Abstract

Modified boundary conditions for composite material are suggested. The modified RT-retrieval procedure yields bulk values of effective impedance and refractive index, which are independent of system size and boundary realization, whereas the conductivities of the excess surface currents depend on the property of the interface. Simultaneous treatment of all the possible realizations of the system removes the dependence. The accuracy of the latter procedure is the same as the usage of static effective parameters, namelykeffd.

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2010 (3)

N. A. Enkin, A. M. Merzlikin, and A. P. Vinogradov, “The difference of the refraction laws in composite materials from the Fresnel laws,” J. Commun. Technol. Electron. 55(5), 565–571 (2010).
[CrossRef]

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[CrossRef]

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B 405(14), 2930–2934 (2010).
[CrossRef]

2009 (1)

C. R. Simovski, “Material parameters of metamaterials,” Opt. Spectrosc. 107(5), 726–753 (2009).
[CrossRef]

2008 (2)

W. Śmigaj and B. Gralak, “Validity of the effective-medium approximation of photonic crystals,” Phys. Rev. B 77(23), 235445 (2008).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Size dependence and convergence of the retrieval parameters of metamaterials,” Photon. Nanostructures 6(1), 96–101 (2008).
[CrossRef]

2007 (4)

O. Acher, J. M. Lerat, and N. Malléjac, “Evaluation and illustration of the properties of metamaterials using field summation,” Opt. Express 15(3), 1096–1106 (2007).
[CrossRef] [PubMed]

C. R. Simovski, “Application of the Fresnel formulas for reflection and transmission of electromagnetic waves beyond the quasi-static approximation,” J. Commun. Technol. Electron. 52(9), 953–971 (2007).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75(19), 195111 (2007).
[CrossRef]

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
[CrossRef]

2006 (1)

2004 (1)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

2002 (6)

A. P. Vinogradov and I. I. Skidanov, “Generalization of Drude’s formulas for the transition layer to chiral media,” J. Commun. Technol. Electron. 47, 517–520 (2002).

A. P. Vinogradov, “On the form of constitutive equations in electrodynamics,” Physics-Uspekhi 45(3), 331–338 (2002).
[CrossRef]

A. P. Vinogradov and A. M. Merzlikin, “On the problem of homogenizing one-dimensional systems,” J. Exp. Theor. Phys. 94(3), 482–488 (2002).
[CrossRef]

C. R. Simovski and B. Sauviac, “On the bulk averaging approach for obtaining the effective parameters of thin magnetic granular films,” Eur. Phys. J. Appl. Phys. 17(1), 11–20 (2002).
[CrossRef]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

2001 (1)

A. P. Vinogradov and A. M. Merzlikin, “Electrodynamic properties of a finely layered medium,” Dokl. Phys. 46(12), 832–834 (2001).
[CrossRef]

1999 (2)

A. P. Vinogradov, K. N. Rosanov, and D. P. Makhnovsky, “Effective boundary layer in composite material,” J. Commun. Technol. Electron. 44, 317–322 (1999).

A. P. Vinogradov and A. V. Aivazyan, “Scaling theory for homogenization of the Maxwell equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 987–993 (1999).
[CrossRef]

1995 (2)

K. W. Whites, “Full-wave computation of constitutive parameters for lossless composite chiral materials,” IEEE Trans. Antenn. Propag. 43(4), 376–384 (1995).
[CrossRef]

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

1993 (1)

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

1974 (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62(1), 33–36 (1974).
[CrossRef]

1968 (1)

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time domain techniques,” IEEE Trans. Instrum. Meas. 17, 395–402 (1968).
[CrossRef]

1967 (1)

G. Franceschetti, “A complete analysis of the reflection and transmission methods for measuring the complex permeability and permittivity of materials at microwave frequencies,” 36,757–764 (1967).

1955 (1)

S. M. Rytov, “Electromagnetic properties of laminated medium,” Zh. Eksp. Teor. Fiz. 29, 605–616 (1955) [(Sov. Phys. - JETP. 2, 466–475 (1956)].

Acher, O.

Aivazyan, A. V.

A. P. Vinogradov and A. V. Aivazyan, “Scaling theory for homogenization of the Maxwell equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 987–993 (1999).
[CrossRef]

Bergman, D. J.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Chan, C. T.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Chen, X.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Enkin, N. A.

N. A. Enkin, A. M. Merzlikin, and A. P. Vinogradov, “The difference of the refraction laws in composite materials from the Fresnel laws,” J. Commun. Technol. Electron. 55(5), 565–571 (2010).
[CrossRef]

Fietz, C.

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B 405(14), 2930–2934 (2010).
[CrossRef]

Franceschetti, G.

G. Franceschetti, “A complete analysis of the reflection and transmission methods for measuring the complex permeability and permittivity of materials at microwave frequencies,” 36,757–764 (1967).

Gralak, B.

