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A Drude-Two-CP-FDTD method for Drude-critical points model of metal nanofilms

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Abstract

Based on Drude-critical points (Drude-Two-CP) model for a dispersive media, a finite-difference time-domain (FDTD) method for metal nanofilms is proposed. By establishing the corresponding relationship between Drude-Two-CP model and Drude–Lorentz model, the conversion coefficients between the two models are calculated. And we modify the Drude-Two-CP model into the form of standard Lorentz model. The transformation relationship between the two models is conducive to the modular programming of FDTD. Formula deduction and calculation results show that Drude-Two-CP model has higher fitting accuracy and fitting formulas are more complex. Using the proposed FDTD method, we have calculated the reflection, transmission and extinction coefficients of gold and aluminium nanofilms. The results show that the FDTD results are in good agreement with those of Drude-Two-CP model, which are better than those of Drude–Lorentz model. Therefore, the Drude-Two-CP-FDTD method proposed in this paper is helpful for improving the accurate modelling and calculation of nano-optical structures.

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References

  1. J. Jacob, A. Babu, G. Mathew, V. Mathew, Propagation of surface plasmon polaritons in anisotropic MIM and IMI structures. Superlattices Microstruct. 44(3), 282–290 (2008)

    Article  ADS  Google Scholar 

  2. C. **ao, Z. Chen, M. Qin, D. Zhang, L. Fan, SPPs characteristics of Ag/SiO2 sinusoidal nano-grating in SERS application. Optik 168, 650–659 (2018)

    Article  ADS  Google Scholar 

  3. Q. Shang, S. Zhang, Z. Liu, J. Chen, P. Yang, C. Li, W. Li, Y. Zhang, Q. **ong, X. Liu, Q. Zhang, Surface plasmon enhanced strong exciton-photon coupling in hybrid inorganic-organic perovskites nanowires. Nano Lett. 18(6), 3335–3343 (2018)

    Article  ADS  Google Scholar 

  4. K.-L. Lee, C.-C. Chang, M.-L. You, M.-Y. Pan, P.-K. Wei, Enhancing surface sensing sensitivity of metallic nanostructures using blue-shifted surface plasmon mode and fano resonance. Sci. Rep. 8, 1–12 (2018)

    Article  ADS  Google Scholar 

  5. B. Huang, Z. Luo, W. **a, H. Yang, G. He, Transmission of light through slits array in a metal-insulator-metal structure. Opt. Commun. 383, 165–168 (2017)

    Article  ADS  Google Scholar 

  6. A. Fantoni, J. Costa, M. Fernandes, Y. Vygranenko, M. Vieira, Theory and FDTD simulations of an amorphous silicon planar waveguide structure suitable to be used as a surface plasmon resonance biosensor. Opt. Pura Y Apl. 53(2), 1–8 (2020)

    Article  Google Scholar 

  7. G.-Y. Yao, Q.-L. Liu, Z.-Y. Zhao, Studied localized surface plasmon resonance effects of Au Nanoparticles on TiO\(_{\rm 2}\) by FDTD simulations. Catalysts 8(6), 236–15 (2018)

    Google Scholar 

  8. Z. Zeng, Y. Liu, J. We, Recent advances in surface-enhanced raman spectroscopy (SERS): Finite-difference time-domain (FDTD) method for SERS and sensing applications. Trends Anal. Chem. 75, 162–173 (2016)

    Article  Google Scholar 

  9. M. Rana, B. Hossain, R. Islam, Y. G. Guo, Surface plasmon polariton propagation modeling for graphene parallel pair sheets using FDTD, IEEE International Conference on Applied Superconductivity and Electromagnetic Devices. (IEEE, 2015), pp. 179-180

  10. B.H. Jung, Z. Mei, T.K. Sarkar, M. Salazar-Palma, Analysis of transient wave propagation in an arbitrary frequency-dispersive media using the associated laguerre functions in the FDTD-MOD method. Microwave Opt. Technol. Lett. 54(4), 925–930 (2012)

    Article  Google Scholar 

  11. I. Valuev, A. Deinega, S. Belousov, Implementation of the iterative finite-difference time-domain technique for simulation of periodic structures at oblique incidence. Comput. Phys. Commun. 185(4), 1273–1281 (2014)

