OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 2 — Feb. 1, 2002
  • pp: 289–296

Limits to the determination of the nonlinear refractive index by the Z-scan method

R. de Nalda, R. del Coso, J. Requejo-Isidro, J. Olivares, A. Suarez-Garcia, J. Solis, and C. N. Afonso  »View Author Affiliations

JOSA B, Vol. 19, Issue 2, pp. 289-296 (2002)

View Full Text Article

Acrobat PDF (286 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze the limitations imposed by sample absorption on the determination of the nonlinear refractive index by the Z-scan technique. By using a nanostructured thin film consisting of Cu nanocrystals embedded in a dielectric Al2O3 matrix as an example, we show that thermo-optical effects appearing when linear absorption is significant can be strongly misleading in the interpretation of the results of a Z scan. Even though this effect is not new, the widespread use of the Z-scan technique during the past several years makes it necessary to analyze explicitly the conditions under which the technique can be reliably applied and when more sophisticated techniques should be used instead. We discuss the contributions to the signal under different experimental conditions, several diagnostic techniques to discriminate true nonlinear effects from thermally induced phenomena, and different methods to reduce the thermal contribution.

© 2002 Optical Society of America

OCIS Codes
(000.2170) General : Equipment and techniques
(160.4330) Materials : Nonlinear optical materials
(190.3270) Nonlinear optics : Kerr effect
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(190.4870) Nonlinear optics : Photothermal effects

