M.; Stockman, M., Theory and technology of SPASERs: Review, Adv. Opt. Photon., 9, 79 (2017) · doi:10.1364/AOP.9.000079
[17] Balykin, V. I., Plasmonic nanolaser: Current state and prospects, Phys. Usp., 61, 846-879 (2018) · doi:10.3367/UFNe.2017.09.038206
[18] Sudarkin, A. N.; Demkovich, P. A., Excitation of surface electromagnetic wave on the boundary of a metal with an amplified medium, Sov. Phys. Tech. Phys., 34, 764 (1988)
[19] D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90 (027402) (2003).
[20] Noginov, M. A.; Zhu, G.; Belgrave, A. M., Demonstration of a spaser-based nanolaser, Nature, 460, 1110-1113 (2009) · doi:10.1038/nature08318
[21] M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, et al., “Roadmap on plasmonics,” J. Opt. 20 N043001 (2018).
[22] Liaw, J.-W.; Chen, H.-C.; Kuo, M.-K., Comparison of Au and Ag nanoshells’ metal-enhanced fluorescence, J. Quant. Spectrosc. Radiat. Transfer, 146, 321-330 (2014) · doi:10.1016/j.jqsrt.2014.02.025
[23] Li, Q.; Zhang, W.; Zhao, D.; Qiu, M., Photothermal enhancement in core-shell structured plasmonic nanoparticles, Plasmonics, 9, 623 (2014) · doi:10.1007/s11468-014-9673-8
[24] S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. A. Mortensen, “Nonlocal optical response in metallic nanostructures: Topical review,” J. Phys. Condens. Matter 27, N183204 (2015).
[25] Barbry, M.; Koval, P.; Marchesin, F.; Esteban, R., Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics, Nano Lett., 15, 3410 (2015) · doi:10.1021/acs.nanolett.5b00759
[26] David, C.; García de Abajo, F. J., Spatial nonlocality in the optical response of metal nanoparticles, J. Phys. Chem. C, 115, 19470 (2011) · doi:10.1021/jp204261u
[27] Ciraci, C.; Pendry, J. B.; Smith, D. R., Hydrodynamic model for plasmonics: A macroscopic approach to a microscopic problem, Chem. Phys. Chem., 14, 1109 (2013) · doi:10.1002/cphc.201200992
[28] Derkachova, A.; Kolwas, K.; Demchenko, I., Dielectric function for gold in plasmonics applications: Size dependence of plasmon resonance frequencies and damping rates for nanospheres, Plasmonics, 11, 941 (2016) · doi:10.1007/s11468-015-0128-7
[29] Mortensen, N. A.; Raza, S.; Wubs, M.; Søndergaard, T.; Bozhevolnyi, S. I., A generalized nonlocal optical response theory for plasmonic nanostructures, Nature Commun., 5, 3809 (2014) · doi:10.1038/ncomms4809
[30] Huang, Y.; Gao, L., Superscattering of light from core-shell nonlocal plasmonic nanoparticles, J. Phys. Chem. C, 118, 30170 (2014) · doi:10.1021/jp508289z
[31] Wubs, M.; Mortensen, N. A., Quantum Plasmonics (2017), Cham: Springer International, Cham
[32] Kahnert, M., Numerical solutions of the macroscopic Maxwell equations for scattering by nonspherical particles: A tutorial review, J. Quant. Spectrosc. Radiat. Transfer, 178, 22 (2016) · doi:10.1016/j.jqsrt.2015.10.029
[33] Gallinet, B.; Butet, J.; Martin, O. J. F., Numerical methods for nanophotonics: standard problems and future challenges (review), Laser Photon. Rev., 9, 577 (2015) · doi:10.1002/lpor.201500122
[34] Yurkin, M. A., Handbook of Molecular Plasmonics (2013)
[35] Taflove, A.; Hagness, S. C., Computational Electrodynamics: The Finite-Difference Time-Domain Method (2005), Boston: Artech, Boston · Zbl 0963.78001