    Article  ADS  Google Scholar 

  12. H.-S. Ee, K.-D. Song, S.-K. Kim, H.-G. Park, Finite-difference time-domain algorithm for quantifying light absorption in silicon nanowires. Israel J. Chem. 52, 1027–1036 (2012)

    Article  Google Scholar 

  13. M. Benavides-Cruz, C. Calderón-Ramón, J.F. Gomez-Aguilar, M. Rodríguez-Achach, I. Cruz-Orduña, J.R. Laguna-Camacho, L.J. Morales-Mendoza, M. Enciso-Aguilar, H. Pé rez-Meana, J.E. Escalante-Martínez, J.E. López-Calderón, G. Juárez-Morales, Numerical simulation of metallic nanostructures interacting with electromagnetic fields using the Lorentz–Drude model and FDTD method. Int. J. Modern Phys. C 27(4), 1650043-10 (2016)

    Article  ADS  Google Scholar 

  14. O. Ramadan, Systematic wave-equation finite difference time domain formulations for modeling electromagnetic wave-propagation in general linear and nonlinear dispersive materials. Int. J. Modern Phys. C 26(4), 1550046-15 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. P. Chen, C.-H. Wang, J.-R. Ho, A lattice boltzmann model for electromagnetic waves propagating in a one-dimensional dispersive medium. Comput. Math. Appl. 65(6), 961–973 (2013)

    Article  MathSciNet  Google Scholar 

  16. J.M. McMahon, S.K. Gray, G.C. Schatz, Calculating nonlocal optical properties of structures with arbitrary shape. Phys. Rev. B 82(3), 035423-12 (2010)

    Article  ADS  Google Scholar 

  17. G.M. Aqeel, A. Syed Qaisar A. Naqvi, Study of scattering from a periodic grating structure using Lorentz–Drude model and Chandezon method. Optik 133, 9–16 (2017)

  18. W.H.P. Pernice, F.P. Payne, D.F.G. Gallagher, An FDTD method for the simulation of dispersive metallic structures. Opt. Quantum Electron. 38(9), 843–856 (2006)

    Google Scholar 

  19. A.D. Rakic, A.B. Djurisic, J.M. Elazar, M.L. Majewski, Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 37(22), 5271–5283 (1998)

    Article  ADS  Google Scholar 

  20. A. Vial, Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method. J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007)

    Article  ADS  Google Scholar 

  21. P.G. Etchegoin, E.C. Le Ru, M. Meyer, An analytic model for the optical properties of gold. J. Chem. Phys. 125(16), 164705-3 (2006)

    Article  ADS  Google Scholar 

  22. R. Letizia, D. Pinto, S.S.A. Obayya, Accurate analysis of plasmonic devices with a new drude two critical points MRTD method. IEEE Photonics Technol. Lett. 24(18), 1587–1590 (2012)

    Article  ADS  Google Scholar 

  23. A. Deinega, S. John, Effective optical response of silicon to sunlight in the finite-difference time-domain method. Opt. Lett. 37(1), 112–114 (2012)

    Article  ADS  Google Scholar 

  24. J.W. You, E. Threlfall, D.F.G. Gallagher, N.C. Panoiu, Computational analysis of dispersive and nonlinear 2D materials by using a GS-FDTD method. J. Opt. Soc. Am. B 35(11), 2754–2763 (2018)

    Article  ADS  Google Scholar 

  25. H. Wang, W. Bo, Z. Huang, W. **anliang, A symplectic FDTD algorithm for the simulations of lossy dispersive materials. Comput. Phys. Commun. 185(3), 862–872 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Vial, T. Laroche, Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method. J. Phys. D : Appl. Phys. 40(22), 7152–7158 (2007)

    Article  ADS  Google Scholar 

  27. W. Qihong, Determination of extinction coefficient of optical thin films from the special absorption (in Chinese). Acta Opt. Sinica 8(2), 157–161 (1988)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the Natural Science Foundation of Hebei Province Youth Fund (Grant No. F2019111025) and the China Agricultural Science and Education Fund (Grant No. NKJ201802040).

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Correspondence to Hong-Wei Yang.

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Hong-Wei Yang and Wan-Chun Tang contributed equally to this work.

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Liu, JX., Jiang, Y., Ming, LH. et al. A Drude-Two-CP-FDTD method for Drude-critical points model of metal nanofilms. Eur. Phys. J. Plus 135, 805 (2020). https://doi.org/10.1140/epjp/s13360-020-00824-8

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