Abstract

In this paper, we consider a particular uniaxial material able to achieve the DB boundary condition. We show how, for particular transverse electromagnetic properties, this material behaves like a perfectly matched layer (PML). Moreover, we find that, with an approximation, the material becomes passive, i.e., loses the active part of the permittivity and of the permeability typical of a PML. In this case, the uniaxial medium becomes realizable as a particular absorbing metamaterial. We present simulations with both guided and free-space waves to show the absorbing behavior of the proposed material.

© 2013 Optical Society of America

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  1. I. V. Lindell and A. H. Sihvola, “Electromagnetic boundary and its realization with anisotropic metamaterials,” Phys. Rev. E 79, 026604 (2009).
    [CrossRef]
  2. M. Silverinha and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 075119 (2007).
    [CrossRef]
  3. L. Sun and W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 984–989 (2012).
    [CrossRef]
  4. I. V. Lindell and A. H. Sihvola, “Zero-axial-parameter (ZAP) medium sheet,” Prog. Electromagn. Res. 89, 213–224 (2009).
    [CrossRef]
  5. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  6. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
    [CrossRef]
  7. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
    [CrossRef]
  8. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16, 7181–7188 (2008).
    [CrossRef]
  9. G. Dayal and S. A. Ramakrishna, “Design of highly absorbing metamaterials for infrared frequencies,” Opt. Express 20, 17503–17508 (2012).
    [CrossRef]
  10. F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 8014 (2003).
    [CrossRef]
  11. S. A. Tretyakov, “The perfectly matched layer as a synthetic material with active inclusions,” Electromagnetics 20, 155–166 (2000).
    [CrossRef]
  12. S. A. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML),” J. Electromagn. Waves Appl. 12, 821–837 (1998).
    [CrossRef]
  13. R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using artificial engineered materials,” IEEE Trans. Antennas Propag. 45, 656–671 (1997).
    [CrossRef]
  14. F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998).
    [CrossRef]
  15. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
    [CrossRef]
  16. H. Wallén, H. Kettunen, and A. Sihvola, “Mixing formulas and plasmonic composites,” in Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, S. Zouhdi, A. Sihvola, and A. P. Vinogradov, eds. (Springer2009), Part III.

2012 (2)

2009 (2)

I. V. Lindell and A. H. Sihvola, “Zero-axial-parameter (ZAP) medium sheet,” Prog. Electromagn. Res. 89, 213–224 (2009).
[CrossRef]

I. V. Lindell and A. H. Sihvola, “Electromagnetic boundary and its realization with anisotropic metamaterials,” Phys. Rev. E 79, 026604 (2009).
[CrossRef]

2008 (2)

2007 (1)

M. Silverinha and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 075119 (2007).
[CrossRef]

2006 (1)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

2003 (1)

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 8014 (2003).
[CrossRef]

2000 (1)

S. A. Tretyakov, “The perfectly matched layer as a synthetic material with active inclusions,” Electromagnetics 20, 155–166 (2000).
[CrossRef]

1998 (2)

S. A. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML),” J. Electromagn. Waves Appl. 12, 821–837 (1998).
[CrossRef]

F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998).
[CrossRef]

1997 (1)

R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using artificial engineered materials,” IEEE Trans. Antennas Propag. 45, 656–671 (1997).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Averitt, R. D.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Bingham, C. M.

Chew, W. C.

F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998).
[CrossRef]

Dayal, G.

Elser, J.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Engheta, N.

M. Silverinha and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 075119 (2007).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Kettunen, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Mixing formulas and plasmonic composites,” in Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, S. Zouhdi, A. Sihvola, and A. P. Vinogradov, eds. (Springer2009), Part III.

Landy, N. I.

Lindell, I. V.

I. V. Lindell and A. H. Sihvola, “Electromagnetic boundary and its realization with anisotropic metamaterials,” Phys. Rev. E 79, 026604 (2009).
[CrossRef]

I. V. Lindell and A. H. Sihvola, “Zero-axial-parameter (ZAP) medium sheet,” Prog. Electromagn. Res. 89, 213–224 (2009).
[CrossRef]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef]

Narimanov, E. E.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Padilla, W. J.

Podolskiy, V. A.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Ramakrishna, S. A.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef]

Sihvola, A.

H. Wallén, H. Kettunen, and A. Sihvola, “Mixing formulas and plasmonic composites,” in Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, S. Zouhdi, A. Sihvola, and A. P. Vinogradov, eds. (Springer2009), Part III.

Sihvola, A. H.

I. V. Lindell and A. H. Sihvola, “Electromagnetic boundary and its realization with anisotropic metamaterials,” Phys. Rev. E 79, 026604 (2009).
[CrossRef]

I. V. Lindell and A. H. Sihvola, “Zero-axial-parameter (ZAP) medium sheet,” Prog. Electromagn. Res. 89, 213–224 (2009).
[CrossRef]

Silverinha, M.

M. Silverinha and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 075119 (2007).
[CrossRef]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef]

Sun, L.

Tao, H.

Teixeira, F. L.

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 8014 (2003).
[CrossRef]

F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998).
[CrossRef]

Tretyakov, S. A.

