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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 16, Iss. 11 — Nov. 1, 1999
  • pp: 1921–1935

Nonlinear optical waveguide spectroscopy of a conjugated polymer: poly(p-phenylenevinylene)

K. Ueberhofen, A. Deutesfeld, K. Koynov, and C. Bubeck  »View Author Affiliations


JOSA B, Vol. 16, Issue 11, pp. 1921-1935 (1999)
http://dx.doi.org/10.1364/JOSAB.16.001921


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Abstract

We have measured intensity-dependent prism coupling of poly(p-phenylenevinylene) thin films with picosecond laser pulses in the range 750–1600 nm. We developed a refined evaluation method that yields the signs and absolute values of the nonlinear refractive index n2 and the nonlinear absorption coefficient α2. Strong two-photon absorption levels were found at 2.8 and 3.1 eV. We observed a resonance at 1.3 eV that behaves as saturable absorption, and several additional resonances and sign changes of n2 at even lower photon energies. We demonstrate reversible refractive-index changes Δn=+0.002 at 910–950 nm on a picosecond time scale. Even larger Δn appear feasible.

© 1999 Optical Society of America

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(130.2790) Integrated optics : Guided waves
(160.5470) Materials : Polymers
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.4400) Nonlinear optics : Nonlinear optics, materials
(310.2790) Thin films : Guided waves

Citation
K. Ueberhofen, A. Deutesfeld, K. Koynov, and C. Bubeck, "Nonlinear optical waveguide spectroscopy of a conjugated polymer: poly(p-phenylenevinylene)," J. Opt. Soc. Am. B 16, 1921-1935 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-11-1921


