Abstract

By the use of sum rules, the largest third-order molecular nonlinear-optical susceptibilities allowed by quantum mechanics are determined. The theoretical upper limit is found to depend only on the first excited-state transition energy and on the number of electrons, in agreement with experimental data.

© 2000 Optical Society of America

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References

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  1. S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
    [CrossRef] [PubMed]
  2. F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
    [CrossRef]
  3. C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
    [CrossRef]
  4. A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
    [CrossRef]
  5. M. G. Kuzyk and C. W. Dirk, Phys. Rev. A 41, 5098 (1990).
    [CrossRef] [PubMed]
  6. S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
    [CrossRef] [PubMed]
  7. U. Gubler, Ch. Bosshard, P. Gunter, M. Y. Balakina, J. Cornil, J. L. Bredas, R. E. Martin, and F. Diederich, Opt. Lett. 24, 1599 (1999).
    [CrossRef]
  8. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, New York, 1977).
    [CrossRef]
  9. M. G. Kuzyk and C. W. Dirk, Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, New York, 1998).
  10. H. Kuhn, J. Chem. Phys. 17, 1198 (1949).
  11. M. G. Kuzyk, Phys. Rev. Lett. “Physical limits on electronic nonlinear molecular susceptibilities” (to be published).

1999 (1)

1994 (3)

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
[CrossRef]

1992 (1)

C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

1991 (1)

S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
[CrossRef] [PubMed]

1990 (1)

M. G. Kuzyk and C. W. Dirk, Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

1949 (1)

H. Kuhn, J. Chem. Phys. 17, 1198 (1949).

Balakina, M. Y.

Beratan, D. N.

S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
[CrossRef] [PubMed]

Bethe, H. A.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, New York, 1977).
[CrossRef]

Bosshard, Ch.

Bourhill, G.

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

Bredas, J. L.

U. Gubler, Ch. Bosshard, P. Gunter, M. Y. Balakina, J. Cornil, J. L. Bredas, R. E. Martin, and F. Diederich, Opt. Lett. 24, 1599 (1999).
[CrossRef]

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

Chang, L.-T.

C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

Cheng, L.-T.

S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
[CrossRef] [PubMed]

Cornil, J.

Diederich, F.

Dirk, C. W.

C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

M. G. Kuzyk and C. W. Dirk, Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, New York, 1998).

Garito, A. F.

A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
[CrossRef]

Gorman, C. B.

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

Gubler, U.

Gunter, P.

Kuhn, H.

H. Kuhn, J. Chem. Phys. 17, 1198 (1949).

Kuzyk, M. G.

C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

M. G. Kuzyk and C. W. Dirk, Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, New York, 1998).

M. G. Kuzyk, Phys. Rev. Lett. “Physical limits on electronic nonlinear molecular susceptibilities” (to be published).

Marder, S. R.

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
[CrossRef] [PubMed]

Martin, R. E.

Meyers, F.

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

Perry, J. W.

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

Pierce, B. M.

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

Salpeter, E. E.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, New York, 1977).
[CrossRef]

Shi, R. F.

A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
[CrossRef]

Wu, M.

A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
[CrossRef]

Int. J. Quantum Chem. (1)

C. W. Dirk, L.-T. Chang, and M. G. Kuzyk, Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

J. Am. Chem. Soc. (1)

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, J. Am. Chem. Soc. 116, 10,703 (1994).
[CrossRef]

J. Chem. Phys. (1)

H. Kuhn, J. Chem. Phys. 17, 1198 (1949).

Opt. Lett. (1)

Phys. Rev. A (1)

M. G. Kuzyk and C. W. Dirk, Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Phys. Today (1)

A. F. Garito, R. F. Shi, and M. Wu, Phys. Today 47(5), 51 (1994).
[CrossRef]

Science (2)

S. R. Marder, D. N. Beratan, and L.-T. Cheng, Science 252, 103 (1991).
[CrossRef] [PubMed]

S. R. Marder, C. B. Gorman, F. Meyers, J. W. Perry, G. Bourhill, J. L. Bredas, and B. M. Pierce, Science 265, 632 (1994).
[CrossRef] [PubMed]

Other (3)

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, New York, 1977).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, New York, 1998).

M. G. Kuzyk, Phys. Rev. Lett. “Physical limits on electronic nonlinear molecular susceptibilities” (to be published).

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Figures (3)

Fig. 1
Fig. 1

γ normalized to the centrosymmetric two-level model, as a function of energy ratio E for several normalized transition moments X.

Fig. 2
Fig. 2

γ normalized to the centrosymmetric two-level model, as a function of normalized transition moment X for several energy ratios E.

Fig. 3
Fig. 3

γ as a function of molecular length, for data (circles and squares) and theory (curves). Open circles are dispersed to zero frequency by a two-level model. γC is the centrosymmetric two-level model value.

Equations (16)

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

n=0En-12Em+Epxmnxnp=2N2mδm,p,
x102=22mE10N-n=2En0E10xn02,
γxxxx=4e43n,m,lx0nx¯nmx¯mlxl0Ωn0Ωm0Ωl0-n,mx0nxn0x0mxm0Ωn0Ωn0Ωm0,
γ3L=4e4E103x102Δx102-x102+x102x122-x202E+x202x122-x102E2+x202Δx202-x202E3+2 Rex01Δx10x12x20E+x01Δx20x12x20E2,
x012E10+x022E20=2N/2m.
-x012E10+x122E21=2N/2m.
x01Δx10E10+x02x21E21+E20=0,
x02Δx20E20+x01x12E10-E21=0,
x02=Ex012L2-x0121/2,
x12=E1-Ex012L2+x0121/2,
x01Δx10=2-E1-Ex012L4-x0141/2,
x02Δx20=2E-1x01E1-Ex012L2+x0121/2,
x01x12x20Δx20=x022Δx202/1-2E.
x02x21x10Δx10=Ex012Δx102/E-2.
γ2L=4e4E103x102Δx102-x102=4e4E103x102L44-5X4=γ2Lc4-5X4,
-e44m2N2E105γ4e44m2N2E105.

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