Skip to main content
Log in

Homogenization of nanowire-based composites with anisotropic unit-cell and layered substructure

  • Plasmonics, Photonics, and Metamaterials Research Letter
  • Published:
MRS Communications Aims and scope Submit manuscript

Abstract

We analyze the optical properties of composite materials that combine nanowire and nanolayer platforms. We revisit effective-medium theory (EMT) description of wire materials with high filling fraction positioned in anisotropic unit cells and present a simple numerical technique to extend Maxwell-Garnett formalism in this limit. We also demonstrate that the resulting EMT can be combined with transfer-matrix technique to adequately describe photonic band gap behavior, previously observed in epitaxially grown semiconductor multilayer nanowires.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  1. H.N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V.M. Menon: Topological transitions in metamaterials. Science 336, 205–209 (2012).

    Article  CAS  Google Scholar 

  2. O. Kidwai, S.V. Zhukovsky, and J.E. Sipe: Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation. Opt. Lett. 36, 2530–2532 (2011).

    Article  Google Scholar 

  3. C.L. Cortes, W. Newman, S. Molesky, and Z. Jacob: Quantum nanopho-tonics using hyperbolic metamaterials. J. Opt. 14, 063001 (2012).

    Article  Google Scholar 

  4. B.M. Wells, A.V. Zayats, and V.A. Podolskiy: Nonlocal optics of plasmonic nanowire metamaterials. Phys. Rev. B 89, 035111 (2014).

    Article  Google Scholar 

  5. A.V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G.A. Wurtz, R. Atkinson, R. Pollard, V.A. Podolskiy, and A.V. Zayats: Plasmonic nano-rod metamaterials for biosensing. Nat. Mater. 8, 867–871 (2009).

    Article  CAS  Google Scholar 

  6. V.A. Podolskiy, P. Ginzburg, B. Wells, and A.V. Zayats: Light emission in nonlocal plasmonic metamaterials. Faraday Discuss. 178, 61–70 (2015).

    Article  CAS  Google Scholar 

  7. W. Cai, U.K. Chettiar, A.V. Kildishev, and V.M. Shalaev: Optical cloaking with metamaterials. Nat Photonics 1, 224–227 (2007).

    Article  CAS  Google Scholar 

  8. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A.M. Stacy, and X. Zhang: Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930–930 (2008).

    Article  CAS  Google Scholar 

  9. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar: Hyperbolic metamaterials. Nat. Photonics 7, 948–957 (2013).

    Article  CAS  Google Scholar 

  10. T. Kuykendall, P. Ulrich, S. Aloni, and P. Yang: Complete composition tunability of InGaN nanowires using a combinatorial approach. Nat. Mater. 6, 951–956 (2007).

    Article  CAS  Google Scholar 

  11. Y.L. Chang, J.L. Wang, F. Li, and Z. Mi: High efficiency green, yellow, and amber emission from InGaN/GaN dot-in-a-wire heterostructures on Si (111). Appl. Phys. Lett. 96, 013106 (2010).

    Article  Google Scholar 

  12. Y. Li, F. Qian, J. Xiang, and C.M. Lieber: Nanowire electronic and optoelectronic devices. Mater. Today 5, 18–27 (2006).

    Article  Google Scholar 

  13. K. Bertness, N. Sanford, and A.V. Davydov: GaN nanowires grown by molecular beam epitaxy. IEEE J. Sel. Top. Quantum Electron. 17, 847–858 (2011).

    Article  CAS  Google Scholar 

  14. W. Guo, M. Zhang, A. Banerjee, and P. Bhattacharya: Catalyst-free InGaN/ GaN nanowire light emitting diodes grown on (001) silicon by molecular beam epitaxy. Nano Lett. 10, 3355–3359 (2010).

    Article  CAS  Google Scholar 

  15. M. Fickenscher, T. Shi, H.E. Jackson, L.M. Smith, J.M. Yarrison-Rice, C. Zheng, P. Miller, J. Etheridge, B.M. Wong, Q. Gao, and S. Deshpande: Optical, structural, and numerical investigations of GaAs/AIGaAs core-multishell nanowire quantum well tubes. Nano Lett. 13, 1016–1022 (2013).

    Article  CAS  Google Scholar 

  16. F. Qian, Y. Li, S. Gradecak, H.G. Park, Y. Dong, Y. Ding, Z.L. Wang, and C.M. Lieber: Multi-quantum-well nanowire heterostructures for wavelength-controlled lasers. Nat. Mater. 7, 701–706 (2008).

    Article  CAS  Google Scholar 

  17. T. Frost, S. Jahangir, E. Stark, S. Deshpande, A. Hazari, C. Zhao, B.S. Ooi, and P. Bhattacharya: Monolithic electrically injected nanowire array edge-emitting laser on (001) silicon. Nano Lett. 14, 4535–4541 (2014).

    Article  CAS  Google Scholar 

  18. S. Arafin, X. Liu, and Z. Mi: Review of recent progress of Ill-nitride nanowire lasers. J. Nanophotonics 7, 074599–074599 (2013).

    Article  Google Scholar 

  19. S.M. Rytov: Electromagnetic properties of a finely stratified medium. Sov. Phys. - JETP 2.3, 466–475 (1956).

    Google Scholar 

  20. P. Yeh, A. Yariv, and C.S. Hong: Electromagnetic propagation in periodic stratified media. I. General theory. JOSA 67, 423–438 (1977).

    Article  Google Scholar 

  21. J. Heo, Z. Zhou, W. Guo, B.S. Ooi, and P. Bhattacharya: Characteristics of AIN/GaN nanowire Bragg mirror grown on (001) silicon by molecular beam epitaxy. Appl. Phys. Lett. 103, 181102 (2013).

    Article  Google Scholar 

  22. J.C. Maxwell Garnett: Colours in metal glasses, in metallic films, and in metallic solutions. II. Philos. Trans. R. Soc. Lond. A 205, 237–288 (1906).

    Article  Google Scholar 

  23. W.T. Perrins, D.R. McKenzie, and R.C. McPhedran: Transport properties of regular arrays of cylinders. Proc. R. Soc. Lond. A 369, 207–225 (1979). The Royal Society.

    Article  CAS  Google Scholar 

  24. R.E. Meredith and C.W. Tobias: Resistance to potential flow through a cubical array of spheres. J. Appl. Phys. 31, 1270–1273 (1960).

    Article  Google Scholar 

  25. J. Elser, R. Wangberg, V.A. Podolskiy, and E.E. Narimanov: Nanowire metamaterials with extreme optical anisotropy. Appl. Phys. Lett. 89, 261102 (2006).

    Article  Google Scholar 

  26. L. Rayleigh: LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium. Lond. Edinb. Dublin Philos. Mag. J. Sci. 34, 481–502 (1892).

    Article  Google Scholar 

  27. G.W. Milton: The Theory of Composites (Cambridge University Press, Cambridge, UK, 2002).

    Book  Google Scholar 

  28. Y.A. Godin: Effective complex permittivity tensor of a periodic array of cylinders. J. Math. Phys. 54, 053505 (2013).

    Article  Google Scholar 

  29. COMSOL Multiphysics® v.4.4. www.comsol.com. COMSOL AB, Stockholm, Sweden.

Download references

Acknowledgment

This work was partially supported by the US Army research office (Grant no. W911NF-12-1-0533).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Brian M. Wells.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wells, B.M., Guo, W. & Podolskiy, V.A. Homogenization of nanowire-based composites with anisotropic unit-cell and layered substructure. MRS Communications 6, 23–29 (2016). https://doi.org/10.1557/mrc.2016.5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/mrc.2016.5

Navigation