, Volume 14, Issue 6, pp 1385–1392 | Cite as

Farfield Under Small Scattering Angle in the Rectangular Ag–Si–SiO2 Cavity

  • Shu Li
  • Yang Zou
  • Huang-qing LiuEmail author
  • Shu-gui Chong
  • Yan-ping Xiao
  • Li-qun Wen


In this paper, the farfield under small scattering angle was investigated in the rectangular Ag–Si–SiO2 cavity by FDTD. The simulation results showed that Re(E) of the farfield was related to the monitoring wavelength and was a function of monitoring wavelengths. Moreover, in the rectangular Ag–Si–SiO2 cavity, the amplitude of Re(E) changed as the silicon height d varied, and maximum amplitude A of Re(E) could be approximated as the functions of transverse length l and thickness t of silver film under small scattering angle. Re(E) was independent of the transverse length w2 and the longitudinal length d of the cavity in RCM and was also irrelevant with the dielectric constant of silver films. The amplitude A of Re(E) increased as l and t of silver film increased.


Farfield Small scattering angle Ag–Si–SiO2 Rectangular cavity 


Funding information

This work was supported by the National Natural Science Foundation of China (Grant Nos 61505052, 11074069, 61176116, and 51571088)


  1. 1.
    Zheng Z, Sun J, Wang W-Q, Yang H (2018) Classification and localization of mixed near-field and far-field sources using mixed-order statistics. Signal Process 143:134–139CrossRefGoogle Scholar
  2. 2.
    Tian Y, Lian Q, Xu H (2018) Mixed near-field and far-field source localization utilizing symmetric nested array. Digital Signal Process 73:16–23CrossRefGoogle Scholar
  3. 3.
    Sylvester J (2006) Notions of support for farfields. Inverse Prob 22(4):1273CrossRefGoogle Scholar
  4. 4.
    Lv C, Li W, Jiang X, Cao J (2014) Far-field super-resolution imaging with a planar hyperbolic metamaterial lens. EPL 105:28003CrossRefGoogle Scholar
  5. 5.
    Cheng K, Lu G, Zhong X (2017) The Poynting vector and angular momentum density of Swallowtail-Gauss beams. Opt Commun 396:58–65CrossRefGoogle Scholar
  6. 6.
    Abolhassani M (2013) Rigorous formula for electromagnetic field power based on Poynting vector. Optik - Int J Light Electron Optics 124(20):4425–4428CrossRefGoogle Scholar
  7. 7.
    Song L, Shuangying Z, Shaobin L (2005) A revised piecewise linear recursive convolution FDTD method for magnetized plasmas. Plasma Sci Technol 7(6):3122–3126CrossRefGoogle Scholar
  8. 8.
    Nakamura H, Kashima N, Takayama A, Sawada K, Tamura Y, Fujiwara S, Kubo S (2013) Optimization of a corrugated millimeter-wave waveguide and a miter bend by FDTD simulation. J Phys Conf Ser 410:012046CrossRefGoogle Scholar
  9. 9.
    Song D-J, Yang H-W, Wang G-B (2016) A research for plasma electromagnetic character using JEC-CN-FDTD algorithm based on ICCG method. Optik - Int J Light Electron Optics 127(3):1121–1125CrossRefGoogle Scholar
  10. 10.
    Christensen J, Manjavacas A, Thongrattanasiri S, Koppens FHL, García de Abajo FJ (2012) Graphene plasma waveguiding and hybridization in individual and paired nanoribbons. ACS Nano 6(1):431–440CrossRefGoogle Scholar
  11. 11.
    Bao G, Li P, Wang Y (2016) Near-field imaging with far-field data. Appl Math Lett 60:36–42CrossRefGoogle Scholar
  12. 12.
    Huang Z, Xu K, Pan D (2017) High efficient unidirectional surface plasma excitation utilizing coupling between metal-insulator-metal waveguide and metal-insulator interface. Opt Commun 389:128–132CrossRefGoogle Scholar
  13. 13.
    Wittenberg V, Rosenblit M, Sarusi G (2017) Surface plasma enhanced SWIR absorption at the ultra n-doped substrate/PbSe nanostructure layer interface. Infrared Phys Technol 84:43–49CrossRefGoogle Scholar
  14. 14.
    Dan A, Barshilia HC, Chattopadhyay K, Basu B (2017) Solar energy absorption mediated by surface plasma polaritons in spectrally selective dielectric-metal-dielectric coatings: a critical review. Renew Sust Energ Rev 79:1050–1077CrossRefGoogle Scholar
  15. 15.
    Zhai P-W, Li C, Kattawar GW, Yang P (2007) FDTD far-field scattering amplitudes: comparison of surface and volume integration methods. J Quant Spectrosc Radiat Transf 106(1–3):590–594CrossRefGoogle Scholar
  16. 16.
    Li Z, Chi C (2018) Fast computation of far-field pulse-echo PSF of arbitrary arrays for large sparse 2-D ultrasound array design. Ultrasonics 84:63–73CrossRefGoogle Scholar
