Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-30T03:52:26.588Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  15 March 2016

Brian M. Wells ,
Wei Guo  and
Viktor A. Podolskiy
Brian M. Wells*
Affiliation:
Department of Physics, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117, USA Department of Physics and Applied Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA
Wei Guo
Affiliation:
Department of Physics and Applied Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA
Viktor A. Podolskiy
Affiliation:
Department of Physics and Applied Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA
*
Address all correspondence to Brian M. Wells at[email protected]
Get access

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.

Type
Plasmonics, Photonics, and Metamaterials Research Letters
Information
MRS Communications , Volume 6 , Issue 1 , March 2016 , pp. 23 - 29
Copyright
Copyright © Materials Research Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Krishnamoorthy, H.N., Jacob, Z., Narimanov, E., Kretzschmar, I., and Menon, V.M.: Topological transitions in metamaterials. Science 336, 205–209 (2012).CrossRefGoogle ScholarPubMed
2. Kidwai, O., Zhukovsky, S.V., and Sipe, J.E.: Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation. Opt. Lett. 36, 2530–2532 (2011).CrossRefGoogle ScholarPubMed
3. Cortes, C.L., Newman, W., Molesky, S., and Jacob, Z.: Quantum nanophotonics using hyperbolic metamaterials. J. Opt. 14, 063001 (2012).CrossRefGoogle Scholar
4. Wells, B.M., Zayats, A.V., and Podolskiy, V.A.: Nonlocal optics of plasmonic nanowire metamaterials. Phys. Rev. B 89, 035111 (2014).CrossRefGoogle Scholar
5. Kabashin, A.V., Evans, P., Pastkovsky, S., Hendren, W., Wurtz, G.A., Atkinson, R., Pollard, R., Podolskiy, V.A., and Zayats, A.V.: Plasmonic nanorod metamaterials for biosensing. Nat. Mater. 8, 867–871 (2009).CrossRefGoogle ScholarPubMed
6. Podolskiy, V.A., Ginzburg, P., Wells, B., and Zayats, A.V.: Light emission in nonlocal plasmonic metamaterials. Faraday Discuss. 178, 61–70 (2015).CrossRefGoogle ScholarPubMed
7. Cai, W., Chettiar, U.K., Kildishev, A.V., and Shalaev, V.M.: Optical cloaking with metamaterials. Nat. Photonics 1, 224–227 (2007).CrossRefGoogle Scholar
8. Yao, J., Liu, Z., Liu, Y., Wang, Y., Sun, C., Bartal, G., Stacy, A.M., and Zhang, X.: Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930–930 (2008).CrossRefGoogle ScholarPubMed
9. Poddubny, A., Iorsh, I., Belov, P., and Kivshar, Y.: Hyperbolic metamaterials. Nat. Photonics 7, 948–957 (2013).CrossRefGoogle Scholar
10. Kuykendall, T., Ulrich, P., Aloni, S., and Yang, P.: Complete composition tunability of InGaN nanowires using a combinatorial approach. Nat. Mater. 6, 951–956 (2007).CrossRefGoogle ScholarPubMed
11. Chang, Y.L., Wang, J.L., Li, F., and Mi, Z.: High efficiency green, yellow, and amber emission from InGaN/GaN dot-in-a-wire heterostructures on Si (111). Appl. Phys. Lett. 96, 013106 (2010).CrossRefGoogle Scholar
12. Li, Y., Qian, F., Xiang, J., and Lieber, C.M.: Nanowire electronic and optoelectronic devices. Mater. Today 9, 18–27 (2006).CrossRefGoogle Scholar
13. Bertness, K., Sanford, N., and Davydov, A.V.: GaN nanowires grown by molecular beam epitaxy. IEEE J. Sel. Top. Quantum Electron. 17, 847–858 (2011).CrossRefGoogle Scholar
14. Guo, W., Zhang, M., Banerjee, A., and Bhattacharya, P.: Catalyst-free InGaN/GaN nanowire light emitting diodes grown on (001) silicon by molecular beam epitaxy. Nano Lett. 10, 3355–3359 (2010).CrossRefGoogle ScholarPubMed
15. Fickenscher, M., Shi, T., Jackson, H.E., Smith, L.M., Yarrison-Rice, J.M., Zheng, C., Miller, P., Etheridge, J., Wong, B.M., Gao, Q., and Deshpande, S.: Optical, structural, and numerical investigations of GaAs/AlGaAs core–multishell nanowire quantum well tubes. Nano Lett. 13, 1016–1022 (2013).CrossRefGoogle ScholarPubMed
16. Qian, F., Li, Y., Gradečak, S., Park, H.G., Dong, Y., Ding, Y., Wang, Z.L., and Lieber, C.M.: Multi-quantum-well nanowire heterostructures for wavelength-controlled lasers. Nat. Mater. 7, 701–706 (2008).CrossRefGoogle ScholarPubMed
17. Frost, T., Jahangir, S., Stark, E., Deshpande, S., Hazari, A., Zhao, C., Ooi, B.S., and Bhattacharya, P.: Monolithic electrically injected nanowire array edge-emitting laser on (001) silicon. Nano Lett. 14, 4535–4541 (2014).CrossRefGoogle ScholarPubMed
18. Arafin, S., Liu, X., and Mi, Z.: Review of recent progress of III-nitride nanowire lasers. J. Nanophotonics 7, 074599–074599 (2013).CrossRefGoogle Scholar
19. Rytov, S.M.: Electromagnetic properties of a finely stratified medium. Sov. Phys. – JETP 2.3, 466–475 (1956).Google Scholar
20. Yeh, P., Yariv, A., and Hong, C.S.: Electromagnetic propagation in periodic stratified media. I. General theory. JOSA 67, 423–438 (1977).CrossRefGoogle Scholar
21. Heo, J., Zhou, Z., Guo, W., Ooi, B.S., and Bhattacharya, P.: Characteristics of AlN/GaN nanowire Bragg mirror grown on (001) silicon by molecular beam epitaxy. Appl. Phys. Lett. 103, 181102 (2013).CrossRefGoogle Scholar
22. Maxwell Garnett, J.C.: Colours in metal glasses, in metallic films, and in metallic solutions. II. Philos. Trans. R. Soc. Lond. A 205, 237–288 (1906).Google Scholar
23. Perrins, W.T., McKenzie, D.R., and McPhedran, R.C.: Transport properties of regular arrays of cylinders. Proc. R. Soc. Lond. A 369, 207–225 (1979). The Royal Society.Google Scholar
24. Meredith, R.E. and Tobias, C.W.: Resistance to potential flow through a cubical array of spheres. J. Appl. Phys. 31, 1270–1273 (1960).CrossRefGoogle Scholar
25. Elser, J., Wangberg, R., Podolskiy, V.A., and Narimanov, E.E.: Nanowire metamaterials with extreme optical anisotropy. Appl. Phys. Lett. 89, 261102 (2006).CrossRefGoogle Scholar
26. Rayleigh, L.: 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).CrossRefGoogle Scholar
27. Milton, G.W.: The Theory of Composites (Cambridge University Press, Cambridge, UK, 2002).Google Scholar
28. Godin, Y.A.: Effective complex permittivity tensor of a periodic array of cylinders. J. Math. Phys. 54, 053505 (2013).CrossRefGoogle Scholar
29.COMSOL Multiphysics® v.4.4. www.comsol.com. COMSOL AB, Stockholm, Sweden.Google Scholar