Advertisement

Topology optimization of metal nanostructures for localized surface plasmon resonances

  • Yongbo Deng
  • Zhenyu Liu
  • Chao Song
  • Peng Hao
  • Yihui Wu
  • Yongmin Liu
  • Jan G Korvink
BRIEF NOTE

Abstract

This note presents an inverse design methodology of metal nanostructures for localized surface plasmon resonances, based on the topology optimization approach. Using the proposed method, determination of the metal distribution in nanostructures is implemented for surface enhanced Raman spectroscopy to maximize the enhancement factor. The obtained results demonstrate that the outlined approach can be used to design metal nanostructure with resonant peak and significant enhancement factor at specified incident wavelength, and to control the shift of the resonant peak by topologically optimizing the nanostructure.

Keywords

Topology optimization Metal nanostructure Localized surface plasmon resonances Enhancement factor 

Notes

Acknowledgments

This work is supported by the Open Fund of SKLAO, the National Natural Science Foundation of China (No. 51405465, 51275504), Science and Technology Development Plane of JiLin Province (No. 20140519007JH) and the National High Technology Program of China (No. 2015AA042604).

References

  1. Aizprurua J, Hanarp P, Sutherland DS, Kall M, Bryant GW, Garcia de Agajo FJ (2003) Optical properties of gold nanorings. Phys Rev Lett 90:057401CrossRefGoogle Scholar
  2. Andkjær J, Sigmund O (2011) Topology optimized low-contrast all-dielectric optical cloak. Appl Phys Lett 98:021112CrossRefGoogle Scholar
  3. Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRefGoogle Scholar
  4. Bendsøe M, Sigmund O (2003) Topology optimization-theory methods and applications. Springer, BerlinzbMATHGoogle Scholar
  5. Borrvall T, Petersson J (2003) Topology optimization of fluids in Stokes flow. Int J Numer Methods Fluids 41:77–107MathSciNetCrossRefzbMATHGoogle Scholar
  6. Brongersma ML, Hartman JW, Atwater HA (2000) Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit. Phys Rev B 62:R16356CrossRefGoogle Scholar
  7. Cao YWC, Jin RC, Mirkin CA (2002) Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection. Science 297:1536CrossRefGoogle Scholar
  8. Deng Y, Liu Z, Zhang P, Liu Y, Wu Y (2011) Topology optimization of unsteady incompressible Navier-Stokes flows. J Comput Phys 230:6688–6708MathSciNetCrossRefzbMATHGoogle Scholar
  9. Deng Y, Liu Z, Song C, Wu J, Liu Y, Wu Y (2015) Topology optimization-based computational design methodology for surface plasmon polaritons. Plasmonics 10:569–583Google Scholar
  10. Elghanian R, Storhoff JJ, Mucic RC, Letsinger RL, Mirkin CA (1997) Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles. Science 227:1078CrossRefGoogle Scholar
  11. Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254MathSciNetCrossRefzbMATHGoogle Scholar
  12. Johnson PB, Christy RW (1972) Optical constants of the noble metals. Phys Rev B 6:4370–4379CrossRefGoogle Scholar
  13. Kottman JD, Martin OJF, Smith DR, Schultz S (2001) Dramatic localized electromagnetic enhancement in plasmon resonant nanowires. Chem Phys Lett 341:1CrossRefGoogle Scholar
  14. Lazarov B, Sigmund O (2011) Filters in topology optimization as a solution to Helmholtz type differential equations. Int J Numer Methods Eng 86:765–781MathSciNetCrossRefzbMATHGoogle Scholar
  15. Lindquist NC, Nagpal P, Lesuflfleur A, Norris DJ, Oh SH (2010) Three-dimensional plasmonic nanofocusing. Nano lett 10:1369CrossRefGoogle Scholar
  16. Liu Y, Zentgraf T, Bartal G, Zhang X (2010) Transformational plasmon optics. Nano Lett 10:1991–1997CrossRefGoogle Scholar
  17. Lu Y, Liu GL, Kim J, Mejia YX, Lee LP (2005) Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect. Nano Lett 5:119CrossRefGoogle Scholar
  18. Mandal P, Ramakrishna SA (2011) Dependence of surface enhanced Raman scattering on the plasmonic template periodicity. Opt Lett 36:3705–3707CrossRefGoogle Scholar
  19. Miao X, Lin LY (2007) Large dielectrophoresis force and torque induced by localized surface plasmon resonance of Au nanoparticle array. Opt Lett 32:295–297CrossRefGoogle Scholar
  20. Mock JJ, Smith DR, Schultz S (2003) Local refractive index dependence of plasmon resonance spectra from individual nanoparticles. Nano Lett 3:485CrossRefGoogle Scholar
  21. Moskovits M (1985) Surface-enhanced spectroscopy. Rev Mod Phys 57:783CrossRefGoogle Scholar
  22. Novotny L, Bain RX, Xie XS (1997) Theory of nanometric optical tweezers. Phys Rev Lett 79:645CrossRefGoogle Scholar
  23. Ricard D, Roussignol P, Flytzanis C (1985) Surface-mediated enhancement of optical phase conjugation in metal colloids. Opt Lett 10:511CrossRefGoogle Scholar
  24. Sarid D, Challener W (2010) Modern introduction to surface plasmons: theory, Mathematica modelling and applications. Cambridge University PressGoogle Scholar
  25. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424CrossRefGoogle Scholar
  26. Stockman MI (2004) Nanofocusing of optical energy in tapered plasmonic waveguides. Phys Rev Lett 93:137404CrossRefGoogle Scholar
  27. Su KH, Wei QH, Zhang X, Mock JJ, Smith DR, Schultz S (2003) Interparticle coupling effects on plasmon resonances of nanogold particles. Nano Lett 3:1087–1090CrossRefGoogle Scholar
  28. Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefzbMATHGoogle Scholar
  29. Vogel MW, Gramotnev DK (2008) Optimization of plasmon nano-focusing in tapered metal rods. J Nanophotonics 2:021852CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yongbo Deng
    • 1
  • Zhenyu Liu
    • 1
  • Chao Song
    • 1
  • Peng Hao
    • 1
  • Yihui Wu
    • 1
  • Yongmin Liu
    • 2
    • 3
  • Jan G Korvink
    • 4
  1. 1.State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP)Chinese Academy of SciencesChangchunChina
  2. 2.Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP)Chinese Academy of SciencesChangchunChina
  3. 3.Department of Mechanical and Industrial EngineeringNortheastern UniversityBostonUSA
  4. 4.Department of Electrical and Computer EngineeringNortheastern UniversityBostonUSA

Personalised recommendations