OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 640–644

Relation between nonlinear refractive index and third-order susceptibility in absorbing media

Raúl del Coso and Javier Solis  »View Author Affiliations

JOSA B, Vol. 21, Issue 3, pp. 640-644 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (161 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Expressions relating complex third-order optical susceptibility (χ(3)=χR(3)+iχI(3)) with nonlinear refractive index (n2) and nonlinear absorption coefficient (β) have been formulated that eliminate the commonly used approximation of a negligible linear absorption coefficient. The resulting equations do not show the conventional linear dependence of χR(3) with n2 and χI(3) with β. Nonlinear refraction and absorption result instead from the interplay between the real and imaginary parts of the first- and third-order susceptibilities of the material. This effect is illustrated in the case of a metal–dielectric nanocomposite for which n2 and β values were experimentally obtained by Z-scan measurements and for which the use of the new formulas for χR(3) and χI(3) yield a large correction and a sign reversal for χI(3).

© 2004 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(190.4400) Nonlinear optics : Nonlinear optics, materials

Raúl del Coso and Javier Solis, "Relation between nonlinear refractive index and third-order susceptibility in absorbing media," J. Opt. Soc. Am. B 21, 640-644 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999). [CrossRef] [PubMed]
  2. D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weildman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989). [CrossRef]
  3. N. Bloembergen, “Nonlinear optics of polymers: fundamentals and applications,” J. Nonlinear Opt. Phys. Mater. 5, 1–7 (1996). [CrossRef]
  4. C. J. Hamilton, J. H. Marsh, D. C. Hutchings, J. S. Aitchison, G. T. Kennedy, and W. Sibbett, “Localized Kerr-type nonlinearities in GaAs/AlGaAs multiple-quantum-well structures at 1.55 μm,” Appl. Phys. Lett. 68, 3078–3080 (1996). [CrossRef]
  5. G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998). [CrossRef]
  6. R. F. Haglund, Jr., C. N. Afonso, G. Battaglin, M. Godbole, F. Gonella, J. D. Hamilton, D. H. Lowndes, R. H. Magruder III, P. Mazzoldi, D. H. Osborne, Jr., and J. Solis, “Effects of laser and particle beams on the synthesis and nonlinear optical response of nanostructures,” in Laser Applications in Microelectronic and Optoelectronic Manufacturing II, J. J. Dubowski, ed., Proc. SPIE 2991, 90–101 (1997). [CrossRef]
  7. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  8. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  9. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).
  10. 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). [CrossRef]
  11. R. F. Haglund, Li Yang, Lina Yang, R. Dorsinville, and R. R. Alfano, “Nonlinear optical properties of metal quantum-dot composites synthesized by ion implantation,” Nucl. Instrum. Methods Phys. Res. B 91, 493–504 (1994). [CrossRef]
  12. 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). [CrossRef]
  13. S. M. Lima, H. Jiao, L. A. O. Nunes, and T. Catanuda, “Nonlinear refraction spectroscopy in resonance with laser lines in solids,” Opt. Lett. 27, 845–847 (2002). [CrossRef]
  14. E. Van Keuren, T. Wakebe, R. Andreaus, H. Mohwald, W. Schrof, V. Belov, H. Matsuda, and R. Rangel-Rojo, “Wavelength dependence of the third-order nonlinear optical properties of polythiophene–selenophene derivative film,” Appl. Phys. Lett. 75, 3312–3314 (1999). [CrossRef]
  15. F. Hache, D. Ricard, 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). [CrossRef]
  16. R. del Coso, J. Solis, J. Gonzalo, and C. N. Afonso, “Ultrafast temporal response of the third order nonlinear effects in Cu:Al2O3 nanocomposites” (manuscript available from authors on request).
  17. R. Serna, C. N. Afonso, J. M. Ballesteros, A. Naudon, D. Babonneau, and A. K. Petford-Long, “Size, shape anisotropy, and distribution of Cu nanocrystals prepared by pulsed laser deposition,” Appl. Surf. Sci. 138–139, 1–5 (1999). [CrossRef]
  18. C. N. Afonso, J. Gonzalo, R. Serna, J. C. G. de Sande, C. Ricolleau, C. Grigis, M. Gandais, D. E. Hole, and P. D. Townsend, “Vacuum versus gas environment for the synthesis of nanocomposite films by pulsed laser deposition,” Appl. Phys. A 69, S201–S207 (1999). [CrossRef]
  19. R. Serna, J. Gonzalo, A. Suárez-García, C. N. Afonso, J. P. Barnes, A. K. Petford-Long, R. C. Doole, and D. Hole, “Structural studies of pulsed-laser deposition, nanocomposite, metal-oxide films,” J. Microsc. 201, 250–255 (2001). [CrossRef] [PubMed]
  20. A. Suarez-Garcia, R. del Coso, R. Serna, J. Solis, and C. N. Afonso, “Controlling the transmission at the surface plasmon resonance of nanocomposite films using photonic structures,” Appl. Phys. Lett. 83, 1842–1844 (2003). [CrossRef]
  21. R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. (to be published).

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited