Abstract

We show that lanthanide-doped crystals can be made left handed for a finite spectral range. The electronic transitions in the dopant ions are both dipolar electric and dipolar magnetic allowed. This enables tuning the permittivity and the permeability at the same frequency. The analysis focuses on erbium-doped crystals where left-handed properties are predicted inside an experimentally reachable domain of parameters.

© 2006 Optical Society of America

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References

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  1. V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1964); V. G. Veselago,[Sov. Phys. Usp. 10, 509 (1968)].
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).
    [CrossRef]
  5. M. Ö. Oktel and Ö. E. Müstecaplioglu, Phys. Rev. A 70, 053806 (2004).
    [CrossRef]
  6. Q. Thommen and P. Mandel, Phys. Rev. Lett. 96, 053601 (2006).
    [CrossRef] [PubMed]
  7. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  8. H. A. Bethe, Ann. Phys. 3, 133 (1929); H. A. Bethe,[Selected Works of Hans A. Bethe With Commentary (World Scientific, 1996), Vol. 8].
    [CrossRef]
  9. B. R. Judd, Phys. Rev. 127, 750 (1962).
    [CrossRef]
  10. A. A. Kaminskii, Laser Crystals, Springer Series in Optical Science (Springer, 1997).

2006

Q. Thommen and P. Mandel, Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

2005

2004

M. Ö. Oktel and Ö. E. Müstecaplioglu, Phys. Rev. A 70, 053806 (2004).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1997

A. A. Kaminskii, Laser Crystals, Springer Series in Optical Science (Springer, 1997).

1975

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

1964

V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1964); V. G. Veselago,[Sov. Phys. Usp. 10, 509 (1968)].

1962

B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

1929

H. A. Bethe, Ann. Phys. 3, 133 (1929); H. A. Bethe,[Selected Works of Hans A. Bethe With Commentary (World Scientific, 1996), Vol. 8].
[CrossRef]

Bethe, H. A.

H. A. Bethe, Ann. Phys. 3, 133 (1929); H. A. Bethe,[Selected Works of Hans A. Bethe With Commentary (World Scientific, 1996), Vol. 8].
[CrossRef]

Cai, W.

Chettiar, U. K.

Drachev, V. P.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

Judd, B. R.

B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, Laser Crystals, Springer Series in Optical Science (Springer, 1997).

Kildishev, A. V.

Mandel, P.

Q. Thommen and P. Mandel, Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Müstecaplioglu, Ö. E.

M. Ö. Oktel and Ö. E. Müstecaplioglu, Phys. Rev. A 70, 053806 (2004).
[CrossRef]

Oktel, M. Ö.

M. Ö. Oktel and Ö. E. Müstecaplioglu, Phys. Rev. A 70, 053806 (2004).
[CrossRef]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Sarychev, A. K.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Thommen, Q.

Q. Thommen and P. Mandel, Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1964); V. G. Veselago,[Sov. Phys. Usp. 10, 509 (1968)].

Yuan, H.

Ann. Phys.

H. A. Bethe, Ann. Phys. 3, 133 (1929); H. A. Bethe,[Selected Works of Hans A. Bethe With Commentary (World Scientific, 1996), Vol. 8].
[CrossRef]

Opt. Lett.

Phys. Rev.

B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

Phys. Rev. A

M. Ö. Oktel and Ö. E. Müstecaplioglu, Phys. Rev. A 70, 053806 (2004).
[CrossRef]

Phys. Rev. Lett.

Q. Thommen and P. Mandel, Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Usp. Fiz. Nauk

V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1964); V. G. Veselago,[Sov. Phys. Usp. 10, 509 (1968)].

Other

A. A. Kaminskii, Laser Crystals, Springer Series in Optical Science (Springer, 1997).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

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Figures (2)

Fig. 1
Fig. 1

Field polarization and energy levels of an erbium ion embedded in a host crystal. The probe field polarization dependence on the electronic transitions is schematically indicated, as are the corresponding transition probabilities. The energy levels are shifted by the Zeeman effect due to a static magnetic field B 0 .

Fig. 2
Fig. 2

Dependence of the permittivity and the permeability on the detuning. The erbium-doped crystal displays left-handed properties in a bandwidth of approximately 50 MHz (shaded area). In the case of a vanishing static magnetic field (dotted curve), no left-handed domain is found.

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