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References

  1. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).
  2. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  3. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  4. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
  5. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
  6. G. I. Stegeman, “Nonlinear guided wave optics,” in Contemporary Nonlinear Optics, G. P. Agrawal and R. W. Boyd, eds. (Academic, Boston, Mass., 1992), pp. 1–40.
  7. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single beam n2 measurement,” Opt. Lett. 14, 955–957 (1989).
  8. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
  9. P. K. Tien, “Integrated optics and new wave phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
  10. T. Tamir, ed., Integrated Optics (Springer-Verlag, Berlin, 1979).
  11. R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
  12. P. K. Tien and R. Ulrich, “Theory of prism–film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
  13. R. Ulrich, “Theory of the prism–film coupler by plane-wave analysis,” J. Opt. Soc. Am. 60, 1337–1350 (1970).
  14. Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
  15. G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
  16. Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, “Nonlinear optical coupling to planar GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 48, 272–274 (1986).
  17. R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, “Nonlinear optical processes in a polymer waveguide: grating coupler measurements of electronic and thermal nonlinearities,” Appl. Phys. Lett. 53, 2011–2013 (1988).
  18. G. Assanto, B. Svensson, D. Kuchibhatla, U. J. Gibson, C. T. Seaton, and G. I. Stegeman, “Prism coupling into ZnS waveguides: a classic example of a nonlinear coupler,” Opt. Lett. 11, 644–646 (1986).
  19. R. M. Fortenberry, R. Moshefzadeh, G. Assanto, X. Mai, E. M. Wright, C. T. Seaton, and G. I. Stegeman, “Power-dependent coupling and fast switching in distributed coupling to ZnO waveguides,” Appl. Phys. Lett. 49, 687–689 (1986).
  20. R. M. Fortenberry, G. Assanto, R. Moshefzadeh, C. T. Seaton, and G. I. Stegeman, “Pulsed excitation of nonlinear distributed coupling into zinc oxide optical waveguides,” J. Opt. Soc. Am. B 5, 425–431 (1988).
  21. M. Sinclair, D. Mc Branch, D. Moses, and A. J. Heeger, “Time-resolved waveguide modulation of a conjugated polymer,” Appl. Phys. Lett. 53, 2374–2376 (1988).
  22. B. Rossi, H. J. Byrne, W. Blau, G. Pratesi, and S. Sottini, “Linear and nonlinear waveguiding in Rhodamine-doped epoxy films,” J. Opt. Soc. Am. B 8, 2449–2452 (1991).
  23. U. Bartuch, A. Bräuer, P. Dannberg, H.-H. Hörhold, and D. Raabe, “Measurement of high nonresonant third-order nonlinearity in MP-PPV waveguides,” Int. J. Optoelectron. 7, 275–279 (1992).
  24. H. Rigneault, F. Flory, and S. Monneret, “Nonlinear totally reflecting prism coupler: thermomechanic effects and intensity-dependent refractive index of thin films,” Appl. Opt. 34, 4358–4369 (1995).
  25. G. M. Carter and Y. J. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
  26. C. Liao and G. I. Stegeman, “Nonlinear prism coupler,” Appl. Phys. Lett. 44, 164–166 (1984).
  27. G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegemann, “Theory of pulsed excitation of nonlinear distributed prism couplers,” J. Opt. Soc. Am. B 5, 432–442 (1988).
  28. J. Staromlynska, R. Zanoni, and G. I. Stegeman, “Electronic versus thermal response for nonlinear prism coupling,” Appl. Opt. 31, 1170–1172 (1992).
  29. F. Pardo, H. Chellil, A. Koster, N. Paraire, and S. Laval, “Experimental and theoretical study of ultrafast switching using guided mode excitation in silicon on sapphire,” IEEE J. Quantum Electron. QE-23, 545–549 (1987).
  30. G. Vitrant and P. Arlot, “Demonstration of optical bistability with a nonlinear prism coupler,” J. Appl. Phys. 61, 4744–4748 (1987).
  31. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
  32. J. Fick and G. Vitrant, “Fast optical switching in nonlinear prism couplers,” Opt. Lett. 20, 1462–1464 (1995).
  33. L. A. Hornak, ed., Polymers for Lightwave and Integrated Optics (Marcel Dekker, New York, 1992).