R. de Nalda, R. del Coso, J. Requejo-Isidro, J. Olivares, A. Suarez-Garcia, J. Solis, and C. N. Afonso, "Limits to the determination of the nonlinear refractive index by the Z-scan method," J. Opt. Soc. Am. B 19, 289-296 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. M. Sheik-Bahae, A. A. Said, T. 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).
  2. R. L. Sutherland, ed., Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).
  3. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089–2094 (1987).
  4. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
  5. M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system related materials,” IEEE J. Quantum Electron. QE-11, 259–265 (1975).
  6. A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. QE-9, 1064–1071 (1973).
  7. P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in electric field strength,” Phys. Rev. 137, A801–A818 (1965).
  8. W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
  9. Y. Bae, J. J. Song, and Y. B. Kim, “Photoacoustic study of two-photon absorption in hexagonal ZnS,” J. Appl. Phys. 53, 615–619 (1982).
  10. S. M. Mian, B. Taheri, and J. P. Wicksted, “Effects of beam ellipticity on z-scan measurements,” J. Opt. Soc. Am. B 13, 856–863 (1996).
  11. Y. L. Huang and C. K. Sun, “Z-scan measurement with an astigmatic Gaussian beam,” J. Opt. Soc. Am. B 17, 43–47 (2000).
  12. P. Chen, D. A. Oulianov, I. V. Tomov, and P. M. Rentzepis, “Two- dimensional z-scan for arbitrary beam shape and sample thickness,” J. Appl. Phys. 85, 7043–7050 (1999).
  13. P. B. Chapple, J. Staromlynska, and R. G. McDuff, “Z-scan studies in the thin- and the thick-sample limits,” J. Opt. Soc. Am. B 11, 975–982 (1994).
  14. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
  15. S. Bian, M. Martinelli, and R. J. Horowicz, “Z-scan formula for saturable Kerr media,” Opt. Commun. 172, 347–353 (1999).
  16. A. Marcano, O. H. Maillotte, D. Gindre, and D. Métin, “Picosecond nonlinear refraction measurement in single-beam open z-scan by charge-coupled device image processing,” Opt. Lett. 21, 101–103 (1996).
  17. F. E. Hernández, A. Marcano, and H. Maillotte, “Sensitivity of the total beam profile distortion z-scan for the measurement of nonlinear refraction,” Opt. Commun. 134, 529–536 (1997).
  18. T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
  19. A. Marcano, F. E. Hernández, and A. D. Sena, “Two-color near-field eclipsing z-scan technique for the determination of nonlinear refraction,” J. Opt. Soc. Am. B 14, 3363–3367 (1997).
  20. K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, and A. Nakamura, “Optical nonlinearities of a high concentration of small particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
  21. D. Ricard, P. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511–513 (1985).
  22. H. B. Liao, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Large third order nonlinear optical susceptibility of Au–Al2O3 composite films near the resonant frequency,” Appl. Phys. B 65, 673–676 (1997).
  23. R. H. Magruder III, L. Yang, R. F. Haglund, Jr., C. W. White, L. Yang, R. Dorsinville, and R. R. Alfano, “Optical properties of gold nanocluster composites formed by deep ion implantation in silica,” Appl. Phys. Lett. 62, 1730–1732 (1993).
  24. F. Hache, D. Richard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
  25. J. M. Ballesteros, J. Solís, R. Serna, and C. N. Afonso, “Nanocrystal size dependence of the third order nonlinear optical response of Cu:Al2O3 thin films,” Appl. Phys. Lett. 74, 2791–2793 (1999).
  26. M. Falconieri, G. Salvetti, E. Cattaruzza, F. Gonella, G. Mattei, P. Mazzoldi, M. Piovesan, G. Battaglin, and R. Polloni, “Large third order optical nonlinearity of nanocluster-doped glass formed by ion implantation of copper and nickel in silica,” Appl. Phys. Lett. 73, 288–290 (1998).
  27. Y. Takeda, T. Hioki, T. Motohiro, and S. Noda, “Large third-order optical nonlinearity of tin microcrystallite-doped silica glass formed by ion implantation,” Appl. Phys. Lett. 63, 3420–3422 (1993).
  28. M. Sheik-Bahae, A. A. Said, and E. W. Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
  29. J. M. Ballesteros, R. Serna, J. Solís, C. N. Afonso, A. K. Petford-Long, D. H. Osborne, and R. F. Haglund, Jr., “Pulsed laser deposition of Cu:Al2O3 nanocrystal thin films with high third order optical susceptibility,” Appl. Phys. Lett. 71, 2445–2447 (1997).
  30. L. R. Doolittle, “Algorithms for the rapid simulation of Rutherford backscattering spectra,” Nucl. Instrum. Methods B 9, 344–351 (1985).
  31. R. Serna, C. N. Afonso, C. Ricolleau, Y. Wang, Y. Zheng, M. Gandais, and I. Vickridge, “Artificially nanostructured Cu:Al2O3 films produced by pulsed laser deposition,” Appl. Phys. A 71, 583–586 (2000).
  32. A. Naudon and D. Thiaudière, “Grazing-incidence small-angle scattering. Morphology of deposited clusters and nanostructure of thin films,” J. Appl. Crystallogr. 30, 822–827 (1997).
  33. A. Naudon, D. Babonneau, D. Thiaudière, and S. Lequien, “Grazing-incidence small-angle X-ray scattering applied to the characterization of aggregates in surface regions,” Physica B 283, 69–74 (2000).
  34. Peak power refers to the maximum power of the laser pulse and the mean power to the total power of the train of pulses. Intensity refers to the energy density, i.e., the power of a laser pulse (peak or total) divided by the area of the laser beam.
  35. R. F. Haglund, Jr., L. Yang, R. H. Magruder, III, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of a Cu:silica nanocluster composite,” Opt. Lett. 18, 373–375 (1993).
  36. L. Yang, D. H. Osborne, R. F. Haglund, Jr., R. H. Magruder, C. W. White, R. A. Zuhr, and H. Hosono, “Probing interface properties of nanocomposites by third order nonlinear optics,” Appl. Phys. A 62, 403–415 (1996).
  37. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331–333 (1974).
  38. T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
  39. M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature coefficient of optical path length in soda lime glass at different wavelengths,” J. Appl. Phys. 75, 3732–3737 (1994).
  40. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982).
  41. T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, and Y. Asahara, “Subpicosecond time response of third order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
  42. M. Falconieri, “Thermo-optical effects in z-scan measurements using high-repetition-rate lasers,” J. Opt. A: Pure Appl. Opt. 1, 662–667 (1999).
  43. S. Vijayalakshmi, H. Grebel, Z. Iqbal, and C. W. White, “Ar-tificial dielectrics: nonlinear properties of Si nanoclusters formed by ion implantation in SiO2 glassy matrix,” J. Appl. Phys. 84, 6502–6506 (1998).
  44. X. Zhu and Z. Meng, “The optical nonlinearity and structure for a PbO, TiO2, SiO2 and K2O quaternary glass systems,” J. Appl. Phys. 75, 3756–3760 (1994).
  45. A. A. Andrade, E. Tenório, T. Catunda, M. L. Baesso, A. Cassanho, and H. P. Jenssen, “Discrimination between electronic and thermal contributions to the nonlinear refractive index of SrAlF5:Cr+3,” J. Opt. Soc. Am. B 16, 395–400 (1999).
  46. Y. M. Cheung and S. K. Gayen, “Optical nonlinearities of tea studied by z-scan and four-wave mixing techniques,” J. Opt. Soc. Am. B 11, 636–643 (1994).
  47. B. Taheri, A. F. Munoz, W. D. St. John, J. P. Wicksted, R. C. Powell, D. H. Blackburn, and D. C. Cranmer, “Effects of the structure and composition of lead glasses on the thermal lensing of pulsed radiation,” J. Appl. Phys. 71, 3693–3700 (1992).
  48. M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
  49. R. F. Haglund, Handbook of Optical Properties. Vol. II: Optics of Small Particles, Interfaces and Surfaces, R. E. Hummel and P. Wissmann, eds. (CRC Press, Boca Raton, Fla., 1997).
  50. L. Yang, “Nonlinear optics of noble metal crystallites embedded in a dielectric matrix,” Ph.D. dissertation (Vanderbilt University, Nashville, Tenn., 1993).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited