Abstract

Metals typically have very large nonlinear susceptibilities (106 times larger than those of typical dielectrics), but because they are nearly opaque their nonlinear properties are effectively inaccessible. We demonstrate numerically that a multilayer metal–dielectric structure in which the metal is the dominant nonlinear χ3 material can have much larger intensity-dependent changes in the complex amplitude of the transmitted beam than a bulk sample containing the same thickness of metal. For 80 nm of copper the magnitude of the nonlinear phase shift is predicted to be as much as 40 times larger for the layered copper–silica sample, and the transmission is also greatly increased. The effective nonlinear refractive-index coefficient n2 of this composite material can be as large as 3+6i×10-9 cm2/W, which is among the largest values for known, reasonably transmissive materials.

© 1999 Optical Society of America

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References

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  1. F. Hache, D. Ricard, and C. Flytzanis, J. Opt. Soc. Am. B 3, 1647 (1986).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
    [CrossRef]
  9. Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
    [CrossRef] [PubMed]
  10. The attenuation constant ?=2?/cIm n is given by the intensity decay equation dI/dz=-?I, and the absorption constant ?=?/cIm ? is given by the steady-state Poynting theorem, dS/dz=-?cUE, where UE is the electric-field energy density.
  11. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  12. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
    [CrossRef]
  13. M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
    [CrossRef]
  14. D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 356.
  15. B. H. Billings, section ed., in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6.

1998 (2)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

1997 (1)

1995 (1)

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

1994 (2)

1989 (2)

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

A. E. Neeves and M. H. Birnboim, J. Opt. Soc. Am. B 6, 787 (1989).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1986 (1)

1935 (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Alfano, R. R.

Asahara, Y.

Becker, K.

Billings, B. H.

B. H. Billings, section ed., in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6.

Birnboim, M. H.

Bloemer, M. J.

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

Boyd, R. W.

D. D. Smith, G. L. Fischer, R. W. Boyd, and D. A. Gregory, J. Opt. Soc. Am. B 14, 1625 (1997).
[CrossRef]

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Bruggeman, D. A. G.

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Dorsinville, R.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Fischer, G. L.

D. D. Smith, G. L. Fischer, R. W. Boyd, and D. A. Gregory, J. Opt. Soc. Am. B 14, 1625 (1997).
[CrossRef]

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Flytzanis, C.

Garnett, J. C. Maxwell

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Gehr, R. J.

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Gregory, D. A.

Hache, F.

Haglund, R. F.

Hata, C.

Haus, J. W.

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

Hunter, W. R.

D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 356.

Ikushima, A. J.

Inguva, R.

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

Jenekhe, S. A.

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Kaneko, S.

Lynch, D. W.

D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 356.

Magruder, R. H.

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Nakamura, A.

Neeves, A. E.

Omi, S.

Osaheni, J. A.

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Pethel, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Ricard, D.

Scalora, M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

Sipe, J. E.

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Smith, D. D.

Smith, F. M.

Tanji, H.

Tokizaki, T.

Uchida, K.

Weller-Brophy, L. A.

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yang, L.

Zuhr, R. A.

Ann. Phys. (Leipzig) (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Appl. Phys. Lett. (1)

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

J. Appl. Phys. (1)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

J. Opt. Soc. Am. B (5)

Philos. Trans. R. Soc. London (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Phys. Rev. A (1)

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Layered geometries have also been studied in the context of all-dielectric nonlinear composite materials.?See, for example, G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995); R. L. Nelson and R. W. Boyd, Appl. Phys. Lett. 74, 2417 (1999).
[CrossRef] [PubMed]

Other (3)

The attenuation constant ?=2?/cIm n is given by the intensity decay equation dI/dz=-?I, and the absorption constant ?=?/cIm ? is given by the steady-state Poynting theorem, dS/dz=-?cUE, where UE is the electric-field energy density.

D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 356.

B. H. Billings, section ed., in American Institute of Physics Handbook, 3rd ed., D. E. Gray, ed. (McGraw-Hill, New York, 1982), Sec. 6.

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Figures (3)

Fig. 1
Fig. 1

Cross sections of (a) a silica and copper PBG structure and (b) a bulk sample of copper, with representative distributions of the electric field superimposed. The particular distribution shown in (a) corresponds to a sample with copper and silica layer thicknesses of 16 and 100 nm, respectively, at a wavelength of 650 nm.

Fig. 2
Fig. 2

(a) Linear transmission spectrum, as a function of silica layer thickness, of the silica–copper PBG structure, with dCu=16 nm and λ=650 nm. (b) Average of the squared field strength in the metal layers (normalized to the incident field), along with the phase sensitivity F [defined in Eq. (7)].

Fig. 3
Fig. 3

Ratio of the nonlinear phase shift of the PBG structure to that of a bulk copper sample, under the same conditions as in Fig. 2.

Equations (8)

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

dE/dz=ikH,
dH/dz=iklinz+12πχ11113zE2E,
Ei=12E0+H0/n0,
Er=12E0-H0/n0,
Et=12EL+HL/n0,
0=12EL-HL/n0,
FΔϕpbg2πλ0LΔndz
Δϕpbg=2πλn2effIL,

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