Abstract

According to general relativity, the frequency of electromagnetic radiation is altered by the expansion of the universe. This effect—commonly referred to as the cosmological redshift—is of utmost importance for observations in cosmology. Here we show that this redshift can be reproduced on a much smaller scale using an optical analogue inside a dielectric metamaterial with time-dependent material parameters. To this aim, we apply the framework of transformation optics to the Robertson-Walker metric. We demonstrate theoretically how perfect redshifting or blueshifting of an electromagnetic wave can be achieved without the creation of sidebands with a device of finite length.

© 2010 Optical Society of America

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  1. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
    [CrossRef] [PubMed]
  2. D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
    [CrossRef]
  3. E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  4. C. Qiang and C. T. Jun, "An electromagnetic black hole made of metamaterials," arXiv:0910.2159v1 [physics.optics] (2009).
  5. N. L. Balazs, "Effect of a gravitational field, due to a rotating body, on the plane of polarization of an electromagnetic wave," Phys. Rev. 110, 236-239 (1957).
    [CrossRef]
  6. J. Plebanski, "Electromagnetic waves in gravitational fields," Phys. Rev. 118, 1396-1408 (1960).
    [CrossRef]
  7. D. F. Felice, "On the gravitational field acting as an optical medium," Gen. Rel. Grav. 2, 347-357 (1971).
    [CrossRef]
  8. A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Phys. 43, 773-793 (1996).
  9. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  10. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  11. U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247-264 (2006).
    [CrossRef]
  12. U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt. 53, 70-152 (2009).
  13. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
    [CrossRef]
  14. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
    [CrossRef]
  15. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
    [CrossRef] [PubMed]
  16. M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (2008).
    [CrossRef] [PubMed]
  17. S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett. 100, 123002 (2008).
    [CrossRef] [PubMed]
  18. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
    [CrossRef] [PubMed]
  19. D. Kwon and D. H. Werner, "Polarization splitter and polarization rotator designs based on transformation optics," Opt. Express 16, 18731-18738 (2008).
    [CrossRef]
  20. Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2008).
    [CrossRef]
  21. S. Carroll, Spacetime and Geometry (Addison Wesley, New York, 2003).
  22. 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. Applic. 6, 87-95 (2008).
    [CrossRef]
  23. N. V. Budko, "Electromagnetic radiation in a time-varying background medium," Phys. Rev. A 80, 053817 (2009).
    [CrossRef]
  24. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  25. C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
    [CrossRef]

2009 (5)

D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt. 53, 70-152 (2009).

N. V. Budko, "Electromagnetic radiation in a time-varying background medium," Phys. Rev. A 80, 053817 (2009).
[CrossRef]

2008 (8)

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
[CrossRef] [PubMed]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (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]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
[CrossRef] [PubMed]

D. Kwon and D. H. Werner, "Polarization splitter and polarization rotator designs based on transformation optics," Opt. Express 16, 18731-18738 (2008).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2008).
[CrossRef]

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. Applic. 6, 87-95 (2008).
[CrossRef]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

2007 (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

2006 (3)

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]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247-264 (2006).
[CrossRef]

2005 (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
[CrossRef]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

1996 (1)

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Phys. 43, 773-793 (1996).

1971 (1)

D. F. Felice, "On the gravitational field acting as an optical medium," Gen. Rel. Grav. 2, 347-357 (1971).
[CrossRef]

1960 (1)

J. Plebanski, "Electromagnetic waves in gravitational fields," Phys. Rev. 118, 1396-1408 (1960).
[CrossRef]

1957 (1)

N. L. Balazs, "Effect of a gravitational field, due to a rotating body, on the plane of polarization of an electromagnetic wave," Phys. Rev. 110, 236-239 (1957).
[CrossRef]

Alekseyev, L. V.

Balazs, N. L.

N. L. Balazs, "Effect of a gravitational field, due to a rotating body, on the plane of polarization of an electromagnetic wave," Phys. Rev. 110, 236-239 (1957).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

Budko, N. V.

N. V. Budko, "Electromagnetic radiation in a time-varying background medium," Phys. Rev. A 80, 053817 (2009).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (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. Applic. 6, 87-95 (2008).
[CrossRef]

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
[CrossRef]

Enoch, S.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Farhat, M.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Felice, D. F.

D. F. Felice, "On the gravitational field acting as an optical medium," Gen. Rel. Grav. 2, 347-357 (1971).
[CrossRef]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
[CrossRef]

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

Guenneau, S.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

Jacob, Z.

