OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27219–27237

Mode-expansion theory for inhomogeneous meta-surfaces

Shiyi Xiao, Qiong He, Che Qu, Xin Li, Shulin Sun, and Lei Zhou  »View Author Affiliations

Optics Express, Vol. 21, Issue 22, pp. 27219-27237 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1890 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Modeling meta-surfaces as thin metamaterial layers with continuously varying bulk parameters, we employed a rigorous mode-expansion theory to study the scattering properties of such systems. We found that a meta-surface with a linear reflection-phase profile could redirect an impinging light to a non-specular channel with nearly 100% efficiency, and a meta-surface with a parabolic reflection-phase profile could focus incident plane wave to a point image. Under certain approximations, our theory reduces to the local response model (LRM) established for such problems previously, but our full theory has overcome the energy non-conservation problems suffered by the LRM. Microwave experiments were performed on realistic samples to verify the key theoretical predictions, which match well with full-wave simulations.

© 2013 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(110.2760) Imaging systems : Gradient-index lenses
(240.0240) Optics at surfaces : Optics at surfaces
(260.2065) Physical optics : Effective medium theory
(160.3918) Materials : Metamaterials
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:

Original Manuscript: September 6, 2013
Revised Manuscript: October 27, 2013
Manuscript Accepted: October 27, 2013
Published: November 1, 2013

Shiyi Xiao, Qiong He, Che Qu, Xin Li, Shulin Sun, and Lei Zhou, "Mode-expansion theory for inhomogeneous meta-surfaces," Opt. Express 21, 27219-27237 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
  4. D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express13(6), 2127–2134 (2005). [CrossRef] [PubMed]
  5. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt.50(9), 1419–1430 (2003).
  6. J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.99(6), 063908 (2007). [CrossRef] [PubMed]
  7. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  8. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  9. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  10. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007). [CrossRef]
  11. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009). [CrossRef] [PubMed]
  12. Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett.102(9), 093901 (2009). [CrossRef] [PubMed]
  13. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010). [CrossRef] [PubMed]
  14. U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett.98(24), 243901 (2007). [CrossRef] [PubMed]
  15. A. O. Pinchuk and G. C. Schatz, “Metamaterials with gradient negative index of refraction,” J. Opt. Soc. Am. A24(10), A39–A44 (2007). [CrossRef] [PubMed]
  16. O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett.96(24), 241110 (2010). [CrossRef]
  17. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010). [CrossRef] [PubMed]
  18. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express18(19), 20321–20333 (2010). [CrossRef] [PubMed]
  19. N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011). [CrossRef] [PubMed]
  20. S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater.11(5), 426–431 (2012). [CrossRef] [PubMed]
  21. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335(6067), 427 (2012). [CrossRef] [PubMed]
  22. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Y. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D.-P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12(12), 6223–6229 (2012). [CrossRef] [PubMed]
  23. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett.100(1), 013101 (2012). [CrossRef]
  24. F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett.12(3), 1702–1706 (2012). [CrossRef] [PubMed]
  25. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012). [CrossRef] [PubMed]
  26. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett.12(11), 5750–5755 (2012). [CrossRef] [PubMed]
  27. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12(9), 4932–4936 (2012). [CrossRef] [PubMed]
  28. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012). [CrossRef] [PubMed]
  29. X. Li, S. Y. Xiao, B. G. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett.37(23), 4940–4942 (2012). [CrossRef] [PubMed]
  30. D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antennas Propag.11(6), 645–651 (1963). [CrossRef]
  31. S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett.37(12), 2391–2393 (2012). [CrossRef] [PubMed]
  32. F. L. Zhang, Q. Zhao, L. Kang, J. Zhou, and D. Lippens, “Experimental verification of isotropic and polarization properties of high permittivity-based metamaterial,” Phys. Rev. B80(19), 195119 (2009). [CrossRef]
  33. J. M. Hao, L. Zhou, and C. T. Chan, “An effective-medium model for high-impedance surfaces,” Appl. Phys. A Mater. Sci. Process.87(2), 281–284 (2007). [CrossRef]
  34. D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech.47(11), 2059–2074 (1999). [CrossRef]
  35. 35. These reflection channels could also be understood as the Floquet modes diffracted by our super-periodic system.
  36. In our computational approach, we have to set the number of sub-cells divided identical to the number plane waves adopted in region (both are 2N + 1), in order to ensure that the number of restraints equals to that of variables.
  37. For two boundary indexes, we have the following off-diagonal matrix elementsH1,2N+1=μM,1xγ, H2N+1,1=μM,2N+1xγ according to the periodic boundary condition.
  38. Since the super-cell length L is very large, the distribution of those discretized kxr,n is almost continuous. Thus, in what follows, we use ρ(kxr) to represent ρ(kxr,n) for simplicity.
  39. C. Qu, S. Y. Xiao, S. L. Sun, Q. He, and L. Zhou, “A theoretical study on the conversion efficiencies of gradient meta-surfaces,” Europhys. Lett.101(5), 54002 (2013). [CrossRef]
  40. A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13(2), 829–834 (2013). [CrossRef] [PubMed]
  41. M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic characterization of substrated metasurfaces,” Metamaterials5(4), 178–205 (2011). [CrossRef]
  42. P. Sheng, “Wave scattering formalism,” in Introduction to Wave Scattering, Localization and Macroscopic Phenomena, R. Hull, R. M. Osgood, eds. (Springer, 2006).
  43. EastFDTD v2.0 Beta, DONGJUN Science and Technology Co., China.
  44. For the ξ = 0.4k0 sample, a super cell contains 10 pairs of “H” (altogether 20 ones) in one supercell, with L1 values of those 10 pairs set as 1.3 mm, 2.68 mm, 2.98 mm, 3.14 mm, 3.24 mm, 3.36 mm, 3.48 mm, 3.66 mm, 4.08 mm, and 5.7 mm. For the ξ = 0.8k0 sample, a super cell contains 10 “H” in one super cell with L1 parameters the same as the case of ξ = 0.4k0.
  45. The gain of the employed double-ridged horn antenna is about 14dB~15dB in this frequency region.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited