Abstract

We seek to identify universal properties shared by all quantum systems with large intrinsic second hyperpolarizability (γint)—an invariant quantity that removes the effects of simple scaling. A large-γint quantum system is generated by varying the shape of a trial potential until γint is optimized. A variety of starting potentials yield a set of systems with distinctly shaped optimized potentials, but are found to share universal properties that separate into classes determined by the magnitude and sign of γint. However, the fact that the best systems are 0.6 times the fundamental limit suggests that exotic Hamiltonians may be required to reach the upper bound. The observed regularity hints at a deeper relationship between optimized systems that may provide useful insights applicable to designing better materials. Being general, this approach applies to any quantum system, including molecules, nanoparticles, or quantum gases.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
    [CrossRef]
  2. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
    [CrossRef]
  3. S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
    [CrossRef]
  4. A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
    [CrossRef]
  5. I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
    [CrossRef]
  6. J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
    [CrossRef]
  7. M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
    [CrossRef]
  8. J. Fu, A. P. Lazaro, D. J. Hagan, E. W. Van Stryland, O. V. Przhonska, M. V. Bondar, Y. L. Slominsky, and A. D. Kachkovski, “Molecular structure—two-photon absorption property relations in polymethine dyes,” J. Opt. Soc. Am. B 24, 56–66 (2007).
    [CrossRef]
  9. M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
    [CrossRef]
  10. Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
    [CrossRef]
  11. P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
    [CrossRef]
  12. M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
    [CrossRef]
  13. M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
    [CrossRef]
  14. M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quant. Opt. 40, 1–13 (2010).
  15. D. S. Watkins and M. G. Kuzyk, “The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability,” J. Chem. Phys. 134, 094109 (2011).
    [CrossRef]
  16. V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
    [CrossRef]
  17. K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
    [CrossRef]
  18. K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).
  19. D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
    [CrossRef]
  20. G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
    [CrossRef]
  21. B. Kirtman and B. Champagne, “Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules,” Int. Rev. Phys. Chem. 16, 389–420 (1997).
    [CrossRef]
  22. A. Painelli, “Vibronic contribution to static NLO properties: exact results for the DA dimer,” Chem. Phys. Lett. 285, 352–358 (1998).
    [CrossRef]
  23. D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
    [CrossRef]
  24. F. Kajzar and J. Messier, “Original technique for third harmonic generation measurements in liquids,” Rev. Sci. Instrum. 58, 2081–2085 (1987).
    [CrossRef]
  25. K. Clays and A. Persoons, “Hyper-Rayleigh Scattering in solution,” Phys. Rev. Lett. 66, 2980–2983 (1991).
    [CrossRef]
  26. J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
    [CrossRef]
  27. C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
    [CrossRef]
  28. B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513–526 (1971).
    [CrossRef]
  29. M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
    [CrossRef]
  30. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
    [CrossRef]
  31. M. G. Kuzyk, “Erratum: physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902(2003).
    [CrossRef]
  32. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135 (2003).
    [CrossRef]
  33. M. G. Kuzyk, “Doubly resonant two-photon absorption cross-sections: it doesn’t get any bigger than this,” J. Nonlinear Opt. Phys. Mater. 13, 461–466 (2004).
    [CrossRef]
  34. M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
    [CrossRef]
  35. J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
    [CrossRef]
  36. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, 1977).
  37. S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
    [CrossRef]
  38. X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
    [CrossRef]
  39. J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
    [CrossRef]
  40. J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
    [CrossRef]
  41. B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).
  42. J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. 23, 1428–1432 (2011).
    [CrossRef]
  43. J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
    [CrossRef]
  44. J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
    [CrossRef]
  45. J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
    [CrossRef]
  46. J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
    [CrossRef]
  47. C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
    [CrossRef]
  48. T. Atherton, J. Lesnefsky, G. Wiggers, and R. Petschek, “Maximizing the hyperpolarizability poorly determines the potential,” J. Opt. Soc. Am. B 29, 513–520 (2012).
    [CrossRef]
  49. M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
    [CrossRef]
  50. S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
    [CrossRef]
  51. H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
    [CrossRef]
  52. H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
    [CrossRef]
  53. J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
    [CrossRef]
  54. B. Champagne and B. Kirtman, “Comment on “Physical limits on electronic nonlinear molecular susceptibilities”,” Phys. Rev. Lett. 95, 109–401 (2005).
    [CrossRef]
  55. D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
    [CrossRef]
  56. O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed. (Butterworth-Heinemanm, 2005).
  57. D. C. Sorensen, “Implicit application of polynomial filters in a k-step Arnoldi method,” SIAM J. Matrix Anal. Appl. 13, 357–385 (1992).
    [CrossRef]
  58. J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Reply to “Comment on pushing the hyperpolarizability to the limit”,” Opt. Lett. 32, 944–945 (2007).
    [CrossRef]
  59. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
    [CrossRef]
  60. M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
    [CrossRef]
  61. M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104(2006).
    [CrossRef]
  62. C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: amethod for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
    [CrossRef]
  63. M. G. Kuzyk and M. C. Kuzyk, “Nature limits the performance of optical devices,” SPIE Newsroom (2008).
  64. S. Shafei and M. G. Kuzyk, “Critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system,” J. Opt. Soc. Am. B 28, 882–891(2011).
    [CrossRef]

