OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 3 — Mar. 1, 2005
  • pp: 655–674

Three-dimensional view of signal propagation in femtosecond four-wave mixing with application to the boxcars geometry

Nadia Belabas and David M. Jonas  »View Author Affiliations

JOSA B, Vol. 22, Issue 3, pp. 655-674 (2005)

View Full Text Article

Acrobat PDF (317 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Maxwell's equations for the apparently complicated generation and propagation of femtosecond four-wave-mixing signals in optically thick samples can be solved by triple Fourier transformation into the three-dimensional (3D) frequency domain. Given the linear absorption and refractive-index spectra, the propagation problem can be solved in three dimensions under the assumption that nonlinear distortions of the excitation pulses can be neglected. A propagation function exactly incorporates the linear evolution of the excitation pulses, the nonlinear generation of the signal, and the linear propagation of the signal. A quantitative treatment of the directional filtering of the 3D susceptibility that arises from excitation with noncollinear pulses and selective interference detection of signal in one phase-matched direction is developed. This 3D treatment is used to examine the influence of phase-matching bandwidth, directional filtering, and sample absorption on femtosecond four-wave-mixing signals in the rectangular and square boxcars phase-matching geometries.

© 2005 Optical Society of America

OCIS Codes
(300.2570) Spectroscopy : Four-wave mixing
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(350.5500) Other areas of optics : Propagation

