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

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

http://dx.doi.org/10.1364/JOSAB.22.000655

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### Abstract

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

**Citation**

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)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-3-655

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### References

- Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
- S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, New York, 1995).
- L. Lepetit and M. Joffre, "Two-dimensional nonlinear optics using Fourier-transform spectral interferometry," Opt. Lett. 21, 564-566 (1996).
- D. M. Jonas, "Two-dimensional femtosecond spectroscopy," Annu. Rev. Phys. Chem. 54, 425-463 (2003).
- D. M. Jonas, "Optical analogs of 2D NMR," Science 300, 1515-1517 (2003).
- M. Khalil, N. Demirdöven, and A. Tokmakoff, "Obtaining absorptive lineshapes in two-dimensional infrared vibrational correlation spectra," Phys. Rev. Lett. 90, 047401 (2003).
- 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).
- R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford U. Press, Oxford, UK, 1987).
- 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).
- O. Kinrot and Y. Prior, "Nonlinear interaction of propagating short pulses in optically dense media," Phys. Rev. A 51, 4996-5007 (1995).
- 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).
- 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).
- 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).
- 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).
- T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
- T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545-592 (2000).
- 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).
- F. C. Spano and W. S. Warren, "Photon echo decays in optically dense media," J. Chem. Phys. 93, 1546-1556 (1990).
- M. Bonn, S. Woutersen, and H. J. Bakker, "Coherent picosecond vibron polaritons as probes of vibrational lifetimes," Opt. Commun. 147, 138-142 (1998).
- 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).
- 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).
- S. Mukamel, "Femtosecond optical spectroscopy: a direct look at elementary chemical events," Annu. Rev. Phys. Chem. 41, 647-681 (1990).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, "Two dimensional Fourier transform electronic spectroscopy," J. Chem. Phys. 115, 6606-6622 (2001).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- J. N. Sweetser, D. N. Fittinghoff, and R. Trebino, "Transient grating frequency-resolved optical gating," Opt. Lett. 22, 519-521 (1997).
- 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).
- 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.
- A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
- A. E. Siegman, "Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating," J. Opt. Soc. Am. 67, 545-550 (1977).
- 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).
- H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
- V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, New York, 1977).
- S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471-503 (1932).
- N. Belabas and M. Joffre, "Visible-infrared two-dimensional Fourier-transform spectroscopy," Opt. Lett. 27, 2043-2045 (2002).
- 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).
- 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).
- J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
- J. C. Slater, Microwave Transmission , 1st ed. (McGraw-Hill, New York, 1942).
- J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory , 3rd ed. (Addison-Wesley, Reading, Mass., 1980).
- D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice-Hall, Englewood Cliffs, N.J., 1994).
- P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, New York, 1991).

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