2012 (1)

2011 (4)

S. Shafei and M. G. Kuzyk, “Critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system,” J. Opt. Soc. Am. B 28, 882–891(2011).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability,” J. Chem. Phys. 134, 094109 (2011).
[CrossRef]

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. 23, 1428–1432 (2011).
[CrossRef]

2010 (4)

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
[CrossRef]

M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quant. Opt. 40, 1–13 (2010).

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

2009 (3)

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

2008 (4)

P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
[CrossRef]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

2007 (6)

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

J. Fu, A. P. Lazaro, D. J. Hagan, E. W. Van Stryland, O. V. Przhonska, M. V. Bondar, Y. L. Slominsky, and A. D. Kachkovski, “Molecular structure—two-photon absorption property relations in polymethine dyes,” J. Opt. Soc. Am. B 24, 56–66 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Reply to “Comment on pushing the hyperpolarizability to the limit”,” Opt. Lett. 32, 944–945 (2007).
[CrossRef]

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

2006 (5)

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104(2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

2005 (5)

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

B. Champagne and B. Kirtman, “Comment on “Physical limits on electronic nonlinear molecular susceptibilities”,” Phys. Rev. Lett. 95, 109–401 (2005).
[CrossRef]

2004 (4)

M. G. Kuzyk, “Doubly resonant two-photon absorption cross-sections: it doesn’t get any bigger than this,” J. Nonlinear Opt. Phys. Mater. 13, 461–466 (2004).
[CrossRef]

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

2003 (4)

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
[CrossRef]

M. G. Kuzyk, “Erratum: physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902(2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135 (2003).
[CrossRef]

2001 (1)

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

2000 (5)

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
[CrossRef]

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
[CrossRef]

1999 (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

1998 (4)

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

A. Painelli, “Vibronic contribution to static NLO properties: exact results for the DA dimer,” Chem. Phys. Lett. 285, 352–358 (1998).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
[CrossRef]

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

1997 (1)

B. Kirtman and B. Champagne, “Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules,” Int. Rev. Phys. Chem. 16, 389–420 (1997).
[CrossRef]

1994 (1)

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

1993 (1)

G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
[CrossRef]

1992 (2)

C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
[CrossRef]

D. C. Sorensen, “Implicit application of polynomial filters in a k-step Arnoldi method,” SIAM J. Matrix Anal. Appl. 13, 357–385 (1992).
[CrossRef]

1991 (1)

K. Clays and A. Persoons, “Hyper-Rayleigh Scattering in solution,” Phys. Rev. Lett. 66, 2980–2983 (1991).
[CrossRef]

1989 (1)

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: amethod for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

1987 (1)

F. Kajzar and J. Messier, “Original technique for third harmonic generation measurements in liquids,” Rev. Sci. Instrum. 58, 2081–2085 (1987).
[CrossRef]

1977 (1)

J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
[CrossRef]

1971 (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513–526 (1971).
[CrossRef]

Abreu, P. E.

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

Adant, C.

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

Albota, M.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Anderson, H. L.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Asselberghs, I.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Atherton, T.

Barlow, S.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Beljonne, D.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Benedict, J. B.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Beratan, D. N.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

Bergey, E. J.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Bethe, H. A.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, 1977).

Biaggio, I.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

Bishop, D. M.

D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
[CrossRef]

Bondar, M. V.

