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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 9 — Sep. 1, 2006
  • pp: 1894–1910

Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers

Evgueni Parilov and M. J. Potasek  »View Author Affiliations

JOSA B, Vol. 23, Issue 9, pp. 1894-1910 (2006)

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We introduce a generalized numerical method to calculate short-pulsed laser propagation in a wide class of multiphoton absorbing materials. The method has no restrictions on the input pulse widths varying from nanosecond to femtosecond, and its numerical solution is both radially and temporarily dependent, enabling us to check numerically the validity of assuming radially constant solutions, which ensures that the true peak intensity falls below the damage causing level. A new feature of our technique enables us to determine quantitatively the contributions to the total absorption due to every electronic energy level. We found excellent agreement between our calculations and experiments using sample materials ranging from reverse saturable absorbers, two-photon absorbers with excited-state absorption to three-photon absorbers. We applied our technique to a two-photon absorber with excited-state absorption and found approximately 1 order of magnitude increase in the absorption when femtosecond pulses were used in place of nanosecond pulses.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.4180) Nonlinear optics : Multiphoton processes
(190.4400) Nonlinear optics : Nonlinear optics, materials

ToC Category:
Nonlinear Optics

Original Manuscript: March 9, 2006
Revised Manuscript: April 24, 2006
Manuscript Accepted: May 2, 2006

Evgueni Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am. B 23, 1894-1910 (2006)