  34. F. Kajzar and J. D. Swalen, eds., Organic Thin Films for Waveguiding Nonlinear Optics (Gordon & Breach, Amsterdam, 1996).
  35. H. S. Nalwa, “Nonlinear optical properties of π-conjugated materials,” in Conductive Polymers: Transport, Photophysics and Applications, Vol. 4 of Handbook of Organic Conductive Molecules and Polymers, H. S. Nalwa, ed. (Wiley, New York, 1997), pp. 261–363.
  36. D. D. C. Bradley, “Precursor-route poly(p-phenylene-vinylene): polymer characterization and control of electronic properties,” J. Phys. D 20, 1389–1410 (1987).
  37. J. D. Stenger-Smith, R. W. Lenz, and G. Wegner, “Spectroscopic and cyclic voltammetric studies of poly(p-phenylene vinylene) prepared from two different sulphonium salt precursor polymers,” Polymer 30, 1048–1053 (1989).
  38. T. Kaino, K.-I. Kubodera, S. Tomaru, and T. Kurihara, “Optical third-harmonic generation from poly(p-phenylenevinylene) thin films,” Electron. Lett. 23, 1095–1097 (1987).
  39. D. D. C. Bradley and Y. Mori, “Third harmonic generation in precursor route poly(p-phenylenevinylene),” Jpn. J. Appl. Phys. 28, 174–177 (1989).
  40. C. Bubeck, A. Kaltbeitzel, R. W. Lenz, D. Neher, J. D. Stenger-Smith, and G. Wegner, “Nonlinear optical properties of poly(p-phenylenevinylene) thin films,” in Nonlinear Optical Effects in Organic Polymers, J. Messier, F. Kajzar, P. N. Prasad, and D. Ulrich, eds. (Kluwer, Dordrecht, The Netherlands, 1989), pp. 143–147.
  41. T. Kurihara, Y. Mori, T. Kaino, H. Murata, N. Takada, T. Tsutsui, and S. Saito, “Spectra of χ(3)(−3ω; ω, ω, ω) in poly(2, 5-dimethoxy p-phenylene vinylene) (MO-PPV) for various conversion levels,” Chem. Phys. Lett. 183, 534–538 (1991).
  42. A. Mathy, K. Ueberhofen, R. Schenk, H. Gregorius, R. Garay, K. Müllen, and C. Bubeck, “Third-harmonic-generation spectroscopy of poly(p-phenylenevinylene): a comparison with oligomers and scaling laws for conjugated polymers,” Phys. Rev. B 53, 4367–4376 (1996).
  43. B. P. Singh, P. N. Prasad, and F. E. Karasz, “Third-order non-linear optical properties of oriented films of poly(p-phenylene vinylene) investigated by femtosecond degenerate four wave mixing,” Polymer 29, 1940–1942 (1988).
  44. C. Bubeck, A. Kaltbeitzel, A. Grund, and M. LeClerc, “Resonant degenerate four wave mixing and scaling laws for saturable absorption in thin films of conjugated polymers and Rhodamine 6G,” Chem. Phys. 154, 343–348 (1991).
  45. Y. Pang, M. Samoc, and P. N. Prasad, “Third-order nonlinearity and two-photon-induced molecular dynamics: femtosecond time-resolved transient absorption, Kerr gate, and degenerate four-wave mixing studies in poly(p-phenylene vinylene)/sol-gel silica film,” J. Chem. Phys. 94, 5282–5290 (1991).
  46. J. Swiatkiewicz, P. N. Prasad, and F. E. Karasz, “Anisotropy in the complex refractive index and the third-order nonlinear optical susceptibility of a stretch-oriented film of poly(p-phenylene vinylene),” J. Appl. Phys. 74, 525–530 (1993).
  47. A. Samoc, M. Samoc, M. Woodruff, and B. Luther-Davies, “Tuning the properties of poly(p-phenylenevinylene) for use in all-optical switching,” Opt. Lett. 20, 1241–1243 (1995).
  48. J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. McKay, R. H. Friend, P. L. Burn, and A. B. Holmes, “Light-emitting diodes based on conjugated polymers,” Nature (London) 347, 539–541 (1990).
  49. C. J. Baker, O. M. Gelsen, and D. D. C. Bradley, “Location of the lowest even parity excited singlet state in poly(p-phenylenevinylene) by two-photon fluorescence spectroscopy,” Chem. Phys. Lett. 201, 127–131 (1993).
  50. U. Lemmer, R. Fischer, J. Feldmann, R. F. Mahrt, J. Yang, A. Greiner, H. Bässler, E. O. Göbel, H. Heesel, and H. Kurz, “Time-resolved studies of two-photon absorption processes in poly(p-phenylenevinylene)s,” Chem. Phys. Lett. 203, 28–32 (1993).
  51. Z. G. Soos, S. Etemad, D. S. Galvao, and S. Ramasesha, “Fluorescence and topological gap of conjugated phenylene polymers,” Chem. Phys. Lett. 194, 341–346 (1992).
  52. R. H. Friend, D. D. C. Bradley, and P. D. Townsend, “Photo-excitation in conjugated polymers,” J. Phys. D 20, 1367–1384 (1987).
