Abstract

We investigate extraordinary features of optical parametric amplification of Stokes electromagnetic waves that originate from the three-wave mixing of a backward phonon wave with negative group velocity and two ordinary electromagnetic waves. Such properties were earlier shown to exist only in plasmonic negative-index metamaterials that are very challenging to fabricate. Nonlinear optical photonic devices with properties similar to those predicted for negative-index metamaterials are proposed.

© 2011 Optical Society of America

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References

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  1. V. M. Shalaev, Nat. Photon. 1, 41 (2007).
    [Crossref]
  2. C. M. Soukoulis and M. Wegener, Science 330, 1633 (2010).
    [Crossref] [PubMed]
  3. N. I. Zheludev, Opt. Photon. News 22 (3), 30 (2011)
    [Crossref]
  4. A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
    [Crossref] [PubMed]
  5. A. K. Popov, Eur. Phys. J. D 58, 263 (2010).
    [Crossref]
  6. A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
    [Crossref]
  7. A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
    [Crossref]
  8. L. I. Mandelstam, Zh. Eksp. Teor. Fiz. 15, 475 (1945).
  9. Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).
    [Crossref]
  10. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  11. D. L. Bobroff, J. Appl. Phys. 36, 1760 (1965).
    [Crossref]
  12. J. B. Khurgin, Nat. Photon. 1, 446 (2007).
    [Crossref]
  13. V. S. Gorelik, Contemporary Problems of Raman Spectroscopy (Nauka, 1978), p. 28 (in Russian).
  14. E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
    [Crossref]
  15. Y. Chen and J. D. Lee, Int. J. Eng. Sci. 41, 871 (2003).
    [Crossref]

2011 (1)

N. I. Zheludev, Opt. Photon. News 22 (3), 30 (2011)
[Crossref]

2010 (2)

C. M. Soukoulis and M. Wegener, Science 330, 1633 (2010).
[Crossref] [PubMed]

A. K. Popov, Eur. Phys. J. D 58, 263 (2010).
[Crossref]

2007 (2)

J. B. Khurgin, Nat. Photon. 1, 446 (2007).
[Crossref]

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[Crossref]

2006 (3)

A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
[Crossref] [PubMed]

A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
[Crossref]

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[Crossref]

2003 (1)

Y. Chen and J. D. Lee, Int. J. Eng. Sci. 41, 871 (2003).
[Crossref]

1966 (1)

E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
[Crossref]

1965 (2)

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).
[Crossref]

D. L. Bobroff, J. Appl. Phys. 36, 1760 (1965).
[Crossref]

1945 (1)

L. I. Mandelstam, Zh. Eksp. Teor. Fiz. 15, 475 (1945).

Anastassakis, E.

E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
[Crossref]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).
[Crossref]

Bobroff, D. L.

D. L. Bobroff, J. Appl. Phys. 36, 1760 (1965).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Burstein, E.

E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
[Crossref]

Chen, Y.

Y. Chen and J. D. Lee, Int. J. Eng. Sci. 41, 871 (2003).
[Crossref]

Gorelik, V. S.

V. S. Gorelik, Contemporary Problems of Raman Spectroscopy (Nauka, 1978), p. 28 (in Russian).

Iwasa, S.

E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
[Crossref]

Khurgin, J. B.

J. B. Khurgin, Nat. Photon. 1, 446 (2007).
[Crossref]

Lee, J. D.

Y. Chen and J. D. Lee, Int. J. Eng. Sci. 41, 871 (2003).
[Crossref]

Mandelstam, L. I.

L. I. Mandelstam, Zh. Eksp. Teor. Fiz. 15, 475 (1945).

Popov, A. K.

A. K. Popov, Eur. Phys. J. D 58, 263 (2010).
[Crossref]

A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
[Crossref]

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[Crossref]

A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
[Crossref] [PubMed]

Shalaev, V. M.

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[Crossref]

A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
[Crossref]

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[Crossref]

A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
[Crossref] [PubMed]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).
[Crossref]

Slabko, V. V.

A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
[Crossref]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, Science 330, 1633 (2010).
[Crossref] [PubMed]

Wegener, M.

C. M. Soukoulis and M. Wegener, Science 330, 1633 (2010).
[Crossref] [PubMed]

Zheludev, N. I.