W. Śmigaj and B. Gralak, “Validity of the effective-medium approximation of photonic crystals,” Phys. Rev. B 77(23), 235445 (2008).
[CrossRef]

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Size dependence and convergence of the retrieval parameters of metamaterials,” Photon. Nanostructures 6(1), 96–101 (2008).
[CrossRef]

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Size dependence and convergence of the retrieval parameters of metamaterials,” Photon. Nanostructures 6(1), 96–101 (2008).
[CrossRef]

Lerat, J. M.

Ludwig, A.

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[CrossRef]

Makhnovsky, D. P.

A. P. Vinogradov, K. N. Rosanov, and D. P. Makhnovsky, “Effective boundary layer in composite material,” J. Commun. Technol. Electron. 44, 317–322 (1999).

Malléjac, N.

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Merzlikin, A. M.

N. A. Enkin, A. M. Merzlikin, and A. P. Vinogradov, “The difference of the refraction laws in composite materials from the Fresnel laws,” J. Commun. Technol. Electron. 55(5), 565–571 (2010).
[CrossRef]

A. P. Vinogradov and A. M. Merzlikin, “On the problem of homogenizing one-dimensional systems,” J. Exp. Theor. Phys. 94(3), 482–488 (2002).
[CrossRef]

A. P. Vinogradov and A. M. Merzlikin, “Electrodynamic properties of a finely layered medium,” Dokl. Phys. 46(12), 832–834 (2001).
[CrossRef]

Nicolson, A. M.

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time domain techniques,” IEEE Trans. Instrum. Meas. 17, 395–402 (1968).
[CrossRef]

O’Brien, S.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
[CrossRef]

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006).
[CrossRef]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
[CrossRef]

Rosanov, K. N.

A. P. Vinogradov, K. N. Rosanov, and D. P. Makhnovsky, “Effective boundary layer in composite material,” J. Commun. Technol. Electron. 44, 317–322 (1999).

Ross, G. F.

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time domain techniques,” IEEE Trans. Instrum. Meas. 17, 395–402 (1968).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of laminated medium,” Zh. Eksp. Teor. Fiz. 29, 605–616 (1955) [(Sov. Phys. - JETP. 2, 466–475 (1956)].

Sarychev, A. K.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Sauviac, B.

C. R. Simovski and B. Sauviac, “On the bulk averaging approach for obtaining the effective parameters of thin magnetic granular films,” Eur. Phys. J. Appl. Phys. 17(1), 11–20 (2002).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Shvets, G.

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B 405(14), 2930–2934 (2010).
[CrossRef]

Simovski, C. R.

C. R. Simovski, “Material parameters of metamaterials,” Opt. Spectrosc. 107(5), 726–753 (2009).
[CrossRef]

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
[CrossRef]

C. R. Simovski, “Application of the Fresnel formulas for reflection and transmission of electromagnetic waves beyond the quasi-static approximation,” J. Commun. Technol. Electron. 52(9), 953–971 (2007).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75(19), 195111 (2007).
[CrossRef]

C. R. Simovski and B. Sauviac, “On the bulk averaging approach for obtaining the effective parameters of thin magnetic granular films,” Eur. Phys. J. Appl. Phys. 17(1), 11–20 (2002).
[CrossRef]

Skidanov, I. I.

A. P. Vinogradov and I. I. Skidanov, “Generalization of Drude’s formulas for the transition layer to chiral media,” J. Commun. Technol. Electron. 47, 517–520 (2002).

Smigaj, W.

W. Śmigaj and B. Gralak, “Validity of the effective-medium approximation of photonic crystals,” Phys. Rev. B 77(23), 235445 (2008).
[CrossRef]

Smith, D. R.

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Size dependence and convergence of the retrieval parameters of metamaterials,” Photon. Nanostructures 6(1), 96–101 (2008).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[CrossRef] [PubMed]

Tretyakov, S. A.

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75(19), 195111 (2007).
[CrossRef]

Vinogradov, A. P.

N. A. Enkin, A. M. Merzlikin, and A. P. Vinogradov, “The difference of the refraction laws in composite materials from the Fresnel laws,” J. Commun. Technol. Electron. 55(5), 565–571 (2010).
[CrossRef]

A. P. Vinogradov and I. I. Skidanov, “Generalization of Drude’s formulas for the transition layer to chiral media,” J. Commun. Technol. Electron. 47, 517–520 (2002).

A. P. Vinogradov, “On the form of constitutive equations in electrodynamics,” Physics-Uspekhi 45(3), 331–338 (2002).
[CrossRef]

A. P. Vinogradov and A. M. Merzlikin, “On the problem of homogenizing one-dimensional systems,” J. Exp. Theor. Phys. 94(3), 482–488 (2002).
[CrossRef]

A. P. Vinogradov and A. M. Merzlikin, “Electrodynamic properties of a finely layered medium,” Dokl. Phys. 46(12), 832–834 (2001).
[CrossRef]

A. P. Vinogradov, K. N. Rosanov, and D. P. Makhnovsky, “Effective boundary layer in composite material,” J. Commun. Technol. Electron. 44, 317–322 (1999).