Boudon, C.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Bredas, J. L.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

Breiten, B.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Brown, E. C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Bures, F.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

Cardoso, C.

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

Cariati, E.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Champagne, B.

B. Champagne and B. Kirtman, “Comment on “Physical limits on electronic nonlinear molecular susceptibilities”,” Phys. Rev. Lett. 95, 109–401 (2005).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
[CrossRef]

B. Kirtman and B. Champagne, “Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules,” Int. Rev. Phys. Chem. 16, 389–420 (1997).
[CrossRef]

Chemla, D. S.

J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
[CrossRef]

Chen, Q. Y.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Cheng, L.

C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
[CrossRef]

Chernyak, V.

V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
[CrossRef]

Clays, K.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

K. Clays and A. Persoons, “Hyper-Rayleigh Scattering in solution,” Phys. Rev. Lett. 66, 2980–2983 (1991).
[CrossRef]

Coe, B. J.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Das, G. P.

G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
[CrossRef]

Diederich, F.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

Dirk, C. W.

C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: amethod for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

Dougherty, T. J.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Drobizhev, M.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Dudis, D.

G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
[CrossRef]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Dzenis, Y.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Ehrlich, J. E.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Eichinger, B. E.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Facchetti, A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Firestone, K. A.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Frank, B.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Fu, J.

Fu, J.-Y.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Ghanty, T. K.

P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
[CrossRef]

Gisselbrecht, J. P.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Guo, K.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Hagan, D. J.

Haller, M.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Hao, J.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Heikal, A. A.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Hess, S. E.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Ho, S. T.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Hu, X.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

Hu, Z.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

Jarowski, P. D.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Jen, A. K. Y.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Jiang, H.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Kachkovski, A. D.

Kajzar, F.

F. Kajzar and J. Messier, “Original technique for third harmonic generation measurements in liquids,” Rev. Sci. Instrum. 58, 2081–2085 (1987).
[CrossRef]

Kaminsky, W.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Kang, H.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Karotki, A.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Kawata, S.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

Keinan, S.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

Kelley, A. M.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Kirtman, B.

B. Champagne and B. Kirtman, “Comment on “Physical limits on electronic nonlinear molecular susceptibilities”,” Phys. Rev. Lett. 95, 109–401 (2005).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
[CrossRef]

B. Kirtman and B. Champagne, “Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules,” Int. Rev. Phys. Chem. 16, 389–420 (1997).
[CrossRef]

Kogej, T.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Kuang, L.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Kuzyk, M. C.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

M. G. Kuzyk and M. C. Kuzyk, “Nature limits the performance of optical devices,” SPIE Newsroom (2008).

Kuzyk, M. G.

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. 23, 1428–1432 (2011).
[CrossRef]

S. Shafei and M. G. Kuzyk, “Critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system,” J. Opt. Soc. Am. B 28, 882–891(2011).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability,” J. Chem. Phys. 134, 094109 (2011).
[CrossRef]

M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quant. Opt. 40, 1–13 (2010).

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Reply to “Comment on pushing the hyperpolarizability to the limit”,” Opt. Lett. 32, 944–945 (2007).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104(2006).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

M. G. Kuzyk, “Doubly resonant two-photon absorption cross-sections: it doesn’t get any bigger than this,” J. Nonlinear Opt. Phys. Mater. 13, 461–466 (2004).
[CrossRef]

M. G. Kuzyk, “Erratum: physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902(2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities: erratum,” Opt. Lett. 28, 135 (2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
[CrossRef]

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: amethod for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

M. G. Kuzyk and M. C. Kuzyk, “Nature limits the performance of optical devices,” SPIE Newsroom (2008).

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

Laporta, P. R.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Lazaro, A. P.

Lee, I.-Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Lesnefsky, J.

Levin, M. D.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Liao, Y.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Lim, J. H.

Liu, Z.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Liu, Z. F.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Luo, J.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Macchioni, A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Marder, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Marder, S. R.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Marks, T. J.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

May, J. C.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef]

McCord-Maughon, D.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Messier, J.

F. Kajzar and J. Messier, “Original technique for third harmonic generation measurements in liquids,” Rev. Sci. Instrum. 58, 2081–2085 (1987).
[CrossRef]

Michinobu, T.

Milne, B. F.

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

Moonen, N. N. P.

Morgan, J.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Mukamel,

V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
[CrossRef]

Nandi, P. K.