[36] Jin, J. M., The Finite Element Method in Electromagnetics (2014), New York: Wiley-IEEE, New York · Zbl 1419.78001
[37] Busch, K.; König, M.; Niegemann, J., Discontinuous Galerkin methods in nanophotonics, Laser Photon. Rev., 5, 773 (2011) · doi:10.1002/lpor.201000045
[38] Nguyen, N. C.; Peraire, J.; Cockburn, B., Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell’s equations, J. Comput. Phys., 230, 7151 (2011) · Zbl 1230.78031 · doi:10.1016/j.jcp.2011.05.018
[39] Li, L.; Lanteri, S.; Perrussel, R., A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time harmonic Maxwell’s equation, J. Comput. Phys., 256, 563 (2014) · Zbl 1349.78069 · doi:10.1016/j.jcp.2013.09.003
[40] Khlebtsov, N. G., T-matrix method in plasmonics: An overview, J. Quant. Spectrosc. Radiat. Transfer, 123, 184 (2013) · doi:10.1016/j.jqsrt.2012.12.027
[41] Hafner, Ch.; Smajic, J.; Agio, M., Nanoclusters and Nanostructured Surfaces (2010), Valencia, California, US: Am. Sci. Publ., Valencia, California, US
[42] Eremin, Yu. A.; Sveshnikov, A. G., Mathematical models in nanooptics and biophotonics problems on the base of discrete sources method, Comput. Math. Math. Phys., 47, 262 (2007) · Zbl 1210.78004 · doi:10.1134/S0965542507020108
[43] Huang, Y. Q.; Li, J. C.; Yang, W., Theoretical and numerical analysis of a nonlocal dispersion model for light interaction with metallic nanostructures, Comput. Math. Appl., 72, 921 (2016) · Zbl 1359.78016 · doi:10.1016/j.camwa.2016.06.003
[44] Schmitt, N.; Scheid, C.; Lanteri, S., A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account nonlocal dispersion effects, J. Comput. Phys., 316, 396 (2016) · Zbl 1349.65481 · doi:10.1016/j.jcp.2016.04.020
[45] Li, L.; Lanteri, S.; Mortensen, N. A.; Wubs, M., A hybridizable discontinuous Galerkin method for solving nonlocal optical response models, Comput. Phys. Commun., 219, 99 (2017) · Zbl 1411.82052 · doi:10.1016/j.cpc.2017.05.012
[46] Zheng, X.; Kupresak, M.; Mittra, R., A boundary integral equation scheme for simulating the nonlocal hydrodynamic response of metallic antennas at deep-nanometer scales, IEEE Trans. Antennas Propag., 66, 4759 (2018) · doi:10.1109/TAP.2018.2851290
[47] www.comsol.com
[48] Eremin, Yu. A.; Wriedt, T.; Hergert, W., Analysis of the scattering properties of 3D nonspherical plasmonic nanoparticles accounting for nonlocal effects, J. Mod. Opt., 65, 1778 (2018) · doi:10.1080/09500340.2018.1459911
[49] Eremin, Yu. A.; Sveshnikov, A. G., The concept of quasi-solution to diffraction problems, Mat. Model., 6, 76 (1994) · Zbl 1075.35544
[50] Eremin, Yu. A.; Orlov, N. V.; Sveshnikov, A. G., Generalized Multipole Techniques for Electromagnetic and Light Scattering (1999), Amsterdam: Elsevier Science, Amsterdam
[51] Eremin, Yu. A.; Sveshnikov, A. G., Mathematical models in nanooptics and biophotonics based on the discrete sources method, Comput. Math. Math. Phys., 47, 262-279 (2007) · Zbl 1210.78004 · doi:10.1134/S0965542507020108
[52] Doicu, A.; Eremin, Yu.; Wriedt, T., Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (2000), New York: Academic, New York · Zbl 0948.78007