A. P. Vinogradov and A. V. Aivazyan, “Scaling theory for homogenization of the Maxwell equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 987–993 (1999).
[CrossRef]

Webb, K. J.

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[CrossRef]

Weir, W. B.

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62(1), 33–36 (1974).
[CrossRef]

Whites, K. W.

K. W. Whites, “Full-wave computation of constitutive parameters for lossless composite chiral materials,” IEEE Trans. Antenn. Propag. 43(4), 376–384 (1995).
[CrossRef]

Wu, B.-I.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Yagil, Y.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, “Theory of the optical and microwave properties of metal-dielectric films,” Phys. Rev. B Condens. Matter 51(8), 5366–5385 (1995).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Size dependence and convergence of the retrieval parameters of metamaterials,” Photon. Nanostructures 6(1), 96–101 (2008).
[CrossRef]

Dokl. Phys. (1)

A. P. Vinogradov and A. M. Merzlikin, “Electrodynamic properties of a finely layered medium,” Dokl. Phys. 46(12), 832–834 (2001).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

C. R. Simovski and B. Sauviac, “On the bulk averaging approach for obtaining the effective parameters of thin magnetic granular films,” Eur. Phys. J. Appl. Phys. 17(1), 11–20 (2002).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

K. W. Whites, “Full-wave computation of constitutive parameters for lossless composite chiral materials,” IEEE Trans. Antenn. Propag. 43(4), 376–384 (1995).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time domain techniques,” IEEE Trans. Instrum. Meas. 17, 395–402 (1968).
[CrossRef]

J. Commun. Technol. Electron. (4)

C. R. Simovski, “Application of the Fresnel formulas for reflection and transmission of electromagnetic waves beyond the quasi-static approximation,” J. Commun. Technol. Electron. 52(9), 953–971 (2007).
[CrossRef]

N. A. Enkin, A. M. Merzlikin, and A. P. Vinogradov, “The difference of the refraction laws in composite materials from the Fresnel laws,” J. Commun. Technol. Electron. 55(5), 565–571 (2010).
[CrossRef]

A. P. Vinogradov and I. I. Skidanov, “Generalization of Drude’s formulas for the transition layer to chiral media,” J. Commun. Technol. Electron. 47, 517–520 (2002).

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Figures (1)

Fig. 1
Fig. 1

Re ζ e f f ζ s t a t (solid lines) and Re n e f f n e f f R y t (dashed lines) for asymmetric system (a) and symmetric system (b) as functions of system thickness L. The normalized frequency is k 0 d = 0.05 . In (a) and (b) the Re n e f f tends to the Rytov value given by Eq. (1): n e f f R y t 1.58114 .

Tables (1)

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Table 1 Material Parameters are Shown with Accuracy 10 7

Equations (8)

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cos ( k R y t d c e l l ) = cos ( k 0 ε 1 d 1 ) cos ( k 0 ε 2 d 2 ) ε 1 + ε 2 2 ε 1 ε 2 sin ( k 0 ε 1 d 1 ) sin ( k 0 ε 2 d 2 )
cos ( n k 0 L ) = cos ( n e f f R y t k 0 L ) ( ε 1 ε 2 ) sin ( n e f f R y t k 0 L ) 4 ( ε 1 + ε 2 ) / 2 k 0 d + O ( ( k 0 d ) 2 )
1 / ζ 2 = 0.5 ( ε 1 + ε 2 ) + 0.5 ( ε 1 ε 2 ) k 0 d ( ε 1 + ε 2 ) / 2 ctg ( n e f f R y t k 0 L ) + O ( ( k 0 d ) 2 )
E y ( s a m p l e ) E y ( v a c u u m ) = s M ( l e f t ) H z ( s a m p l e ) ;           H z ( v a c u u m ) H z ( s a m p l e ) = s E ( l e f t ) E y ( s a m p l e )
E y ( v a c u u m ) E y ( s a m p l e ) = s M ( r i g h t ) H z ( s a m p l e ) ;             H z ( s a m p l e ) H z ( v a c u u m ) = s E ( r i g h t ) E y ( s a m p l e )
T 11 u l c = T 22 u l c * = = ( 1 s E l ) ( 1 + s M r ) + ( 1 s E r ) ( 1 + s M l ) 2 ( 1 + s E l s M l ) cos n k 0 L + i ( 1 s E l ) ( 1 s E r ) ζ 2 + ( 1 + s M l ) ( 1 + s M r ) 2 ζ ( 1 + s E l s M l ) sin n k 0 L
T 12 u l c = T 21 u l c * = = s E l + s E r + s M l ( 1 s E r ) + s M r ( 1 + s E l ) 2 ( 1 + s E l s M l ) cos n k 0 L + i ( 1 s M l ) ( 1 + s M r ) ζ 2 ( 1 + s E l ) ( 1 s E r ) 2 ζ ( 1 + s E l s M l ) sin n k 0 L
δ = i { | r ( L i ) r e x a c t ( L i ) | 2 + | t ( L i ) t e x a c t ( L i ) | 2 }

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