P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
[CrossRef]

Nogueira, F.

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

Ohulchanskyy, T. Y.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Orr, B. J.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513–526 (1971).
[CrossRef]

Oseroff, A. R.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Oudar, J. L.

J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
[CrossRef]

Painelli, A.

A. Painelli, “Vibronic contribution to static NLO properties: exact results for the DA dimer,” Chem. Phys. Lett. 285, 352–358 (1998).
[CrossRef]

Panja, N.

P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
[CrossRef]

Parker, T. C.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

Pérez Moreno, J.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Pérez-Moreno, J.

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. 23, 1428–1432 (2011).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

Perry, J. W.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Persoons, A.

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

K. Clays and A. Persoons, “Hyper-Rayleigh Scattering in solution,” Phys. Rev. Lett. 66, 2980–2983 (1991).
[CrossRef]

Petschek, R.

Pierce, B. M.

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

Prasad, P. N.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Przhonska, O. V.

Pudavar, H. E.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Qiu, L.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Ratner, M. A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

Rebane, A.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

Reid, P. J.

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

Righetto, S.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Rockel, H.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Roy, I.

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

Rumi, M.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Salpeter, E. E.

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, 1977).

Sargent, E. H.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Schweizer, W. B.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Seiler, P.

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Shafei, S.

S. Shafei and M. G. Kuzyk, “Critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system,” J. Opt. Soc. Am. B 28, 882–891(2011).
[CrossRef]

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
[CrossRef]

Shen, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

Slominsky, Y. L.

Sorensen, D. C.

D. C. Sorensen, “Implicit application of polynomial filters in a k-step Arnoldi method,” SIAM J. Matrix Anal. Appl. 13, 357–385 (1992).
[CrossRef]

Stern, C. L.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Subramaniam, G.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Sun, H.-B.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

Szafruga, U. B.

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

T., Y. W.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Takada, K.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

Tanaka, T.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

Taylor, P. N.

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Taylor, R. L.

O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed. (Butterworth-Heinemanm, 2005).

Thayumanavan, S.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

Therien, M. J.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

Tretiak, S.

V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
[CrossRef]

Tripathy, K.

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

Ugo, R.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Van Stryland, E. W.

Wang, M.

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

Wang, Z. Y.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Ward, J. F.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513–526 (1971).
[CrossRef]

Watkins, D. S.

D. S. Watkins and M. G. Kuzyk, “The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability,” J. Chem. Phys. 134, 094109 (2011).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Reply to “Comment on pushing the hyperpolarizability to the limit”,” Opt. Lett. 32, 944–945 (2007).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104(2006).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

Webb, W. W.

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

Wiggers, G.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

Wright, P.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

Wu, X.-L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Xiao, D.

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

Yang, W.

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

Yang, W. T.

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

Yang, Y.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Yeates, A. T.

G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
[CrossRef]

Zhao, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

Zhou, J.

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Reply to “Comment on pushing the hyperpolarizability to the limit”,” Opt. Lett. 32, 944–945 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef]

Zhu, J. Z.

O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed. (Butterworth-Heinemanm, 2005).

Zhu, P.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Zienkiewicz, O. C.

O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed. (Butterworth-Heinemanm, 2005).

Zuccaccia, C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Adv. Mater. (1)

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. 23, 1428–1432 (2011).
[CrossRef]

Angew. Chem., Int. Ed. (1)

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem., Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

Chem. Phys. Lett. (4)

V. Chernyak, S. Tretiak, and Mukamel, “Electronic versus vibrational optical nonlinearities of push-pull polymers,” Chem. Phys. Lett. 319, 261–264 (2000).
[CrossRef]

D. M. Bishop, B. Champagne, and B. Kirtman, “Comment on “Electronic versus vibrational optical nonlinearities of push-pull polymers” by V. Chernyak, S. Tretiak, and S. Mukamel,” Chem. Phys. Lett. 329, 329–330 (2000).
[CrossRef]

G. P. Das, A. T. Yeates, and D. Dudis, “Vibronic contribution to static molecular hyperpolaribilties,” Chem. Phys. Lett. 212, 671–676 (1993).
[CrossRef]

A. Painelli, “Vibronic contribution to static NLO properties: exact results for the DA dimer,” Chem. Phys. Lett. 285, 352–358 (1998).
[CrossRef]

Chem. Rev. (1)

J. L. Bredas, C. Adant, A. Persoons, and B. M. Pierce, “Third-order nonlinear-optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278(1994).
[CrossRef]

Eur. J. Org. Chem. (1)

B. Frank, P. R. Laporta, B. Breiten, M. C. Kuzyk, P. D. Jarowski, W. B. Schweizer, P. Seiler, I. Biaggio, C. Boudon, J. P. Gisselbrecht, and F. Diederich, “Comparison of CC triple and double bonds as spacers in push-pull chromophores,” Eur. J. Org. Chem. 2011, 4307–4317 (2011).