  53. D. D. C. Bradley, N. F. Colaneri, and R. H. Friend, “Photoexcitation in poly(p-phenylene vinylene),” Synth. Met. 29, E121–E127 (1989).
  54. N. F. Colaneri, D. D. C. Bradley, R. H. Friend, P. L. Burn, A. B. Holmes, and C. W. Spangler, “Photoexcited states in poly(p-phenylene vinylene): comparison with trans, trans-distyrylbenzene, a model oligomer,” Phys. Rev. B 42, 11670–11681 (1990).
  55. M. B. Sinclair, D. McBranch, T. W. Hagler, and A. J. Heeger, “Subpicosecond photoinduced absorption in poly(2, 5-thienylene vinylene) and poly(3-methoxy-6-(2-ethyl-hexyloxy) phenylene vinylene),” Synth. Met. 49–50, 593–602 (1992).
  56. X. Wei, B. C. Hess, Z. V. Vardeny, and F. Wudl, “Studies of photoexcited states in polyacetylene and poly(paraphenylenevinylene) by absorption detected magnetic resonance: the case of neutral photoexcitations,” Phys. Rev. Lett. 68, 666–669 (1992).
  57. I. D. W. Samuel, F. Raksi, D. D. C. Bradley, R. H. Friend, P. L. Burn, A. B. Holmes, H. Murata, T. Tsutsui, and S. Saito, “Femtosecond transient absorption measurements in poly(arylenevinylene)s,” Synth. Met. 55–57, 15–21 (1993).
  58. K. Pichler, D. A. Halliday, D. D. C. Bradley, R. H. Friend, P. L. Burn, and A. B. Holmes, “Photoinduced absorption of structurally improved poly(p-phenylene vinylene)—no evidence for bipolarons,” Synth. Met. 55–57, 230–234 (1993).
  59. L. J. Rothberg and M. Yan, “Time-resolved mid-infrared spectroscopy in conjugated polymers,” in Relaxation in Polymers, T. Kobayashi, ed. (World Scientific, Singapore, 1993), pp. 308–329.
  60. J. W. P. Hsu, M. Yan, T. M. Jedju, L. J. Rothberg, and B. R. Hsieh, “Assignment of the picosecond photoinduced absorption in phenylene vinylene polymers,” Phys. Rev. B 49, 712–715 (1994).
  61. J. M. Leng, S. Jeglinski, X. Wei, R. E. Benner, Z. V. Vardeny, F. Guo, and S. Mazumdar, “Optical probes of excited states in poly(p-phenylenevinylene),” Phys. Rev. Lett. 72, 156–159 (1994).
  62. H. A. Mizes and E. M. Conwell, “Photoinduced charge transfer in poly(p-phenylene vinylene),” Phys. Rev. B 50, 11243–11246 (1994).
  63. L. J. Rothberg, M. Yan, F. Papadimitrakopoulos, M. E. Galvin, E. W. Kwock, and T. M. Miller, “Photophysics of phenylenevinylene polymers,” Synth. Met. 80, 41–58 (1996).
  64. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
  65. K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
  66. R. Burzynski, P. N. Prasad, and F. E. Karasz, “Large optical birefringence in poly(p-phenylene vinylene) films measured by optical waveguide techniques,” Polymer 31, 627–630 (1990).
  67. F. Michelotti, T. Gabler, H.-H. Hörhold, R. Waldhausl, and A. Bräuer, “Prism coupling in DMOP-PPV optical waveguides,” Opt. Commun. 114, 247–254 (1995).
  68. K. Ueberhofen, R. O. Garay, K. Müllen, and C. Bubeck, “Nonlinear optical waveguide spectroscopy of poly(p-phenylenevinylene),” in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 11 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 308–310.
  69. J. R. Heflin and A. F. Garito, “Third-order optical processes in linear chains: electron correlation theory and experimental dispersion measurements,” in Ref. 33, pp. 501–542.
  70. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).
  71. J. Lekner, Theory of Reflection (Nijhoff, Dordrecht, The Netherlands, 1987).
  72. J. D. Swalen, “Optical properties of Langmuir–Blodgett films,” J. Mol. Electron. 2, 155–181 (1986).
  73. P. G. Kryukov, Y. A. Matveets, D. N. Nikogosyan, A. V. Sharkov, E. M. Goreev, and S. D. Fanchenko, “Generation of frequency-tunable single ultrashort light pulses in an LiIO3 crystal,” Sov. J. Quantum Electron. 7, 127–128 (1977).
  74. E. P. Ippen and C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed., Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), pp. 83–122.
  75. M. E. Lines, “Physical properties of materials: theoretical overview,” in Handbook of Infrared Optical Materials, P. Klocek, ed. (Marcel Dekker, New York, 1991), p. 57.
  76. D. McBranch, M. Sinclair, A. J. Heeger, A. O. Patil, S. Shi, S. Askari, and F. Wudl, “Linear and nonlinear optical studies of poly(p-phenylene vinylene),” Synth. Met. 29, E85–E90 (1989).