[53] Trenogin, V. A., Functional Analysis (1980), Moscow: Nauka, Moscow · Zbl 0517.46001
[54] Eremin, Yu. A.; Sveshnikov, A. G.; Skobelev, S. P., Null field method in wave diffraction problems, Comput. Math. Math. Phys., 51, 1391-1394 (2011) · Zbl 1249.78018 · doi:10.1134/S0965542511080070
[55] Kupradze, V. D., On the approximate solution of problems in mathematical physics, Russ. Math. Surv., 22, 58-108 (1967) · Zbl 0155.43204 · doi:10.1070/RM1967v022n02ABEH001210
[56] Aleksidze, M. A., Solution of Boundary Value Problems by Expansion in Nonorthogonal Functions (1978), Moscow: Nauka, Moscow · Zbl 0509.65054
[57] Popovidi, R. S.; Tsverikmazashvili, Z. S., Numerical study of a diffraction problem by a modified method of nonorthogonal series, USSR Comput. Math. Math. Phys., 17, 93-103 (1977) · Zbl 0379.35056 · doi:10.1016/0041-5553(77)90039-8
[58] R. Zaridze, G. Bit-Babik, K. Tavzarashvili, et al., “The method of auxiliary sources (MAS): Solution of propagation, diffraction, and inverse problems using MAS,” Applied Computational Electromagnetics, Ed. by N. K. Uzunoglu, K. S. Nikita, and D. I. Kaklamani, NATO ASI Ser. (Springer, Berlin, 2000), Vol. 171, p. 33.
[59] Okuno, Y.; Yasuura, K., Numerical algorithm based on the mode-matching method with a singular-smoothing procedure for analyzing edge-type scattering problems, IEEE Trans. Antennas Propag., 30, 580 (1982) · Zbl 0947.78538 · doi:10.1109/TAP.1982.1142858
[60] Matsushima, A.; Matsuda, T.; Okuno, Y., The Generalized Multipole Technique for Light Scattering (2018)
[61] Leviatan, Y., Analytic continuation considerations when using generalized formulations for scattering problems, IEEE Trans. Antennas Propag., 38, 1259 (1990) · doi:10.1109/8.56964
[62] Tsitsas, N. L.; Zouros, G. P.; Fikioris, G.; Leviatan, Y., On methods employing auxiliary sources for two-dimensional electromagnetic scattering by noncircular shapes, IEEE Trans. Antennas Propag., 66, 5443 (2018) · doi:10.1109/TAP.2018.2855963
[63] Fikioris, G.; Tsitsas, N. L., The Generalized Multipole Technique for Light Scattering (2018)
[64] Yu. A. Eremin and A. G. Sveshnikov, “Discrete sources method in electromagnetic scattering,” Usp. Sovrem. Radioelektron., No. 10, 3-40 (2003). · Zbl 0774.65087
[65] Grishina, N. V.; Eremin, Yu. A.; Sveshnikov, A. G., Analysis of scattering properties of nonaxiosymmetric substrate defects by the discrete-source method, Opt. Spectrosc., 117, 964-970 (2014) · doi:10.1134/S0030400X14110071
[66] Hafner, Ch., Post-Modern Electromagnetics Using Intelligent Maxwell Solvers (1999), Chichester: Wiley, Chichester
[67] Hafner, Ch.; Smajic, J.; Agio, M., Nanoclusters and Nanostructured Surfaces (2010), Valencia, California, US: Am. Sci. Publ., Valencia, California, US
[68] Wriedt, T.; Eremin, Yu., The Generalized Multipole Technique for Light Scattering (2018)
[69] Eremin, Yu. A.; Sveshnikov, A. G., Study of scattering by dielectric bodies based on the discrete source method, Izv. Vyssh. Uch. Zaved. Radiofiz., 28, 647 (1985)
[70] N. V. Grishina, Yu. A. Eremin, and A. G. Sveshnikov, “Analysis of extraordinary scatters based on the discrete source method,” Vestn. Mosk. Gos. Univ., Ser. Fiz. Astron., No. 2, 18 (2003).