N. I. Zheludev, Opt. Photon. News 22 (3), 30 (2011)
[Crossref]

Appl. Phys. B (1)

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[Crossref]

Eur. Phys. J. D (1)

A. K. Popov, Eur. Phys. J. D 58, 263 (2010).
[Crossref]

Int. J. Eng. Sci. (1)

Y. Chen and J. D. Lee, Int. J. Eng. Sci. 41, 871 (2003).
[Crossref]

J. Appl. Phys. (1)

D. L. Bobroff, J. Appl. Phys. 36, 1760 (1965).
[Crossref]

Laser Phys. Lett. (1)

A. K. Popov, V. V. Slabko, and V. M. Shalaev, Laser Phys. Lett. 3, 293 (2006).
[Crossref]

Nat. Photon. (2)

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[Crossref]

J. B. Khurgin, Nat. Photon. 1, 446 (2007).
[Crossref]

Opt. Lett. (1)

Opt. Photon. News (1)

N. I. Zheludev, Opt. Photon. News 22 (3), 30 (2011)
[Crossref]

Phys. Rev. (1)

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787(1965).
[Crossref]

Phys. Rev. Lett. (1)

E. Anastassakis, S. Iwasa, and E. Burstein, Phys. Rev. Lett. 17, 1051 (1966).
[Crossref]

Science (1)

C. M. Soukoulis and M. Wegener, Science 330, 1633 (2010).
[Crossref] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

L. I. Mandelstam, Zh. Eksp. Teor. Fiz. 15, 475 (1945).

Other (2)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

V. S. Gorelik, Contemporary Problems of Raman Spectroscopy (Nauka, 1978), p. 28 (in Russian).

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Figures (2)

Fig. 1
Fig. 1

Negative dispersion of optical phonons and two phase-matching options: (a) copropagating and (b) contrapropagating fundamental and Stokes waves. Insets: relative directions of the energy flows and the wave vectors.

Fig. 2
Fig. 2

(a) Transmission of the Stokes wave T s ( z = L ) versus intensity of the fundamental control field in the vicinity of the first resonance (copropagating geometry). (b) Crystal thickness corresponding to the first output resonance for the Stokes wave versus intensity of the control field for the copropagating geometry; I min is the threshold intensity. (c) Transmission T s ( z = 0 ) versus intensity of the funda mental beam (contrapropagating geometry). (d) Comparison of the output intensities of the Stokes wave versus intensity of the control field for copropagating and contrapropagating coupling geometries, L = l p .

Equations (14)

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E l , s = ( 1 / 2 ) ε l , s ( z , t ) e i k l , s z i ω l , s t + c . c . , Q v = ( 1 / 2 ) Q ( z , t ) e i k v z i ω v t + c . c .
ω l = ω s + ω v ( k v ) , k l = k s ( ω s ) + k v ,
ε l z + 1 v l gr ε l t = i π ω l 2 k l c 2 N α Q ε s Q , ε s z + 1 v s gr ε s t = i π ω s 2 k s c 2 N α Q ε l Q * ,
Q z + 1 v v gr Q t + Q τ v v gr = i 1 4 ω v v v gr N α Q ε l ε s * .
ω v = ω 0 2 β k v 2 .
v v gr = β k v / ω v = β / v v ph ,
d Q / d z = i g 1 ε s * Q / ( τ v v gr ) , d ε s / d z = i g 2 Q * ,
Q * = A 1 e β 1 z + A 2 e β 2 z , ε s = A 3 e β 1 z + A 4 e β 2 z ,
T s = | e z { R cos [ R ( L z ) ] + sin [ R ( L z ) ] } R cos ( R L ) + sin ( R L ) | 2 ,
T s = | { β 1 e [ β 2 ( L z ) ] β 2 e [ β 1 ( L z ) ] } / 2 R | 2 ,
T s ( z = L ) 1 / cos 2 ( g L ) ,
T s ( z = 0 ) [ exp ( 2 | g | L ) ] / 4 ,
I min = ( c n s λ s 0 ω v / 8 π 3 l p τ ) | N α / Q | 2 ,
L = [ π tan 1 ( R ) ] / R .

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