Abstract
The discrete source method is generalized so as to investigate the nonlocal effects in multilayered particles on a substrate. The scheme for constructing an approximate solution and the corresponding numerical algorithm are described in detail. The developed approach is used to study the optical characteristics of 3D cavities of plasmonic nanolasers. It is shown that the amplitude of surface plasmon resonance and the amplification factor of the near-field intensity are reduced significantly when the nonlocal effects are taken into account. It is also shown that the amplification factor can be increased by more than twice by varying the material and thickness of the cavity shell and the direction of the incident wave.
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REFERENCES
M. Pelton and G. Bryant, Introduction to Metal-Nanoparticle Plasmonics (Wiley, New York, 2013).
A. Polman and H. A. Atwater, “Plasmonics: Optics at the nanoscale,” Mater. Today 8 (1), 56 (2005).
D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
M. I. Stockman, “Nanoplasmonic sensing and detection,” Science 348, 287–288 (2015).
J. N. Anker, W. P. Hall, O. Lyandres, et al., “Biosensing with plasmonic nanosensors,” Nat. Mater 7, 442–453 (2008).
D. Xu, X. Xiong, L. Wu, et al., “Quantum plasmonics: New opportunity in fundamental and applied photonics. Review,” Adv. Opt. Photonics 10 (4), 703–756 (2018).
M. I. Stockman, K. Kneipp, S. I. Bozhevolnyi, et al., “Roadmap on plasmonics,” J. Opt. 20 (043001) (2018).
R. F. Oulton, “Surface plasmon lasers: Sources of nanoscopic light. Review,” Mater. Today 15 (1–2), 26–34 (2012).
M. Premaratne and M. Stockman, “Theory and technology of SPASERs: Review,” Adv. Opt. Photonics 9 (1), 79–128 (2017).
V. I. Balykin, “Plasmonic nanolaser: Current state and prospects,” Phys. Usp. 61, 846–879 (2018).
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).
H.-P. Solowan and C. Kryschi, “Facile design of a plasmonic nanolaser,” Condens. Mat. 2 (8), 1–7 (2017).
M. A. Noginov, G. Zhu, A. M. Belgrave, et al., “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1113 (2009).
A. D. Phan, D. T. Nga, and N. A. Viet, “Theoretical model for plasmonic photothermal response of gold nanostructures solutions,” Opt. Commun. 410, 108–111 (2018).
Y. Jeong, Y.-M. Kook, K. Lee, and W.-G. Koh, “Metal enhanced fluorescence (MEF) for biosensors: General approaches and a review of recent developments,” Biosensors Bioelectron. 111, 102–116 (2018).
T. Dong, Y. Shi, H. Liu, F. Chen, et al., “Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects,” J. Phys. D: Appl. Phys. 50 (495302) (2017).
A. I. Fernandez-Dominguez, A. Wiener, F. J. Garcia-Vidal, et al., “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108 (106802) (2012).
N. A. Mortensen, S. Raza, M. Wubs, et al., “A generalized nonlocal optical response theory for plasmonic nanostructures,” Nat. Commun. 5 (3809) (2014).
G. Toscano, J. Straubel, A. Kwiatkowski, et al., “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6 (7132) (2015).
M. Barbry, P. Koval, F. Marchesin, et al., “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15 (3410) (2015).
M. Wubs and A. Mortensen, “Nonlocal response in plasmonic nanostructures,” Quantum Plasmonics, Ed. by S. I. Bozhevolnyi (Springer, Switzerland, 2017), pp. 279–302.
Yu. A. Eremin and A. G. Sveshnikov, “Mathematical models in nanooptics and biophotonics based on the discrete sources method,” Comput. Math. Math. Phys. 47 (2), 262–279 (2007).
E. Ringe, B. Sharma, R.-I. Henry, et al., “Single nanoparticle plasmonics,” Phys. Chem. Chem. Phys. 15 (4110) (2013).
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), 572–580 (2018).
Yu. A. Eremin and A. G. Sveshnikov, “Analysis method for the scattering properties of plasmonic particles on a substrate accounting for nonlocal effects,” Dokl. Math. 96 (3), 641–645 (2017).
C. Jerez-Hanckes and J.-C. Nedelec, “Asymptotics for Helmholtz and Maxwell solutions in 3-D open waveguides,” Research Report No. 2010-07 (Swiss Federal Inst. Technol., Zurich, 2010).
N. Schmitt, C. Scheid, S. Lanteri, A. Moreau, and J. Viquerat, “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, 396–415 (2016).
M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1969).
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).
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Eremin, Y.A., Sveshnikov, A.G. Discrete Source Method for the Study of Influence Nonlocality on Characteristics of the Plasmonic Nanolaser Resonators. Comput. Math. and Math. Phys. 59, 2164–2172 (2019). https://doi.org/10.1134/S0965542519100063
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DOI: https://doi.org/10.1134/S0965542519100063