  17. 17.
    Kyoung JS, Seo MA, Park HR, Ahn KJ, Kim DS (2010) Farfield detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism. Opt Commun 283(24):4907–4910CrossRefGoogle Scholar
  18. 18.
    Chen B, Basaran C (2012) Far-field modeling of Moiré interferometry using scalar diffraction theory. Opt Lasers Eng 50(8):1168–1176CrossRefGoogle Scholar
  19. 19.
    Chaumet PC, Zhang T, Sentenac A (2015) Fast far-field calculation in the discrete dipole approximation. J Quant Spectrosc Radiat Transf 165:88–92CrossRefGoogle Scholar
  20. 20.
    Bonato C, Hagemeier J, Gerace D, Thon SM, Bouwmeester D (2013) Far-field emission profiles from L3 photonic crystal cavity modes. Photonics Nanostruct Fundam Appl 11(1):37–47CrossRefGoogle Scholar
  21. 21.
    Arca A, Clark M, Somekh M (2010) Surface plasmon resonator: design, construction, and observation in the. J Appl Phys 108:103109CrossRefGoogle Scholar
  22. 22.
    Li S, Liu HQ, Liu L-h, Qi-Lin XZ (2018) Effect of silver film thickness on the surface plasma resonance in the rectangular Ag-Si-SiO2 cavity. J Phys Commun 2:055024CrossRefGoogle Scholar
  23. 23.
    Dong Xiang (2012) Optical propagation properties of subwavelength metal gratings and plasma waveguides, Doctoral Dissertations (Hunan University):5Google Scholar
  24. 24.
    Zhong Shunshi, Niu Maode (1995) Theoretical basis of electromagnetic field, Xi'an Electronic and Science University PressGoogle Scholar
  25. 25.
    Jerry D, Wilson Anthony J, Buffa Bo Lou (2003) College Physics (5th Edition), Prentice HallGoogle Scholar
  26. 26.
    Paul Peter Urone (1998) College Physics, Brooks/Cole Publishing CompanyGoogle Scholar
  27. 27.
    Raymond A, Serway J S (1985) College Physics, Saunders College PublishingGoogle Scholar
  28. 28.
    William H. Hayt Jr., John A. Buck (2014), Engineering electromagnetic, Beijing: Tsinghua University PressGoogle Scholar
  29. 29.
    Jinau Kong (2000) Electromagnetic wave theory 2, higher education pressGoogle Scholar
  30. 30.
    Ulaby FT (2002) Fundamentals of applied electromagnetic. Science Press, BeijingGoogle Scholar
  31. 31.
    Zhang S, Li G-C, Chen Y, Zhu X (2016) Pronounced fano resonance in single gold split nanodisks with 15 nm split gaps for intensive second harmonic generation. ACS Nano 10(12):11105–11114CrossRefGoogle Scholar
  32. 32.
    Yang Z-J (2015) Coherent energy transfers between orthogonal radiant and weakly radiant plasmonic nanorod resonators. J Phys Chem C 119:26079–26085CrossRefGoogle Scholar
  33. 33.
    Gao W, Shu J, Qiu C, Xu Q (2012) Excitation of plasmonic waves in graphene by guided-mode resonances. Acsnano 6(9):7806–7813Google Scholar
  34. 34.
    Montgomery PC, Serio B, Anstotz F, Montaner D (2013) Farfield optical nanoscopy: how far can you go in nanometric characterization without resolving all the details. Appl Surf Sci 281:89–95CrossRefGoogle Scholar
  35. 35.
    Bozhevolnyia SI, Pedersenb K, Skettrupc T, Xiangsu Z, Belmontec M (1998) Far-and near-field second-harmonic imaging of ferroelectric domain walls. Opt Commun 152(4–6):221–224CrossRefGoogle Scholar
  36. 36.
    Wan J, Rybin O, Shulga S (2018) Farfield focusing for a microwave patch antenna with composite substrate. Results in Physics 8:971–976CrossRefGoogle Scholar
  37. 37.
    Sun W, Hu Y, Weimer C, Ayers K, Lee T (2017) A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics. J Quant Spectrosc Radiat Transf 188:200–213CrossRefGoogle Scholar
  38. 38.
    Muller J, Parent G, Fumeron S, Jeandel G, Lacroix D (2011) Near-field and far-field modeling of scattered surface waves, application to the apertureless scanning near-field optical microscopy. J Quant Spectrosc Radiat Transf 112(7):1162–1169CrossRefGoogle Scholar
  39. 39.
    Firoozy N, Tavakoli A (2013) Buried crack reconstruction through far-field electromagnetic inverse scattering measurement. NDT & E International 54:84–90CrossRefGoogle Scholar
  40. 40.
    Terakawa M, Takeda S, Tanaka Y, Obara G, Obara M (2012) Enhanced localized near field and scattered farfield for surface nanophotonics applications. Prog Quantum Electron 36(1):194–271CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Physics & ElectronicsHunan UniversityChangshaChina
  2. 2.ChangshaChina

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