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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 7 — Jul. 1, 2012
  • pp: 1661–1671

Universal properties of the optimized off-resonant intrinsic second hyperpolarizability

David S. Watkins and Mark G. Kuzyk  »View Author Affiliations

JOSA B, Vol. 29, Issue 7, pp. 1661-1671 (2012)

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We seek to identify universal properties shared by all quantum systems with large intrinsic second hyperpolarizability ( γ int )—an invariant quantity that removes the effects of simple scaling. A large- γ int quantum system is generated by varying the shape of a trial potential until γ int 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 γ int . 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

OCIS Codes
(020.5580) Atomic and molecular physics : Quantum electrodynamics
(160.4330) Materials : Nonlinear optical materials
(190.0190) Nonlinear optics : Nonlinear optics
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(160.4236) Materials : Nanomaterials
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Quantum Optics

Original Manuscript: January 24, 2012
Manuscript Accepted: March 19, 2012
Published: June 14, 2012

David S. Watkins and Mark G. Kuzyk, "Universal properties of the optimized off-resonant intrinsic second hyperpolarizability," J. Opt. Soc. Am. B 29, 1661-1671 (2012)

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  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]

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