Graphical retrieval method for
orthorhombic anisotropic materials

doi:10.1364/OE.18.017009

Graphical retrieval method for orthorhombic anisotropic materials

Simin Feng »View Author Affiliations

Optics Express, Vol. 18, Issue 16, pp. 17009-17019 (2010)
http://dx.doi.org/10.1364/OE.18.017009

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Abstract
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References (18)
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Abstract

We apply the equivalent theory to orthorhombic anisotropic materials and provide a general unit-cell design criterion for achieving a length-independent retrieval of the effective material parameters from a single layer of unit cells. We introduce a graphical retrieval method and phase unwrapping techniques. The graphical method utilizes the linear regression technique. Our method can reduce the uncertainty of experimental measurements and the ambiguity of phase unwrapping. Moreover, the graphical method can simultaneously determine the bulk values of the six effective material parameters, permittivity and permeability tensors, from a single layer of unit cells.

OCIS Codes
(310.3840) Thin films : Materials and process characterization
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Metamaterials

History
Original Manuscript: June 7, 2010
Revised Manuscript: June 21, 2010
Manuscript Accepted: July 6, 2010
Published: July 26, 2010

Citation
Simin Feng, "Graphical retrieval method for orthorhombic anisotropic materials," Opt. Express 18, 17009-17019 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17009

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References

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005). [CrossRef] [PubMed]
J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Mater. 8, 568-571 (2009). [CrossRef] [PubMed]
S. Feng and K. Halterman, "Parametrically shielding electromagnetic fields by nonlinear metamaterials," Phys. Rev. Lett. 100, 063901 (2008). [CrossRef] [PubMed]
F. Capolino, ed., Theory and phenomena of metamaterials (CRC Press, Taylor and Francis Group, New York, 2009). [CrossRef]
J. Valentine, S. Zhang, T. Zentgraf, E. U. Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-380 (2008). [CrossRef] [PubMed]
N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008). [CrossRef]
S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
V. M. Shalaev,W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, "Wave propagation retrieval method for metamaterials: Unambiguous restoration of effective parameters," Phys. Rev. B 80, 193101 (2009). [CrossRef]
A. Herpin, "Calcul du pouvoir réflecteur d’un système stratifié quelconque," Compt. Rend. 225, 182-183 (1947).
D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002). [CrossRef]
T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005). [CrossRef]
C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, "Retrieving effective parameters for metamaterials at oblique incidence," Phys. Rev. B 77, 195328 (2008). [CrossRef]
X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004). [CrossRef]
L. I. Epstein, "The design of optical filters," J. Opt. Soc. Am. 42, 806-810 (1952). [CrossRef]
A. Lakhtakia, "Constraints on effective constitutive parameters of certain bianisotropic laminated composite materials," Electromagnetics 29,508-514 (2009). [CrossRef]
M. J. Roberts, S. Feng, M. Moran, and L. Johnson, "Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate," J. Nanophoton. 4, 043511 (2010). [CrossRef]
M. W McCall, A. Lakhtakia, and W. S Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002). [CrossRef]

Andryieuski, A.
Avila, E. U.
Bartal, G.
Brueck, S. R. J.
Cai, W.
Chen, X.
Chettiar, U. K.
Drachev, V. P.
Economou, E. N.
Epstein, L. I.
Fan, W.
Fang, N.
Feng, S.
Fu, L.
Genov, D. A.
Giessen, H.
Grzegorczyk, T. M.
Guo, H.
Halterman, K.
Herpin, A.
Johnson, L.
Kaiser, S.
Kildishev, A. V.
Kong, J. A.
Koschny, T.
Lakhtakia, A.
Lavrinenko, A. V.
Lederer, F.
Lee, H.
Li, J.
Liu, N.
Malloy, K. J.
Malureanu, R.
Markoš, P.
McCall, M. W
Menzel, C.
Moran, M.
Osgood, R. M.
Pacheco, J.
Panoiu, N. C.
Paul, T.
Roberts, M. J.
Rockstuhl, C.
Sarychev, A. K.
Schultz, S.
Schweizer, H.
Shalaev, V. M.
Smith, D. R.
Soukoulis, C. M.
Sun, C.
Valentine, J.
Vier, D. C.
Weiglhofer, W. S
Wu, B.-I.
Yuan, H.-K.
Zentgraf, T.
Zhang, S.
Zhang, X.

Compt. Rend.

A. Herpin, "Calcul du pouvoir réflecteur d’un système stratifié quelconque," Compt. Rend. 225, 182-183 (1947).

Electromagnetics

A. Lakhtakia, "Constraints on effective constitutive parameters of certain bianisotropic laminated composite materials," Electromagnetics 29,508-514 (2009). [CrossRef]

Eur. J. Phys.

M. W McCall, A. Lakhtakia, and W. S Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002). [CrossRef]

J. Nanophoton.

M. J. Roberts, S. Feng, M. Moran, and L. Johnson, "Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate," J. Nanophoton. 4, 043511 (2010). [CrossRef]

J. Opt. Soc. Am.

L. I. Epstein, "The design of optical filters," J. Opt. Soc. Am. 42, 806-810 (1952). [CrossRef]

Nat. Mater.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Mater. 8, 568-571 (2009). [CrossRef] [PubMed]
N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008). [CrossRef]

Nature (London)

J. Valentine, S. Zhang, T. Zentgraf, E. U. Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-380 (2008). [CrossRef] [PubMed]

Opt. Lett.

V. M. Shalaev,W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]

Phys. Rev. B

A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, "Wave propagation retrieval method for metamaterials: Unambiguous restoration of effective parameters," Phys. Rev. B 80, 193101 (2009). [CrossRef]
D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002). [CrossRef]
T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005). [CrossRef]
C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, "Retrieving effective parameters for metamaterials at oblique incidence," Phys. Rev. B 77, 195328 (2008). [CrossRef]

Phys. Rev. E

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004). [CrossRef]

Phys. Rev. Lett.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
S. Feng and K. Halterman, "Parametrically shielding electromagnetic fields by nonlinear metamaterials," Phys. Rev. Lett. 100, 063901 (2008). [CrossRef] [PubMed]

Science

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005). [CrossRef] [PubMed]

Other

F. Capolino, ed., Theory and phenomena of metamaterials (CRC Press, Taylor and Francis Group, New York, 2009). [CrossRef]

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