Int. J. Quantum Chem. (1)

C. W. Dirk, L. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27–36 (1992).
[CrossRef]

Int. Rev. Phys. Chem. (1)

B. Kirtman and B. Champagne, “Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules,” Int. Rev. Phys. Chem. 16, 389–420 (1997).
[CrossRef]

J. Am. Chem. Soc. (6)

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Rockel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J. L. Bredas, “Structure-property relationships for two-photon absorbing chromophores: bis-donor diphenylpolyene and bis(styryl)benzene derivatives,” J. Am. Chem. Soc. 122, 9500–9510 (2000).
[CrossRef]

Y. Liao, B. E. Eichinger, K. A. Firestone, M. Haller, J. Luo, W. Kaminsky, J. B. Benedict, P. J. Reid, and A. K. Y. Jen, “Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophore,” J. Am. Chem. Soc. 127, 2758–2766 (2005).
[CrossRef]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef]

I. Roy, T. Y. Ohulchanskyy, H. E. Pudavar, E. J. Bergey, A. R. Oseroff, J. Morgan, T. J. Dougherty, and P. N. Prasad, “Ceramic-based nanoparticles entrapping water-insoluble photosensitizing anticancer drugs: a novel drug-carrier system for photodynamic therapy,” J. Am. Chem. Soc. 125, 7860–7865 (2003).
[CrossRef]

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef]

J. Chem. Phys. (9)

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104(2006).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef]

J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
[CrossRef]

J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945 (2004).
[CrossRef]

K. Tripathy, J. Pérez Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Erratum: why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 125, 079905 (2006).

D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of p-conjugated pushpull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109, 9987–9994 (1998).
[CrossRef]

D. S. Watkins and M. G. Kuzyk, “The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability,” J. Chem. Phys. 134, 094109 (2011).
[CrossRef]

J. Mater. Chem. (1)

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (2)

M. G. Kuzyk, “Doubly resonant two-photon absorption cross-sections: it doesn’t get any bigger than this,” J. Nonlinear Opt. Phys. Mater. 13, 461–466 (2004).
[CrossRef]

M. G. Kuzyk, “Truncated sum rules and their use in calculating fundamental limits of nonlinear susceptibilities,” J. Nonlinear Opt. Phys. Mater. 15, 77–87 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. 27, 1849–1856 (2010).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. Chem. (1)

C. Cardoso, P. E. Abreu, B. F. Milne, and F. Nogueira, “Computational study of molecules with high intrinsic hyperpolarizabilities,” J. Phys. Chem. 114, 10676–10683 (2010).
[CrossRef]

J. Phys. Chem. A (2)

P. K. Nandi, N. Panja, and T. K. Ghanty, “Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study,” J. Phys. Chem. A 112, 4844–4852 (2008).
[CrossRef]

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef]

J. Phys. Chem. C (2)

X. Hu, D. Xiao, S. Keinan, I. Asselberghs, M. J. Therien, K. Clays, Y. W. T., and D. N. Beratan, “Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and Thomas–Kuhn sum rules,” J. Phys. Chem. C 114, 2349–2359 (2010).
[CrossRef]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

Mol. Phys. (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513–526 (1971).
[CrossRef]

Nano Lett. (1)

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Nature (2)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef]

Nonlinear Opt. Quant. Opt. (1)

M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quant. Opt. 40, 1–13 (2010).