S. A. Tretyakov, “The perfectly matched layer as a synthetic material with active inclusions,” Electromagnetics 20, 155–166 (2000).
[CrossRef]

S. A. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML),” J. Electromagn. Waves Appl. 12, 821–837 (1998).
[CrossRef]

Wallén, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Mixing formulas and plasmonic composites,” in Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, S. Zouhdi, A. Sihvola, and A. P. Vinogradov, eds. (Springer2009), Part III.

Wangberg, R.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Yu, W.

Zhang, X.

Ziolkowski, R. W.

R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using artificial engineered materials,” IEEE Trans. Antennas Propag. 45, 656–671 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Electromagnetics (1)

S. A. Tretyakov, “The perfectly matched layer as a synthetic material with active inclusions,” Electromagnetics 20, 155–166 (2000).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

F. L. Teixeira and W. C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223–225 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using artificial engineered materials,” IEEE Trans. Antennas Propag. 45, 656–671 (1997).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Electromagn. Waves Appl. (1)

S. A. Tretyakov, “Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML),” J. Electromagn. Waves Appl. 12, 821–837 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Phys. Rev. B (1)

M. Silverinha and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 075119 (2007).
[CrossRef]

Phys. Rev. E (1)

I. V. Lindell and A. H. Sihvola, “Electromagnetic boundary and its realization with anisotropic metamaterials,” Phys. Rev. E 79, 026604 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef]

Prog. Electromagn. Res. (1)

I. V. Lindell and A. H. Sihvola, “Zero-axial-parameter (ZAP) medium sheet,” Prog. Electromagn. Res. 89, 213–224 (2009).
[CrossRef]

Radio Sci. (1)

F. L. Teixeira, “On aspects of the physical realizability of perfectly matched absorbers for electromagnetic waves,” Radio Sci. 38(2), 8014 (2003).
[CrossRef]

Other (1)

H. Wallén, H. Kettunen, and A. Sihvola, “Mixing formulas and plasmonic composites,” in Metamaterials and Plasmonics: Fundamentals, Modelling, Applications, S. Zouhdi, A. Sihvola, and A. P. Vinogradov, eds. (Springer2009), Part III.

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Figures (9)

Fig. 1.
Fig. 1.

Geometry of the problem.

Fig. 2.
Fig. 2.

Amplitude of the reflection coefficient at the interface between a vacuum and (solid line) a matched isotropic medium with ϵ=μ=2, (dashed line) a DB medium with ϵt=μt=2 and ϵz=μz=0.1, or (dotted line) ϵz=μz=0.01.

Fig. 3.
Fig. 3.

Amplitude of the reflection coefficient at the interface between an isotropic medium and a matched uniaxial medium as a function of the transverse permittivity of the uniaxial medium. The incidence is at an angle θi=60°. The uniaxial medium is considered with an axial permittivity equal to (solid line) ϵz=0.1, (dashed line) ϵz=0.06, and (dotted line) ϵz=0.03.

Fig. 4.
Fig. 4.

Amplitude of the reflection coefficient in Eq. (12), when (solid line) α=0.1, (dashed line) α=0.01, and (dotted line) α=0.001.

Fig. 5.
Fig. 5.

Phase of the reflection coefficient in Eq. (12) when (solid line) α=0.1, (dashed line) α=0.01, and (dotted line) α=0.001.

Fig. 6.
Fig. 6.

Normalized electric field at a distance λ from the edge of a box layered with (solid line) a vacuum, (dashed line) a PML, and (circles) an a-PML.

Fig. 7.
Fig. 7.

Difference between the fields in Fig. 6. The difference is between the field obtained with a vacuum and the field obtained with the a-PML.

Fig. 8.
Fig. 8.

Normalized electric field in a symmetric slab (solid line) without ending and at a distance λ/2 from (crosses) a PML and (circles) an a-PML.

Fig. 9.
Fig. 9.

Difference between the fields in Fig. 8. The difference is between the field obtained with a vacuum and the fields obtained with (solid line) the PML or (dashed line) the a-PML.

Equations (13)

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uz·D=0;uz·B=0,
ε¯¯=εtI¯¯t+εzuzuz;μ¯¯=μtI¯¯t+μzuzuz,
ΓTE=ζtcosθiζ1[1sin2θiϵ1μ1/(μzϵt)]1/2ζtcosθi+ζ1[1sin2θiϵ1μ1/(μzϵt)]1/2,
ΓTM=ζ1cosθiζt[1sin2θiϵ1μ1/(ϵzμt)]1/2ζ1cosθi+ζt[1sin2θiϵ1μ1/(ϵzμt)]1/2,
μ¯¯=ζ12ε¯¯,
εzεt=ε12.
Γ=cosθi[1sin2θiε12/(εzεt)]1/2cosθi+[1sin2θiε12/(εzεt)]1/2.
εt=Mε1andεz=ε1M,
εt=ε1Meiαandεz=ε1Meiα,
εtε1M(1+iα)andεzε1M(1iα).
εtε1M(1+iα)andεzε1M.
Γ=cosθi[1(1+iα)1sin2θi]1/2cosθi+[1(1+iα)1sin2θi]1/2.
Γiαtan2θi4+iαtan2θi.

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