[71] Eremin, Yu. A., Representation of fields in the discrete source method via sources in the complex plane, Dokl. Akad. Nauk, 270, 864 (1983)
[72] Grishina, N. V.; Eremin, Yu. A.; Sveshnikov, A. G., New concept of the discrete sources method in electromagnetic scattering problems, Math. Models Comput. Simul., 8, 175-182 (2016) · doi:10.1134/S2070048216020071
[73] Eremina, E.; Eremin, Yu.; Wriedt, T., Analysis of light scattering by erythrocytes based on discrete sources method, Opt. Commun., 244, 15 (2005) · doi:10.1016/j.optcom.2004.09.037
[74] Eremina, E.; Eremin, Yu.; Wriedt, T., Modeling of light scattering properties of a nanoshell on a plane interface: Influence of a core material and polarization, J. Comput. Theor. Nanosci., 5, 2186 (2008) · doi:10.1166/jctn.2008.1118
[75] Eremina, E.; Grishina, N.; Eremin, Yu., Total internal reflection microscopy with multilayered interface: Light scattering model based on discrete sources method, J. Opt. A, 8, 999 (2006) · doi:10.1088/1464-4258/8/11/011
[76] Grishina, N. V.; Eremin, Yu. A.; Sveshnikov, A. G., Extraordinary optical transmission through a conducting film with a nanometric inhomogeneity in the evanescent wave region, Dokl. Math., 79, 128-131 (2009) · Zbl 1253.78017 · doi:10.1134/S1064562409010384
[77] Grishina, N. V.; Eremin, Yu. A.; Sveshnikov, A. G., Analysis of scattering properties of embedded particles by applying the discrete sources method, Comput. Math. Math. Phys., 52, 1295-1303 (2012) · Zbl 1274.78043 · doi:10.1134/S0965542512090047
[78] Dmitriev, V. I.; Zakharov, E. V., Integral Equation Method in Computational Electrodynamics (2008), Moscow: MAKS, Moscow
[79] Yu. A. Eremin, E. V. Zakharov, and N. I. Nesmeyanova, “The method of fundamental solutions in problems of diffraction of electromagnetic waves by bodies of revolution,” in Seven Papers in Applied Mathematics (Am. Math. Soc., Providence, R.I., 1985), American Mathematical Society Translations: Ser. 2, Vol. 125, p. 51. · Zbl 0584.35081
[80] Eremin, Yu. A.; Sveshnikov, A. G., Quantum effects on optical properties of a pair of plasmonic particles separated by a subnanometer gap, Comput. Math. Math. Phys., 59, 112-120 (2019) · Zbl 1420.82029 · doi:10.1134/S0965542519010081
[81] Eremin, Yu. A.; Sveshnikov, A. G., Method for analyzing the influence of the quantum nonlocal effect on the characteristics of a plasmonic nanolaser, Dokl. Math., 101, 20-24 (2020) · Zbl 1478.78056 · doi:10.1134/S1064562420010135
[82] Eremin, Yu.; Doicu, A.; Wriedt, T., A numerical method for analyzing the near field enhancement of non-spherical dielectric-core metallic-shell particles accounting for the non-local dispersion, J. Opt. Soc. Am. A, 37, 1135 (2020) · doi:10.1364/JOSAA.392537
[83] Ruppin, R., Optical properties of small metal spheres, Phys. Rev. B, 11, 2871 (1975) · doi:10.1103/PhysRevB.11.2871
[84] Ruppin, R., Optical properties of a spatially dispersive cylinder, J. Opt. Soc. Am. B, 6, 1559 (1989) · doi:10.1364/JOSAB.6.001559
[85] Ruppin, R., Extinction properties of thin metallic nanowires, Opt. Commun., 190, 205 (2001) · doi:10.1016/S0030-4018(01)01063-X
[86] Eremin, Yu.; Doicu, A.; Wriedt, T., Discrete sources method for modeling the nonlocal optical response of a nonspherical particle dimer, J. Quant. Spectrosc. Radiat. Transfer, 217, 35 (2018) · doi:10.1016/j.jqsrt.2018.05.026
[87] C. Tserkezis, W. Yan, W. Hsieh, G. Sun, et al., “On the origin of nonlocal dumping in plasmonic monomers and dimmers,” Int. J. Mod. Phys. B 31, N17400005 (2017).