Nadia Belabas and David M. Jonas, "Three-dimensional view of signal propagation in femtosecond four-wave mixing with application to the boxcars geometry," J. Opt. Soc. Am. B 22, 655-674 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, New York, 1995).
  3. L. Lepetit and M. Joffre, "Two-dimensional nonlinear optics using Fourier-transform spectral interferometry," Opt. Lett. 21, 564-566 (1996).
  4. D. M. Jonas, "Two-dimensional femtosecond spectroscopy," Annu. Rev. Phys. Chem. 54, 425-463 (2003).
  5. D. M. Jonas, "Optical analogs of 2D NMR," Science 300, 1515-1517 (2003).
  6. M. Khalil, N. Demirdöven, and A. Tokmakoff, "Obtaining absorptive lineshapes in two-dimensional infrared vibrational correlation spectra," Phys. Rev. Lett. 90, 047401 (2003).
  7. J. B. Asbury, T. Steinel, C. Stromberg, K. J. Gaffney, I. R. Piletic, A. Goun, and M. D. Fayer, "Hydrogen bond dynamics probed with ultrafast infrared heterodyne detected multidimensional vibrational stimulated echoes," Phys. Rev. Lett. 91, 237402 (2003).
  8. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford U. Press, Oxford, UK, 1987).
  9. M. Cho, D. A. Blank, J. Sung, K. Park, S. Hahn, and G. R. Fleming, "Intrinsic cascading contributions to the fifth- and seventh-order electronically off-resonant spectroscopies," J. Chem. Phys. 112, 2082-2094 (2000).
  10. O. Kinrot and Y. Prior, "Nonlinear interaction of propagating short pulses in optically dense media," Phys. Rev. A 51, 4996-5007 (1995).
  11. S. Yeremenko, M. S. Pshenichnikov, and D. A. Wiersma, "Hydrogen-bond dynamics in water explored by heterodyne-detected photon echo," Chem. Phys. Lett. 367, 107-113 (2003).
  12. M. N. Belov, E. A. Manykin, and M. A. Selifanov, "Self-consistent theory of time-resolved four-wave mixing," Opt. Commun. 99, 101-104 (1993).
  13. S. Mukamel and A. Tortschanoff, "Multiple quantum coherences in liquid state NMR and nonlinear optics: collective vs. local origin," Chem. Phys. Lett. 357, 327-335 (2002).
  14. D. Keusters and W. S. Warren, "Effect of pulse propagation on the two-dimensional photon echo spectrum of multilevel systems," J. Chem. Phys. 119, 4478-4489 (2003).
  15. T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
  16. T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-592 (2000).
  17. R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, "Optical density effects in photon echo experiments," J. Chem. Phys. 76, 31-39 (1982).
  18. F. C. Spano and W. S. Warren, "Photon echo decays in optically dense media," J. Chem. Phys. 93, 1546-1556 (1990).
  19. M. Bonn, S. Woutersen, and H. J. Bakker, "Coherent picosecond vibron polaritons as probes of vibrational lifetimes," Opt. Commun. 147, 138-142 (1998).
  20. B. Lummer, J.-M. Wagner, R. Heitz, A. Hoffman, I. Broser, and R. Zimmerman, "Pulse-propagation-induced higher orders of diffraction in transient four-wave mixing with semiconductors," Phys. Rev. B 54, 16727-16732 (1996).
  21. J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, "Non-Markovian dephasing of molecules in solution measured with three-pulse femtosecond photon echoes," Phys. Rev. Lett. 66, 1138-1141 (1991).
  22. S. Mukamel, "Femtosecond optical spectroscopy: a direct look at elementary chemical events," Annu. Rev. Phys. Chem. 41, 647-681 (1990).
  23. R. W. Ziolkowski and J. B. Judkins, "Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time," J. Opt. Soc. Am. B 10, 186-198 (1993).
  24. J. A. Gruetzmacher and N. F. Scherer, "Finite-difference time-domain simulation of ultrashort pulse propagation incorporating quantum mechanical response functions," Opt. Lett. 28, 573-575 (2003).
  25. N. Bloembergen and P. S. Pershan, "Light waves at the boundary of nonlinear media," Phys. Rev. 128, 606-622 (1962). In addition to the typographical errors noted on p. xx of Bloembergen's book [N. Bloembergen, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992)], the right hand side of Eq. (6.8) should be multiplied by exp (iphis ) and the sign of EM′ should be positive on the right-hand side of Eq. (6.16).
  26. M. Joffre, J. O. White, D. Hulin, A. Migus, E. Toussaere, R. Hierle, S. Gauvin, and J. Zyss, "Femtosecond ultrabroad-band frequency mixing in MNA and KDP thin crystals," Nonlinear Opt. 11, 5-12 (1995).
  27. L. Lepetit, G. Chériaux, and M. Joffre, "Two-dimensional nonlinear optics spectroscopy: simulations and experimental demonstration," J. Nonlinear Opt. Phys. Mater. 5, 465-476 (1996).
  28. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Second-harmonic generation frequency resolved optical gating in the single-cycle regime," IEEE J. Quantum Electron. 35, 459-478 (1999).
  29. A. Baltuska, M. F. Emde, M. S. Pshenichnikov, and D. A. Wiersma, "Early-time dynamics of the photoexcited hydrated electron," J. Phys. Chem. A 103, 10065-10082 (1999).
  30. J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
  31. N. Belabas and D. M. Jonas, "Fourier algorithm for four-wave mixing signals from optically dense systems with memory," Opt. Lett. 29, 1811-1813 (2004).
  32. S. M. Gallagher, A. W. Albrecht, J. D. Hybl, B. L. Landin, B. Rajaram, and D. M. Jonas, "Heterodyne detection of the complete electric field of femtosecond four-wave mixing signals," J. Opt. Soc. Am. B 15, 2338-2345 (1998).
  33. L. Lepetit, G. Chériaux, and M. Joffre, "Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995).
  34. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the intensity and phase of ultraweak, ultrashort laser pulses," Opt. Lett. 21, 884-886 (1996).
  35. A. W. Albrecht, J. D. Hybl, S. M. Gallagher Faeder, and D. M. Jonas, "Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions," J. Chem. Phys. 111, 10934-10956 (1999).
  36. C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, "Spectral resolution and sampling issues in Fourier-transform spectral interferometry," J. Opt. Soc. Am. B 17, 1795-1802 (2000).
  37. J. N. Sweetser, D. N. Fittinghoff, and R. Trebino, "Transient grating frequency-resolved optical gating," Opt. Lett. 22, 519-521 (1997).
  38. T. J. Butenhoff and E. A. Rohlfing, "Laser-induced gratings in free jets. I. Spectroscopy of predissociating NO2," J. Chem. Phys. 98, 5460-5468 (1993).
  39. P. H. Vaccaro, "Degenerate four-wave mixing spectroscopy," in Nonlinear Spectroscopy for Molecular Structure Determination , R. W. Field, E. Hirota, J. P. Maier, and S. Tsuchiya, eds. (Blackwell, Oxford, UK, 1997), pp. 75-126.
  40. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  41. A. E. Siegman, "Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating," J. Opt. Soc. Am. 67, 545-550 (1977).
  42. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, "Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical grating," IEEE J. Quantum Electron. 32, 1253-1264 (1996).
  43. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  44. V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, New York, 1977).
  45. S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471-503 (1932).
  46. N. Belabas and M. Joffre, "Visible-infrared two-dimensional Fourier-transform spectroscopy," Opt. Lett. 27, 2043-2045 (2002).
  47. D. E. Thompson and J. C. Wright, "Model for spectral artifacts in two-dimensional four-wave mixing spectra from absorption and refractive index dispersion at infrared resonances," J. Phys. Chem. A 104, 11282-11289 (2000).
  48. S.-C. Sheng and A. E. Siegman, "Nonlinear-optical calculations using fast transform methods: second-harmonic generation with depletion and diffraction," Phys. Rev. A 21, 599-606 (1980).
  49. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  50. J. C. Slater, Microwave Transmission , 1st ed. (McGraw-Hill, New York, 1942).
  51. J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory , 3rd ed. (Addison-Wesley, Reading, Mass., 1980).
  52. D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice-Hall, Englewood Cliffs, N.J., 1994).
  53. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, New York, 1991).

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