Abstract

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

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  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).

2003 (1)

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]

2002 (2)

2001 (1)

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]

1999 (4)

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]

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]

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]

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]

1998 (1)

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998).
[CrossRef]

1997 (1)

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]

1996 (2)

N. Bloembergen, “Nonlinear optics of polymers: fundamentals and applications,” J. Nonlinear Opt. Phys. Mater. 5, 1–7 (1996).
[CrossRef]

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]

1994 (1)

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]

1990 (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).
[CrossRef]

1989 (1)

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]

1988 (1)

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]

Afonso, C. N.

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]

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]

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]

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]

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]

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]

Aitchison, J. S.

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]

Alfano, R. R.

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]

Andreaus, R.

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]

Babonneau, D.

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]

Ballesteros, J. M.

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]

Banfi, G.

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998).
[CrossRef]

Barnes, J. P.

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]

Battaglin, G.

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]

Belov, V.

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]

Bloembergen, N.

N. Bloembergen, “Nonlinear optics of polymers: fundamentals and applications,” J. Nonlinear Opt. Phys. Mater. 5, 1–7 (1996).
[CrossRef]

Blow, K. J.

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]

Borrelli, N. F.

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]

Catanuda, T.

Cotter, D.

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]

de Nalda, R.

de Sande, J. C. G.

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]

Degiorgio, V.

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998).
[CrossRef]

del Coso, R.

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]

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]

Doole, R. C.

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]

Dorsinville, R.

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]

Dumbaugh, W. H.

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]

Ellis, A. D.

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]

Flytzanis, C.

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]

Gandais, M.

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]

Godbole, M.

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]

Gonella, F.

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]

Gonzalo, J.

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]

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]

Grigis, C.

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]

Hache, F.

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]

Hagan, D. J.

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]

Haglund, R. F.

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]

Haglund Jr., R. F.

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]

Hall, D. W.

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]

Hamilton, C. J.

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]

Hamilton, J. D.

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]

Hole, D.

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]

Hole, D. E.

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]

Hutchings, D. C.

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]

Jiao, H.

Kelly, A. E.

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]

Kennedy, G. T.

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]

Kreibig, U.

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]

Lima, S. M.

Lowndes, D. H.

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]

Magruder III, R. H.

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]

Manning, R. J.

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]

Marsh, J. H.

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]

Matsuda, H.

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]

Mazzoldi, P.

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]

Mohwald, H.

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]

Naudon, A.

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]

Nesset, D.

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]

Newhouse, M. A.

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]

Nunes, L. A. O.

Olivares, J.

Osborne Jr., D. H.

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]

Petford-Long, A. K.

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]

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]

Phillips, I. D.

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]

Poustie, A. J.

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]

Rangel-Rojo, R.

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]

Requejo-Isidro, J.

Ricard, D.

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998).
[CrossRef]

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]

Ricolleau, C.

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]

Rogers, D. C.

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]

Said, A. A.

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]

Schrof, W.

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]

Serna, R.

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]

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]

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]

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]

Sheik-Bahae, M.

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]

Sibbett, W.

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]

Solis, J.

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]

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]

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]

Suarez-Garcia, A.

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]

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]

Suárez-García, A.

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]

Townsend, P. D.

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]

Van Keuren, E.

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]

Van Stryland, E. W.

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]

Wakebe, T.

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]

Wei, T.

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]

Weildman, D. L.

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]

Yang, Li

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]

Yang, Lina

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]

Adv. Phys. (1)

G. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47, 447–510 (1998).
[CrossRef]

Appl. Phys. A (2)

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]

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]

Appl. Phys. Lett. (4)

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]

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]

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]

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]

Appl. Surf. Sci. (1)

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]

IEEE J. Quantum Electron. (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).
[CrossRef]

J. Microsc. (1)

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]

J. Nonlinear Opt. Phys. Mater. (1)

N. Bloembergen, “Nonlinear optics of polymers: fundamentals and applications,” J. Nonlinear Opt. Phys. Mater. 5, 1–7 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nucl. Instrum. Methods Phys. Res. B (1)

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]

Opt. Lett. (1)

Proc. SPIE (1)

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]

Science (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]

Other (5)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).

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).

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).

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Figures (2)

Fig. 1
Fig. 1

Calculated n2/n2(k0=0) ratio as a function of k0/n0. The curves correspond to the different indicated values of the χI(3)/χR(3) ratio.

Fig. 2
Fig. 2

Real and imaginary parts of the third-order nonlinear susceptibility of the Cu:Al2O3 nanocomposites shown in Table 1 as a function of k0. The plotted values correspond to the determination of χR(3) and χI(3) from the experimental values of n2 and β measured by Z-scan by use of Eqs. (1)—open squares, χR(3), open triangles, χI(3)—and by use of the correct expression for absorbing materials, Eqs. (15) and (16)—filled squares, χR(3), filled triangles, χI(3).

Tables (1)

Tables Icon

Table 1 Structural and Optical Properties of Cu:Al2O3 Nanocomposites

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

χR(3)=(4/3)n020cn2,
χI(3)=(n020cλ/3π)β,
P˜=0[χ˜(1)E˜+χ˜(2)E˜E˜+χ˜(3)E˜E˜E˜*+],
D˜=0E˜+P˜=0(1+χ˜)E˜=E˜.
χ˜=χ˜(1)+χ˜(3)E˜E˜*,
χ(ω)=χ(1)(ω)+3χ(3)(ω)|E|2,
1=0(n2-k2),
2=0(2nk);
n=||+120,
k=||-120.
=(1)+Δ,
Δ1=30χR(3)|E|2,
Δ2=30χI(3)|E|2.
n=n0+Δn=n0+n2I,
α=α0+Δα=α0+βI,
k=k0+Δk=k0+k2I,
1=1(1)+Δ1=0[(n0+Δn)2-(k0+Δk)2]
 Δ1=0[2(n0Δn-k0Δk)+(Δn)2+(Δk)2],
3χR(3)|E|2=2I(n0n2-k0k2)
 χR(3)=(4n00c/3)(n0n2-k0k2).
χI(3)=(4n00c/3)(n0k2+k0n2).
n2=340c(n02+k02) χR(3)+k0n0χI(3),
k2=340c(n02+k02) χI(3)-k0n0χR(3);
β=3πλ0c(n02+k02) χI(3)-k0n0χR(3).
n2n2(k0=0)=1+k02n02-11+k0n0 χI(3)χR(3).

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