[88] Boardman, A.; Ruppin, R., The boundary conditions between two spatially dispersive media, Surface Sci., 112, 153 (1981) · doi:10.1016/0039-6028(81)90339-3
[89] Komar, P.; Gosecka, M.; Gadzinowski, M., Core-shell spheroidal microparticles with polystyrene cores and rich in polyglycidol shells, Polymer, 146, 6 (2018) · doi:10.1016/j.polymer.2018.05.039
[90] Bhatia, P.; Verma, S. S.; Sinha, M. M., Tuning the optical properties of Fe-Au core-shell nanoparticles with spherical and spheroidal nanostructures, Phys. Lett. A, 383, 2542 (2019) · doi:10.1016/j.physleta.2019.05.009
[91] Evlyukin, A.; Nerkararyan, K. V.; Bozhevolnyi, S. I., Core-shell particles as efficient broadband absorbers in infrared optical range, Opt. Express., 27, 17474 (2019) · doi:10.1364/OE.27.017474
[92] Rajkumar, S.; Prabaharan, M., Multi-functional core-shell Fe_3O_4Au nanoparticles for cancer diagnosis and therapy, Colloids Surf. B: Biointerfaces, 174, 252 (2019) · doi:10.1016/j.colsurfb.2018.11.004
[93] Eremin, Yu. A.; Sveshnikov, A. G., Discrete source method for the study of influence nonlocality on characteristics of the plasmonic nanolaser resonators, Comput. Math. Math. Phys., 59, 2164 (2019) · Zbl 1451.78035 · doi:10.1134/S0965542519100063
[94] N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, Ordinary Differential Equations (Nauka, Moscow, 1975; Mir, Moscow, 1977).
[95] Morozow, V. A., Regularization methods for ill-posed problems, SIAM Rev., 36, 505-506 (1994) · doi:10.1137/1036120
[96] Voevodin, V. V.; Kuznetsov, Yu. A., Matrices and Computations (1984), Moscow: Nauka, Moscow · Zbl 0537.65024
[97] Colton, D.; Kress, R., Integral Equation Methods in Scattering Theory (1984), New York: Wiley, New York · Zbl 0522.35001
[98] http://www.refractiveindex.info.
[99] Sidorenko, I.; Nizamov, Sh.; Hergenröder, R., Computer assisted detection and quantification of single adsorbing nanoparticles by differential surface plasmon microscopy, Microchim Acta., 183, 101 (2015) · doi:10.1007/s00604-015-1599-0
[100] D. Avşar, H. Ertürk, and M. P. Mengüç, “Plasmonic responses of metallic/dielectric core-shell nanoparticles on a dielectric substrate,” Mater. Res. Express. 6, N065006 (2019).
[101] Eremin, Yu. A., Analysis of the influence of nonlocality on characteristics of the near field of a layered particle on a substrate, Opt. Spectrosc., 128, 1500-1507 (2020) · doi:10.1134/S0030400X20090088
[102] Eremin, Yu. A.; Sveshnikov, A. G., The influence of the asymmetry of the geometry of a core-shell particle on a substrate on the optical characteristics accounting for spatial dispersion, Moscow Univ. Phys. Bull., 75, 480-487 (2020) · doi:10.3103/S0027134920050100
[103] Jerez-Hanckes, C.; Nédélec, J.-C., Asymptotics for Helmholtz and Maxwell solutions in 3-D open waveguides, Commun. Comput. Phys., 11, 629 (2012) · Zbl 1373.78074 · doi:10.4208/cicp.231209.150910s
[104] Born, M.; Wolf, E., Principles of Optics (1969), Oxford: Pergamon, Oxford · Zbl 1430.78001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.