Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Journal of Chemical Physics

Volumn 126, Issue 4, 2007, Pages

  Yetzbacher, Michael K ^a   Belabas, Nadia ^a,b   Kitney, Katherine A ^a   Jonas, David M ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIV PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DIMENSIONLESS PARAMETER; DIRECTIONAL FILTER; PHASE-MATCHING DISTORTION; TWO-DIMENSIONAL FOURIER TRANSFORM (2DFT);

BROWNIAN MOVEMENT; ELECTRIC DISTORTION; FOURIER TRANSFORM INFRARED SPECTROSCOPY; FREQUENCY DOMAIN ANALYSIS; LIGHT ABSORPTION; RELAXATION PROCESSES;

MAXWELL EQUATIONS;

EID: 33847762844     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2426337     Document Type: Article

References (93)

1. D. M. Jonas, Annu. Rev. Phys. Chem. 54, 425 (2003).
2. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1987).
3. L. Lepetit and M. Joffre, Opt. Lett. 21, 564 (1996).
4. J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, J. Chem. Phys. 115, 6606 (2001). The 2D experiments of this reference used a beam separation of 8 mm on each side of the square at the 10 cm focal length achromatic lens, resulting in half angles of 2.3° and about four grating fringes.
5. N. Belabas and M. Joffre, Opt. Lett. 27, 2043 (2002).
6. R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, J. Chem. Phys. 76, 31 (1982).
7. W. Zhao and J. C. Wright, J. Am. Chem. Soc. 0002-7863 10.1021/ja9926414 121, 10994 (1999); J. B. Asbury, T. Steinel, and M. D. Fayer, Chem. Phys. Lett. 0009-2614 381, 139 (2003); P. C. Chen and C. C. Joyner, Anal. Chem. 77, 5467 (2005).
8. W. Zhao and J. C. Wright, J. Am. Chem. Soc. 0002-7863 10.1021/ja9926414 121, 10994 (1999); J. B. Asbury, T. Steinel, and M. D. Fayer, Chem. Phys. Lett. 0009-2614 381, 139 (2003); P. C. Chen and C. C. Joyner, Anal. Chem. 77, 5467 (2005).
9. W. Zhao and J. C. Wright, J. Am. Chem. Soc. 0002-7863 10.1021/ja9926414 121, 10994 (1999); J. B. Asbury, T. Steinel, and M. D. Fayer, Chem. Phys. Lett. 0009-2614 381, 139 (2003); P. C. Chen and C. C. Joyner, Anal. Chem. 77, 5467 (2005).
10. M. D. Levenson and G. L. Eesley, Appl. Phys. 19, 1 (1979).
11. K. Duppen and D. A. Wiersma, J. Opt. Soc. Am. B 3, 614 (1986).
12. J. D. Hybl, A. W. Albrecht, S. M. Gallagher Faeder, and D. M. Jonas, Chem. Phys. Lett. 297, 307 (1998).
13. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
14. A. E. Siegman, J. Opt. Soc. Am. 67, 545 (1977). The analysis in this reference is not directly applicable to the experiments described in this paper, since the sample length typically truncates the interaction length of the beams.
15. C. Ventalon, J. M. Fraser, M. H. Vos, A. Alexandrou, J. L. Martin, and M. Joffre, Proc. Natl. Acad. Sci. U.S.A. 101, 13216 (2004).
16. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).
17. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
18. N. Belabas and D. M. Jonas, Opt. Lett. 29, 1811 (2004).
19. R. Friedberg and S. R. Hartmann, Phys. Lett. 0375-9601 10.1016/0375-9601(71)90672-4 37A, 285 (1971); strong field excitation 4WM signals may increase with OD beyond OD∼1, see, for example, T. Wang, C. Greiner, J. R. Bochinski, and T. W. Mossberg, Phys. Rev. A 60, R757 (1999).
20. R. Friedberg and S. R. Hartmann, Phys. Lett. 0375-9601 10.1016/0375-9601(71)90672-4 37A, 285 (1971); strong field excitation 4WM signals may increase with OD beyond OD∼1, see, for example, T. Wang, C. Greiner, J. R. Bochinski, and T. W. Mossberg, Phys. Rev. A 60, R757 (1999).
21. D. E. Thompson and J. C. Wright, J. Phys. Chem. A 104, 11282 (2000).
22. S. Mukamel and A. Tortschanoff, Chem. Phys. Lett. 357, 327 (2002).
23. J. Jeener, Chem. Phys. Lett. 0009-2614 368, 247 (2003); S. Mukamel, Chem. Phys. Lett. 368, 249 (2003).
24. J. Jeener, Chem. Phys. Lett. 0009-2614 368, 247 (2003); S. Mukamel, Chem. Phys. Lett. 368, 249 (2003).
25. A. Tortschanoff and S. Mukamel, J. Chem. Phys. 116, 5007 (2002).
26. D. Keusters and W. S. Warren, J. Chem. Phys. 119, 4478 (2003).
