Abstract

Optical parametric amplification controlled by the auxiliary electromagnetic field enables transparency, amplification, and oscillation with no cavity in strongly absorbing negative-index metamaterials. The opposite directions of the wave vector and the Poynting vector in such materials result in extraordinary optical properties, including “backward” phase matching and the generation of entangled pairs of left- and right-handed counterpropagating photons.

© 2006 Optical Society of America

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  1. M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
    [CrossRef]
  2. A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
    [CrossRef] [PubMed]
  3. M. Lapine and M. Gorkunov, Phys. Rev. E 70, 66601 (2004).
    [CrossRef]
  4. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, arXiv.org, http://arxiv.org/abs/physics/0506092.
  5. S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
    [CrossRef]
  6. K. I. Volyak and A. S. Gorshkov, Radiotekh. Elektron. (Moscow) 18, 2075 (1973) (in Russian).
  7. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, 1975), Sec. 17.8.
  8. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
    [CrossRef]
  9. V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
    [CrossRef]
  10. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
    [CrossRef]
  11. A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
    [CrossRef]

2005

V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

2004

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

M. Lapine and M. Gorkunov, Phys. Rev. E 70, 66601 (2004).
[CrossRef]

2003

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

1973

K. I. Volyak and A. S. Gorshkov, Radiotekh. Elektron. (Moscow) 18, 2075 (1973) (in Russian).

1966

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Gorkunov, M.

M. Lapine and M. Gorkunov, Phys. Rev. E 70, 66601 (2004).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Gorshkov, A. S.

K. I. Volyak and A. S. Gorshkov, Radiotekh. Elektron. (Moscow) 18, 2075 (1973) (in Russian).

Harris, S. E.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Kivshar, Yu. S.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, arXiv.org, http://arxiv.org/abs/physics/0506092.

Kuhta, N. A.

V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
[CrossRef]

Lapine, M.

M. Lapine and M. Gorkunov, Phys. Rev. E 70, 66601 (2004).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Milton, G. W.

V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
[CrossRef]

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

Podolskiy, V. A.

V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
[CrossRef]

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Shadrivov, I. V.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, arXiv.org, http://arxiv.org/abs/physics/0506092.

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Volyak, K. I.

K. I. Volyak and A. S. Gorshkov, Radiotekh. Elektron. (Moscow) 18, 2075 (1973) (in Russian).

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

Webb, K. J.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

Yang, M.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, 1975), Sec. 17.8.

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Zharov, A. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, arXiv.org, http://arxiv.org/abs/physics/0506092.

Zharova, N. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

Appl. Phys. Lett.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

V. A. Podolskiy, N. A. Kuhta, and G. W. Milton, Appl. Phys. Lett. 87, 231113 (2005).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104-3 (2005).
[CrossRef]

Phys. Rev. B

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Phys. Rev. E

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

M. Lapine and M. Gorkunov, Phys. Rev. E 70, 66601 (2004).
[CrossRef]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602R (2004).
[CrossRef]

Phys. Rev. Lett.

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Radiotekh. Elektron. (Moscow)

K. I. Volyak and A. S. Gorshkov, Radiotekh. Elektron. (Moscow) 18, 2075 (1973) (in Russian).

Other

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, 1975), Sec. 17.8.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, arXiv.org, http://arxiv.org/abs/physics/0506092.

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Figures (3)

Fig. 1
Fig. 1

OPA processes in NIMs and PIMs. Phase-matching schemes in (a) LHM and (b) RHM. The phase-matched amplification factor for the signal wave ( η 1 a , solid curve), and the conversion factor for the idler wave ( η 2 g , dashed curve) in (c) LHM and (d) RHM with absorption ( α 1 L = 1 , α 2 L = 1 2 ); (d) represents the dependence schematically.

Fig. 2
Fig. 2

Amplification factor for the negative-index signal [ η 1 a ( z ) = a 1 a 1 L 2 ; solid curves in (a)–(f)], the conversion factor for the signal [ η 1 g ( z ) = a 1 a 20 * 2 ; dashed curves in (c)–(f)]; and the conversion factor for the positive-index idler [ η 2 g ( z ) a 2 a 1 L * 2 ; dashed curves in (a) and (b)] for various Δ k and g L . α 1 L = 1 , α 2 L = 1 2 .

Fig. 3
Fig. 3

Output amplification, η 1 a (solid curve), and DFG conversion factor, η 1 g (dashed curve) for the backward wave at z = 0 . (a) Δ k = 0 . (b) Δ k L = π . Insets, sets of periodical resonances for η 1 a , 1 g versus g L . α 1 L = 1 , α 2 L = 1 2 .

Equations (15)

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H j ( z , t ) = h j exp [ i ( k j z ω j t ) ] + c.c.
M 1 , 2 N L = 2 χ eff ( 2 ) h 3 h 2 , 1 * exp { i [ ( k 3 k 2 , 1 ) z ω 1 , 2 t ] } .
d a 1 d z = i g a 2 * exp ( i Δ k z ) + ( α 1 2 ) a 1 ,
d a 2 d z = i g a 1 * exp ( i Δ k z ) ( α 2 2 ) a 2 ,
d [ ( S 1 z ω 1 ) ( S 2 z ω 2 ) ] d z = 0 ,
d [ μ 1 ϵ 1 ( h 1 2 ω 1 ) + μ 2 ϵ 2 ( h 2 2 ω 2 ) ] d z = 0 .
a 1 ( z ) = A 1 exp ( β 1 + z ) + A 2 exp [ ( β 2 + z ) ] ,
a 2 * ( z ) = κ 1 A 1 exp ( β 1 z ) + κ 2 A 2 exp ( β 2 z ) ,
β 1 , 2 ± = β 1 , 2 ± ( i Δ k 2 ) , β 1 , 2 = ( α 1 α 2 ) ( 4 ) ± i R ,
A 1 , 2 = ± [ a 1 L κ 2 , 1 a 20 * exp ( β 2 , 1 + L ) ] D ,
D = κ 2 exp ( β 1 + L ) κ 1 exp ( β 2 + L ) ,
κ 1 , 2 = ( ± R + i s ) g , R = g 2 s 2 ,
s = ( α 1 + α 2 ) ( 4 ) i ( Δ k 2 ) .
a 1 ( z = 0 ) a 1 L = exp [ ( α 1 α 2 4 + i Δ k 2 ) L ] cos R L + ( α 1 + α 2 4 R i Δ k 2 R ) sin R L .
a 1 ( z = 0 ) a 20 * = ( g R ) sin R L cos R L + ( α 1 + α 2 4 R i Δ k 2 R ) sin R L .

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