Kafesaki, M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
[CrossRef]

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Konig, F.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

Kwon, D.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt. 53, 70-152 (2009).

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

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

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247-264 (2006).
[CrossRef]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

Movchan, A. B.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Narimanov, E.

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Pendry, J.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
[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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
[CrossRef] [PubMed]

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

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Phys. 43, 773-793 (1996).

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt. 53, 70-152 (2009).

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247-264 (2006).
[CrossRef]

Plebanski, J.

J. Plebanski, "Electromagnetic waves in gravitational fields," Phys. Rev. 118, 1396-1408 (1960).
[CrossRef]

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (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. Applic. 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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
[CrossRef] [PubMed]

Robertson, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
[CrossRef] [PubMed]

Schurig, D.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (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. Applic. 6, 87-95 (2008).
[CrossRef]

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

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Smith, D. R.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).
[CrossRef] [PubMed]

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

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
[CrossRef]

Starr, A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
[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]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

Ward, A. J.

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Phys. 43, 773-793 (1996).

Werner, D. H.

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
[CrossRef]

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

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

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

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Gen. Rel. Grav. (1)

D. F. Felice, "On the gravitational field acting as an optical medium," Gen. Rel. Grav. 2, 347-357 (1971).
[CrossRef]

J. Mod. Phys. (1)

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Phys. 43, 773-793 (1996).

Nature Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
[CrossRef]

Nature Photon. (1)

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Nature Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nature Phys. 5, 687-692 (2009).
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New J. Phys. (1)

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247-264 (2006).
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Opt. Express (3)

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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. Applic. 6, 87-95 (2008).
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N. V. Budko, "Electromagnetic radiation in a time-varying background medium," Phys. Rev. A 80, 053817 (2009).
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S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, "Scattering theory derivation of a 3D acoustic cloaking shell," Phys. Rev. Lett. 100, 024301 (2008).
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U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt. 53, 70-152 (2009).

Science (4)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, "Fiber-Optical Analog of the Event Horizon," Science 319, 1367-1370 (2008).
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Figures (3)

Fig. 1.
Fig. 1.

A graphical representation of a traveling wave solution inside a medium that is the electromagnetic analogue of the Robertson-Walker metric. (a) The spatial variation at constant time t = 1 and (b) the temporal variation of this solution for fixed location z = 1, when we modulate the permittivity and permeability with a(t) = 1+t.

Fig. 2.
Fig. 2.

A setup where we implement a finite Robertson-Walker device. At the leftmost boundary a monochromatic wave of frequency ω 0 and amplitude A 0 illuminates the device. We modulate the permittivity and permeability as ε(t) = μ(t) = a(t) = 1+t. We show that the output undergoes a frequency shift according to the cosmological redshift formula.

Fig. 3.
Fig. 3.

The wave fronts inside the frequency converter as a function of space and time when the leftmost boundary is illuminated by a monochromatic wave. In this diagram, we have simulated a linear evolution of the scale factor a(t) = t.

Equations (16)

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d s 2 = c 2 d t 2 + a 2 ( t ) [ d r 2 1 κ r 2 + r 2 d Ω 2 ] ,
ω obs ω em = a ( t em ) a ( t obs ) .
ε x x = μ x x = a ( t ) , ε y y = μ y y = a ( t ) , ε z z = μ z z = a ( t ) .
Δ E 1 c 2 t ( a ( t ) t ( a ( t ) E ) ) = 0 ,
E ( r , t ) = 1 a ( t ) G ( r · 1 k c t 0 t d t ˜ a ( t ˜ ) ) 1 E ,
f ( t ) = t 0 t d t ˜ a ( t ˜ ) .
E I ( z , t ) = A 0 e i k 0 ( z ct ) 1 E ,
E II ( z , t ) = G ( z cf ( t ) ) a ( t ) 1 E ,
E III ( z , t ) = H ( z c t ) 1 E ,
A 0 e i k 0 ct = G ( cf ( t ) ) a ( t ) .
G ( x ) = a ( f 1 ( x c ) ) A 0 e i k 0 c f 1 ( x c ) ,
E II ( L , t ) = a ( f 1 ( f ( t ) L c ) ) a ( t ) A 0 e i k 0 c f 1 ( f ( t ) L c ) 1 E .
E III ( z , t ) = E II ( L , t z L c ) .
ω out = ω 0 a ( f 1 ( f ( t ) L c ) ) a ( t ) .
ω out ω 0 = e αL / c .
μ ( ω ) = 1 + F ω 2 ω LC 2 ω 2 ,

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