  77. C. H. Seager, M. Sinclair, D. McBranch, A. J. Heeger, and G. L. Baker, “Photothermal deflection spectroscopy of conjugated polymers,” Synth. Met. 49–50, 91–97 (1992).
  78. A. Mathy, H.-U. Simmrock, and C. Bubeck, “Optical waveguiding in thin films of polyelectrolytes,” J. Phys. D 24, 1003–1008 (1991).
  79. P. N. Prasad and D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991).
  80. H. Vanherzeele, J. S. Meth, S. A. Jenekhe, and M. F. Roberts, “Dispersion of the third-order nonlinear-optical properties of poly(p-phenylene benzobisthiazole) and its molecular composites with polyamides,” J. Opt. Soc. Am. B 9, 524–533 (1992).
  81. C. Bubeck, A. Kaltbeitzel, D. Neher, J. D. Stenger-Smith, G. Wegner, and A. Wolf, “Nonlinear optical properties of thin films of polymers with a one-dimensional conjugated π-electron system,” in Electronic Properties of Conjugated Polymers III, Vol. 19 of Springer Series in Solid-State Science (Springer-Verlag, Berlin, 1989), pp. 214–219.
  82. M. Chandross, S. Mazumdar, S. Jeglinski, X. Wei, Z. V. Vardeny, E. W. Kwock, and T. M. Miller, “Excitons in poly(p-phenylenevinylene),” Phys. Rev. B 50, 14702–14705 (1994).
  83. Th. Gabler, R. Waldhäusl, A. Bräuer, U. Bartuch, R. Stockmann, and H.-H. Hörhold, “Nonresonant n2 and two-photon-absorption dispersion measurements of DPOP-PPV and DP-PPV/DP-DFP polymer strip waveguides,” Opt. Commun. 137, 31–36 (1997).
  84. Th. Gabler, A. Bräuer, R. Waldhäusl, U. Bartuch, H.-H. Hörhold, and F. Michelotti, “Nonresonant n2 and TPA coefficient measurement in polymer waveguides by different measurement techniques,” Pure Appl. Opt. 7, 159–168 (1998).
  85. J. M. Oberski, A. Greiner, and H. Bässler, “Absorption spectra of the anions of phenylenevinylene oligomers and polymer,” Chem. Phys. Lett. 184, 391–397 (1991).
  86. M. Deussen and H. Bässler, “Anion and cation absorption spectra of conjugated oligomers and polymers,” Chem. Phys. 164, 247–257 (1992).
  87. Q. L. Zhou, J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Enhanced nonresonant nonlinear optical processes from populated electronic states,” Phys. Rev. A 43, 1673–1676 (1991).
  88. Q. L. Zhou, J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Excited state nonlinear optics,” in Organic Molecules for Nonlinear Optics and Photonics, J. Messier, F. Kajzar, and P. Prasad, eds., Vol. 194 of NATO ASI Series E (Kluwer Academic, Dordrecht, The Netherlands, 1991), pp. 239–262.
  89. D. C. Rodenberger, J. R. Heflin, and A. F. Garito, “Excited-state enhancement of optical nonlinearities in linear conjugated molecules,” Nature 359, 309–311 (1992).
  90. D. C. Rodenberger, J. R. Heflin, and A. F. Garito, “Excited-state enhancement of third-order optical responses in conjugated organic chains,” Phys. Rev. A 51, 3234–3245 (1995).
  91. B. Lawrence, W. E. Torruellas, M. Cha, M. L. Sundheimer, G. I. Stegemann, J. Meth, S. Etemad, and G. Baker, “Identification and role of two-photon excited states in a π-conjugated polymer,” Phys. Rev. Lett. 73, 597–600 (1994).
  92. W. Schmid, T. Vogtmann, and M. Schwoerer, “Influence of two-photon processes on the nonlinear optical response of polydiacetylene single crystals in the near-resonant spectral range,” Chem. Phys. 204, 147–155 (1996).
  93. M. Samoc, A. Samoc, B. Luther-Davies, and M. Woodruff, “The concept of guiding light with light and negative third-order optical nonlinearities of organics,” Pure Appl. Opt. 5, 681–687 (1996).
  94. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half bandgap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
  95. W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
  96. K. Meerholz, Y. De Nardin, R. Bittner, R. Wortmann, and F. Würthner, “Improved performance of photorefractive polymers based on merocyanine dyes in a polar matrix,” Appl. Phys. Lett. 73, 4–6 (1998).
  97. G. T. Boyd, “Applications requirements for nonlinear-optical devices and the status of organic materials,” J. Opt. Soc. Am. B 6, 685–692 (1989).
  98. J. L. Brédas, C. Adant, P. Tackx, and A. Persoons, “Third-order nonlinear optical response in organic materials: theoretical and experimental aspects,” Chem. Rev. 94, 243–278 (1994).

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