Abstract

Based on the transformation media theory, the authors propose a way to replace a wide window with a narrow slit filled with designed metamaterial to achieve the same transmittance as the one of the window. Numerical simulations for a two dimensional case are given to illustrate the ideas and the performance of the design.

© 2008 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  3. 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," Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  4. H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  5. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
    [CrossRef]
  6. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
    [CrossRef] [PubMed]
  7. H. Chen and C. T. Chan, "Electromagnetic wave manipulation using layered systems," Phys. Rev. B (to be published).
  8. L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2008).
    [CrossRef] [PubMed]
  9. A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
    [CrossRef] [PubMed]
  10. H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
    [CrossRef]
  11. S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
    [CrossRef] [PubMed]
  12. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
    [CrossRef] [PubMed]
  13. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
    [CrossRef]

2008

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2008).
[CrossRef] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

2007

A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

2006

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Chan, C. T.

H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Electromagnetic wave manipulation using layered systems," Phys. Rev. B (to be published).

Chen, H.

H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Electromagnetic wave manipulation using layered systems," Phys. Rev. B (to be published).

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Cui, J.

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Du, C.

Genov, D. A.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Greenleaf, A.

A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Justice, B. J.

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Lassas, M.

A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Lin, L.

Luo, X.

Mock, J. J.

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Starr, A. F.

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Sun, C.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Uhlmann, G.

A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Wang, W.

Zhang, S.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett.

H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Opt. Express

Photon. Nanostruct.: Fundam. Appl.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell�??s equations," Photon. Nanostruct.: Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. B

H. Chen and C. T. Chan, "Electromagnetic wave manipulation using layered systems," Phys. Rev. B (to be published).

Phys. Rev. Lett.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

A. Greenleaf, M. Lassas, and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

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," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Supplementary Material (6)

» Media 1: MOV (6601 KB)     
» Media 2: MOV (6601 KB)     
» Media 3: MOV (6601 KB)     
» Media 4: MOV (6601 KB)     
» Media 5: MOV (6601 KB)     
» Media 6: MOV (6601 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) A rectangular free space sandwiched between two PECs, whose lengths of the sides are w 1 and d 1. (b) The rectangular free space is compressed into a bridge-shaped space. The “bridge” is another smaller rectangle whose lengths of the sides are w 2 and d 2. The original free space and the transformed space are highlighted by grids and yellow color. The green regions are vacuums. The orange regions are PECs.

Fig. 2.
Fig. 2.

Spatial dependence of the material parameters of the designed device for z-polarized TE wave, (a) μxx , (b) μyy = εz , (c) μxy .

Fig. 3.
Fig. 3.

(a) The electric field distribution for an electric line source in the free space. [Media 1] (b) The electric field distribution for an electric line source near a big “window”. [Media 2] (c) The electric field distribution for an electric line source near the designed transformation media device. [Media 3] (d) The electric field distribution for an electric line source near the same small slit as in (c) without the transformation media in it. [Media 4] (e) The electric field distribution for an electric line source directly in front of the big “window”. [Media 5] (f) The electric field distribution for an electric line source directly in front of the designed transformation media device. [Media 6]

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ʌ α α = x α x α .
ε i j = det ( Λ i i ) 1 Λ i i Λ j j ε i j , μ i j = det ( Λ i i ) 1 Λ i i Λ j j μ i j .
μ = ε = Δ i 2 + Γ i 2 Δ i Γ i Δ i 0 Γ i Δ i 1 Δ i 0 0 0 1 Δ i ,
μ = ε = w 2 w 1 0 0 0 w 1 w 2 0 0 0 w 1 w 2 ,
Δ 1 = w 1 w 2 d 1 d 2 ( y d 2 2 ) + w 2 2 w 1 2 , Δ 3 = w 1 w 2 d 1 d 2 ( y + d 2 2 ) + w 2 2 w 1 2 ,
Γ 1 = w 1 w 2 d 1 d 2 w 1 w 2 d 1 d 2 ( y d 2 2 ) + w 2 2 x = w 1 w 2 d 1 d 2 Δ 1 w 1 2 x ,
Γ 3 = w 1 w 2 d 1 d 2 w 1 w 2 d 1 d 2 ( y + d 2 2 ) + w 2 2 x = w 1 w 2 d 1 d 2 Δ 3 w 1 2 x .

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