Opt. Lett. (6)

Phys. Chem. Chem. Phys. (1)

A. Karotki, M. Drobizhev, Y. Dzenis, P. N. Taylor, H. L. Anderson, and A. Rebane, “Dramatic enhancement of intrinsic two-photon absorption in a conjugated porphyrin dimer,” Phys. Chem. Chem. Phys. 6, 7–10 (2004).
[CrossRef]

Phys. Rev. A (2)

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: amethod for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

M. G. Kuzyk, “Erratum: physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 90, 039902(2003).
[CrossRef]

K. Clays and A. Persoons, “Hyper-Rayleigh Scattering in solution,” Phys. Rev. Lett. 66, 2980–2983 (1991).
[CrossRef]

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef]

B. Champagne and B. Kirtman, “Comment on “Physical limits on electronic nonlinear molecular susceptibilities”,” Phys. Rev. Lett. 95, 109–401 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

F. Kajzar and J. Messier, “Original technique for third harmonic generation measurements in liquids,” Rev. Sci. Instrum. 58, 2081–2085 (1987).
[CrossRef]

Science (1)

M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rockel, M. Rumi, G. Subramaniam, and W. W. Webb, “Design of organic molecules with large two-photon absorption cross-sections,” Science 281, 1653–1656 (1998).
[CrossRef]

SIAM J. Matrix Anal. Appl. (1)

D. C. Sorensen, “Implicit application of polynomial filters in a k-step Arnoldi method,” SIAM J. Matrix Anal. Appl. 13, 357–385 (1992).
[CrossRef]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147(1998).
[CrossRef]

Other (3)

O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed. (Butterworth-Heinemanm, 2005).

M. G. Kuzyk and M. C. Kuzyk, “Nature limits the performance of optical devices,” SPIE Newsroom (2008).

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Plenum, 1977).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Second hyperpolarizability landscape.

Fig. 2.
Fig. 2.

(a) Importance of the state n to γ int as a function of n for positive optimized second hyperpolarizability. (b) A log plot better shows the relative importance of the smaller contributions, though values below 10 4 of the largest value for each potential may be inaccurate. Points below the horizontal red dashed line show contributions that are smaller than 10% of the largest contribution.

Fig. 3.
Fig. 3.

Importance of the state n to γ int as a function of n for negative optimized second hyperpolarizability. Points below the horizontal red dashed line shows contributions that are smaller than 10% of the largest contribution.

Fig. 4.
Fig. 4.

Plot of γ int ( n ) , the intrinsic hyperpolarizability when state n is excluded, as a function of state number n .

Fig. 5.
Fig. 5.

Positive and negative contributions to γ int when it is optimized for negative (open symbols) and positive (solid symbols) second hyperpolarizability.

Tables (5)

Tables Icon

Table 1. Summary of Calculations Seeking to Maximize Negative γ int with Different Starting Potentials a

Tables Icon

Table 2. Summary of Calculations Seeking to Maximize Positive γ int with Different Starting Potentials a

Tables Icon

Table 3. Summary of Optimized Potentials with Simple Symmetric Starting Potentials a

Tables Icon

Table 4. Summary of Optimized Potentials with Symmetric Starting Potentials Having Two Wells a

Tables Icon

Table 5. Summary of Optimized Potentials with Asymmetric Starting Potentials a

Equations (16)

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

( e m ) 4 N 2 E 10 5 γ 0 4 ( e m ) 4 N 2 E 10 5 γ MAX ,
γ int = γ / γ MAX ,
τ m p ( N ) = δ m , p 1 2 n = 0 N ( E n m + E n p ) x m n x n p ,
Δ τ ( N ) = m = 0 N / 2 p = 0 N / 2 ( τ m p ( N ) ) 2 N / 2 ,
x 10 max = m E 10 .
γ = a n m | x 0 n | 2 | x m 0 | 2 E n 0 2 E m 0 ,
γ + = + a n m p x 0 n x ¯ n m x ¯ m p x p 0 E n 0 E m 0 E p 0 ,
[ x , [ x , H ] ] = 2 m ,
[ x , A ] = i A p x ,
2 H p x 2 = 1 m ,
H = H ( x , y , p x , p y ) = p x 2 2 m + f ( x , y , p y ) p x + g ( x , y , p y ) ,
2 H p y 2 = p x 2 f p y 2 + 2 g p y 2 = 1 m .
2 f p y 2 = 0
2 g p y 2 = 1 m .
H ( x , p ) = p 2 2 m + d ( r ) p x p y p z + i = 1 3 j = i + 1 3 a i j ( r ) p i p j + i = 1 3 b i ( r ) p i + V ( r ) ,
p 2 ( p e c A ( r ) ) 2 ,

Metrics