## Off-resonance and non-resonant dispersion of Kerr nonlinearity for symmetric molecules [Invited] |

Optics Express, Vol. 19, Issue 23, pp. 22486-22495 (2011)

http://dx.doi.org/10.1364/OE.19.022486

Enhanced HTML Acrobat PDF (779 KB)

### Abstract

The exact formula is derived from the “sum over states” (SOS) quantum mechanical model for the frequency dispersion of the nonlinear refractive index coefficient *n*_{2} for centrosymmetric molecules in the off-resonance and non-resonant regimes. This expression is characterized by interference between terms from two-photon transitions from the ground state to the even-symmetry excited states and one-photon transitions between the ground state and odd-symmetry excited states. When contributions from the two-photon terms exceed those from the one-photon terms, the non-resonant intensity-dependent refractive index *n*_{2}>0, and vice versa. Examples of the frequency dispersion for the three-level SOS model are given. Comparison is made with other existing theories.

© 2011 OSA

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.3270) Nonlinear optics : Kerr effect

(190.5940) Nonlinear optics : Self-action effects

**ToC Category:**

Nonlinear Absorption and Dispersion

**History**

Original Manuscript: August 30, 2011

Revised Manuscript: September 27, 2011

Manuscript Accepted: October 5, 2011

Published: October 25, 2011

**Virtual Issues**

Nonlinear Optics (2011) *Optical Materials Express*

**Citation**

George Stegeman, Mark G. Kuzyk, Dimitris G. Papazoglou, and Stelios Tzortzakis, "Off-resonance and non-resonant dispersion of Kerr nonlinearity for symmetric molecules [Invited]," Opt. Express **19**, 22486-22495 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-22486

Sort: Year | Journal | Reset

### References

- M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25(16), 1183–1185 (2000). [CrossRef] [PubMed]
- C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B Condens. Matter 41(3), 1636–1639 (1990). [CrossRef] [PubMed]
- M. G. Kuzyk, “Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities,” Phys. Rev. A 72(5), 053819 (2005). [CrossRef]
- C. W. Dirk, L. T. Cheng, and M. G. Kuzyk, “A simplified three-level model for describing the molecular third-order nonlinear-optical susceptibility,” Int. J. Quantum Chem. 43(1), 27–36 (1992). [CrossRef]
- D. Lu, G. Chen, J. W. Perry, and W. A. Goddard, “Valence-bond charge-transfer model for nonlinear optical properties of charge-transfer organic molecules,” J. Am. Chem. Soc. 116(23), 10679–10685 (1994). [CrossRef]
- Reviewed in J. M. Hales and J. W. Perry, “Organic and polymeric 3rd-order nonlinear optical materials and device applications,” in Introduction to Organic Electronic and Optoelectronic Materials and Devices, S.-S. Sun and L. Dalton, eds. (CRC, 2008), Chap. 17.
- M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41(9), 5098–5109 (1990). [CrossRef] [PubMed]
- C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2(1), 4–6 (1990). [CrossRef]
- M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electrooptic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7(5), 842–858 (1990). [CrossRef]
- Y. Z. Yu, R. F. Shu, A. F. Garito, and C. H. Grossman, “Origin of negative χ3 in squaraines: experimental observation of two-photon states,” Opt. Lett. 19(11), 786–788 (1994). [CrossRef] [PubMed]
- D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photon. 2(1), 60–200 (2010). [CrossRef]
- J. F. Ward, “Calculation of nonlinear optical susceptibilities using diagrammatic perturbation theory,” Rev. Mod. Phys. 37(1), 1–18 (1965). [CrossRef]
- B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20(3), 513–526 (1971). [CrossRef]
- Reviewed in S. Barlow and S. R. Marder, “Nonlinear optical properties of organic materials,” in Functional Organic Materials: Syntheses, Strategies and Applications, T. J. J. Muller and U. H. F. Bunz, eds. (Wiley, 2007), Chap. 11.
- V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17(16), 13429–13434 (2010). [CrossRef]
- V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18(3), 3011–3012 (2010). [CrossRef]
- W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulae,” Opt. Express 18(7), 6613–6620 (2010). [CrossRef] [PubMed]
- C. Brée, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106(18), 183902 (2011). [CrossRef] [PubMed]
- K. S. Mathis, M. G. Kuzyk, C. W. Dirk, A. Tan, S. Martinez, and G. Gampos, “Mechanisms of the nonlinear optical properties of squaraine dyes in poly(methyl methacrylate) polymer,” J. Opt. Soc. Am. B 15(2), 871–883 (1998). [CrossRef]
- G. Stegeman and H. Hu, “Refractive nonlinearity of linear symmetric molecules and polymers revisited,” Photon. Lett. Poland 1(4), 148–150 (2009). [CrossRef]
- P. McWilliams, P. Hayden, and Z. Soos, “Theory of even-parity state and two-photon spectra of conjugated polymers,” Phys. Rev. B 43(12), 9777–9791 (1991). [CrossRef]
- G. I. Stegeman, “Nonlinear optics of conjugated polymers and linear molecules,” Nonlinear Opt., Quantum Opt. (to be published).
- G. I. Stegeman and R. A. Stegeman, Nonlinear Optics: Phenomena, Materials and Devices (J. Wiley, in press).
- J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, “Determination of the time dependence of n2 in air,” Opt. Commun. 135(4-6), 310–314 (1997). [CrossRef]
- J. Pérez Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123(19), 194101 (2005). [CrossRef] [PubMed]
- J. H. Andrews, J. D. V. Khaydarov, K. D. Singer, D. L. Hull, and K. C. Chuang, “Characterization of excited states of centrosymmetric and noncentrosymmetric squaraines by third-harmonic spectral dispersion,” J. Opt. Soc. Am. 12(12), 2360–2371 (1995). [CrossRef]
- J. Kasparian, P. Béjot, and J.-P. Wolf, “Arbitrary-order nonlinear contribution to self-steepening,” Opt. Lett. 35(16), 2795–2797 (2010). [CrossRef] [PubMed]
- W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, E. Hertz, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82(3), 033826 (2010). [CrossRef]

## 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.