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  1. B. J. Bacskai, J. Skoch, G. A. Hickey, R. Allen, and B. T. Hyman, "Fluorescence resonance energy transfer determinations using multiphoton fluorescence lifetime imaging microscopy to characterize amyloid-beta plaques," J. Biomed. Opt. 8, 368-375 (2003). [CrossRef] [PubMed]
  2. E. S. Marmur, C. D. Schmults, and D. J. Goldberg, "A review of laser and photodynamic therapy for the treatment of nonmelanoma skin cancer," Dermatol. Surg. 30, 264-271 (2004). [CrossRef] [PubMed]
  3. L. W. Tutt and T. F. Boggess, "A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials," Prog. Quantum Electron. 17, 299-305 (1993). [CrossRef]
  4. J. E. Rogers, J. E. Slagle, D. G. McLean, R. L. Sutherland, B. Sankaran, R. Kannan, L.-S. Tan, and P. A. Fleitz, "Understanding the one-photon photophysical properties of a two-photon absorbing chromophore," J. Phys. Chem. A 108, 5514-5520 (2004). [CrossRef]
  5. J. W. Perry, "Organic and metal-containing reverse saturable absorbers for optical limiters," in Nonlinear Optics of Organic Molecules and Polymers, H.S.Nalwa and S.Miyata, eds. (CRC, 1997), pp. 813-839.
  6. M. J. Potasek, S. Kim, and D. McLaughlin, "All optical power limiting," J. Nonlinear Opt. Phys. Mater. 9, 343-365 (2000). [CrossRef]
  7. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, "Nonlinear optical beam propagation for optical limiting," Appl. Opt. 38, 5168-5180 (1999). [CrossRef]
  8. W. Jia, E. P. Douglas, F. Guo, and W. Sun, "Optical limiting of semiconductor nanoparticles for nanosecond laser pulses," Appl. Phys. Lett. 85, 6326-6328 (2004). [CrossRef]
  9. S. M. Kirkpatrick, R. R. Naik, and M. O. Stone, "Nonlinear saturation and determination of the two-photon absorption cross section of green fluorescent protein," J. Phys. Chem. B 105, 2867-2873 (2001). [CrossRef]
  10. S. Maruo and S. J. Kawata, "Two-photon-absorbed near-infrared photopolymerization for three-dimensional microfabridation," J. Microelectromech. Syst. 7, 411-415 (1998). [CrossRef]
  11. B. H. Cumpston, S. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999). [CrossRef]
  12. G. Witzgall, R. Vrijen, and E. Yablonovitch, "Single-shot two-photon exposure of commercial photoresist for the production of three-dimensional structures," Opt. Lett. 23, 1745-1748 (1998). [CrossRef]
  13. W. Denk, J. H. Strickler, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990). [CrossRef] [PubMed]
  14. H. E. Pudavar, M. P. Joshi, P. N. Prasad, and B. A. Reinhardt, "High-density three-dimensional optical data storage in a stacked compact disk format with two-photon writing and single photon readout," Appl. Phys. Lett. 74, 1338-1340 (1999). [CrossRef]
  15. P. N. Prasad, "Emerging opportunities at the interface of photonics, nanotechnology and biotechnology," Mol. Cryst. Liq. Cryst. 415, 1-10 (2004). [CrossRef]
  16. M. Albota, D. Beljonne, J. L. Bredas, J. E. Ehrlich, J. F. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Rochel, M. Rumi, G. Subramaniam, W. W. Webb, X. L. Wu, and C. Xu, "Design of organic molecules with large two-photon absorption cross sections," Science 281, 1653-1656 (1998). [CrossRef] [PubMed]
  17. B. A. Reinhardt, L. L. Brott, S. J. Clarson, A. G. Dillard, J. C. Bhatt, R. Kannan, L. Yuan, G. S. He, and P. N. Prasad, "Highly active two-photon dyes: design, synthesis, and characterization toward application," Chem. Mater. 10, 1863-1874 (1998). [CrossRef]
  18. J. Kleinschmidt, S. Rentsch, W. Tottleben, and B. Wilhelmi, "Measurement of strong nonlinear absorption in stilbene-chloroform solution, explained by the superposition of two-photon absorption and one-photon absorption from the excited state," Chem. Phys. Lett. 24, 133-135 (1974). [CrossRef]
  19. D. A. Oulianov, I. V. Tomov, A. S. Dvornikow, and R. M. Rentzepis, "Observations on the measurements of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001). [CrossRef]
  20. S. Guha, K. Kang, P. Porter, J. F. Roach, D. E. Remy, F. J. Aranda, and D. V. G. L. N. Rao, "Third-order optical nonlinearities of metallotetrabenzoporphyrins and a platinum polyyne," Opt. Lett. 17, 264-266 (1992). [CrossRef] [PubMed]
  21. R. L. Sutherland, M. C. Brant, J. Heinrichs, J. E. Rogers, J. E. Slagle, D. G. McLean, and P. A. Fleitz, "Excited-state characterization and effective three-photon absorption model of two-photon-induced excited state absorption in organic push-pull charge-transfer chromophores," J. Opt. Soc. Am. B 22, 1939-1948 (2005). [CrossRef]
  22. G. S. He, T.-C. Lin, J. Dai, P. N. Prasad, R. Kannan, A. G. Dombroskie, R. A. Vaia, and L.-S. Tan, "Degenerate two-photon-absorption spectral studies of highly two-photon active organic chromophores," J. Phys. Chem. 120, 5275-5284 (2004). [CrossRef]
  23. R. Kannan, G. S. He, T.-C. Lin, P. N. Prasad, R. A. Vaia, and L.-S. Tan, "Toward highly active two-photon absorbing liquids. Synthesis and characterization of 1,3,5-triazine-based octupolar molecules," Chem. Mater. 16, 185-194 (2004). [CrossRef]
  24. D.-Y. Wang, C.-L. Zhan, Y. Chen, Y.-J. Li, Z.-Z. Lu, and Y.-Z. Nie, "Large optical power limiting induced by three-photon absorption of two stibazolium-like dyes," Chem. Phys. Lett. 369, 621-626 (2002). [CrossRef]
  25. I. C. Khoo, A. Diaz, and J. Ding, "Nonlinear-absorbing fiber array for large-dynamic-range optical limiting application against intense short laser pulses," J. Opt. Soc. Am. B 21, 1234-1240 (2004). [CrossRef]
  26. N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982). [CrossRef]
  27. U. Siegner and U. Keller, "Nonlinear optical processes for ultrashort pulse generation," in Handbook of Optics, M.Bass, J.M.Enoch, E.W.Van Stryland, and W.Wolfe, eds. (McGraw-Hill, 2001), Vol. 4, pp. 25-31.
  28. Y. R. Shen, The Principle of Nonlinear Optics (Wiley, 1984).
  29. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1990).
  30. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Plenum, 1975).
  31. A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer Academic, 1999).
  32. R. L. Sutherland, Handbook of Nonlinear Optics (Dekker, 2003). [CrossRef]
  33. J. Moloney and A. Newell, Nonlinear Optics (Westview, 2004).
  34. C. W. Gardiner and M. J. Collet, "Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation," Phys. Rev. A 31, 3761-3774 (1985). [CrossRef] [PubMed]
  35. C. W. Gardiner and A. S. Parkins, "Driving atoms with light of arbitrary statistics," Phys. Rev. A 50, 1792-1806 (1994). [CrossRef] [PubMed]
  36. M. Lax, "Quantum noise IV. Quantum theory of noise sources," Phys. Rev. 145, 110-129 (1966). [CrossRef]
  37. A. Barchielli, "Measurement theory and stochastic differential equations in quantum mechanics," Phys. Rev. A 34, 1642-1649 (1986). [CrossRef] [PubMed]
  38. N. J. Turro, Modern Molecular Photochemistry (Benjamin, 1978).
  39. C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, "Excited-state nonlinear absorption in multi-energy-level molecular systems," Phys. Rev. A 51, 569-575 (1995). [CrossRef] [PubMed]
  40. A. Baev, F. Gel'mukhanov, P. Macak, Y. Luo, and H. Ågren, "General theory for pulse propagation in two-photon active media," J. Phys. Chem. 117, 6214-6220 (2002). [CrossRef]
  41. M. Klessinger and J. Michl, Excited States and Photochemistry of Organic Molecules (VCH, 1995).
  42. D. G. McLean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, and T. Pottenger, "Nonlinear absorption study of a C60-toluene solution," Opt. Lett. 18, 858-860 (1993). [CrossRef] [PubMed]
  43. A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, "Analytical approach to dynamics of reverse saturable absorbers," J. Opt. Soc. Am. B 17, 1884-1894 (2000). [CrossRef]
  44. I. C. Khoo, P. H. Chen, M. V. Wood, and M.-Y. Shih, "Molecular photonics of a highly nonlinear organic fiber core liquid for picosecond-nanosecond optical limiting application," Chem. Phys. 245, 517-531 (1999). [CrossRef]
  45. I.-C. Khoo, A. Diaz, M. V. Wood, and P. H. Chen, "Passive optical limiting of picosecond-nanosecond laser pulses using highly nonlinear organic liquid cored fiber array," IEEE J. Sel. Top. Quantum Electron. 7, 760-768 (2001). [CrossRef]
  46. S. Hughes, J. M. Burzler, and T. Kobayashi, "Modeling of picosecond-pulse propagation for optical limiting applications in the visible spectrum," J. Opt. Soc. Am. B 11, 2925-2929 (1997). [CrossRef]
  47. P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988).

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