27. D. Keusters and W. S. Warren, Chem. Phys. Lett. 383, 21 (2004).
28. A. Baltuska, M. F. Emde, M. S. Pshenichnikov, and D. A. Wiersma, J. Phys. Chem. A 103, 10065 (1999).
29. J. A. Gruetzmacher and N. F. Scherer, Opt. Lett. 28, 573 (2003).
30. M. D. Crisp, Phys. Rev. A 1050-2947 10.1103/PhysRevA.1.1604 1, 1604 (1970); L. Tsang, C. S. Cornish, and W. R. Babbit, J. Opt. Soc. Am. B 20, 379 (2003).
31. M. D. Crisp, Phys. Rev. A 1050-2947 10.1103/PhysRevA.1.1604 1, 1604 (1970); L. Tsang, C. S. Cornish, and W. R. Babbit, J. Opt. Soc. Am. B 20, 379 (2003).
32. M. N. Belov, E. A. Manykin, and M. A. Selifanov, Opt. Commun. 0030-4018 10.1016/0030-4018(93)90712-E 99, 101 (1993); O. Kinrot and Y. Prior, Phys. Rev. A 51, 4996 (1995).
33. M. N. Belov, E. A. Manykin, and M. A. Selifanov, Opt. Commun. 0030-4018 10.1016/0030-4018(93)90712-E 99, 101 (1993); O. Kinrot and Y. Prior, Phys. Rev. A 51, 4996 (1995).
34. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).
35. F. Bloch, Phys. Rev. 70, 460 (1946).
36. V. O. Lorenz and S. T. Cundiff, Phys. Rev. Lett. 95, 163601 (2005).
37. J. R. Klauder and P. W. Anderson, Phys. Rev. 125, 912 (1962).
38. Y. J. Yan and S. Mukamel, J. Chem. Phys. 89, 5160 (1988).
39. Y. Tanimura and S. Mukamel, Phys. Rev. E 1063-651X 10.1103/PhysRevE.47. 118 47, 118 (1993); Y. Gu, A. Widom, and P. M. Champion, J. Chem. Phys. 100, 2547 (1994).
40. Y. Tanimura and S. Mukamel, Phys. Rev. E 1063-651X 10.1103/PhysRevE.47. 118 47, 118 (1993); Y. Gu, A. Widom, and P. M. Champion, J. Chem. Phys. 100, 2547 (1994).
41. N. Belabas and D. M. Jonas, J. Opt. Soc. Am. B 22, 655 (2005). Two imprecise statements (on p. 666, column 1, and on p. 671, column 1, of this reference) that a nonlinear polarization (rather than the field) can be uniquely split into independent source terms for TE and TM waves led to three erroneous statements about the signal field for pure TE excitation. As shown by Eqs. (16b) and (C7) of this reference, the radiated signal electric field is not necessarily parallel to the nonlinear polarization. The appendix of the present paper demonstrates that three statements in this reference are incorrect: (1) that the signal wave is TE (or TM) when all the excitation waves are s (or p) polarized (on p. 671, column 1), (2) that kp P(3) =0 for pure TE excitation (on p. 667, column 2), and (3) that a propagation function (rather than matrix) results from pure TE excitation (on p. 666, column 1). The actual derivation in Appendix C of this reference is based on uniquely decomposing the field Ep into TE and TM components and is unaffected. However, the circumstances in which the exact solution of Maxwell's equations match a well-known approximate solution (discussed on p. 667, column 1) are further limited to the TE component of the exact solution, as discussed in the appendix of the present paper.
42. N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
43. N. Belabas and D. M. Jonas, in Ultrafast Phenomena XIV, edited by, T. Kobayashi, T. Okada, T. Kobayashi, K. A. Nelson, and, S. De Silvestri, (Springer, New York, 2005), p. 572.
44. J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, 4th ed. (Addison-Wesley, Reading, MA, 1992).
45. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, Opt. Lett. 0146-9592 23, 1378 (1998); O. E. Martinez, Opt. Commun. 59, 229 (1986).
46. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, Opt. Lett. 0146-9592 23, 1378 (1998); O. E. Martinez, Opt. Commun. 59, 229 (1986).
47. M. L. Cowan, J. P. Ogilvie, and R. J. D. Miller, Chem. Phys. Lett. 386, 184 (2004).
48. T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. Blankenship, and G. R. Fleming, Nature (London) 434, 625 (2005).
49. See EPAPS Document No. E-JCPSA6-126-006703 for 8 figures not reproduced here and the derivation of Eq. (26). This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http//www.aip.org/pubservs/epaps.html).
50. S. M. Gallagher Faeder and D. M. Jonas, J. Phys. Chem. A 103, 10489 (1999).
51. T. Brixner, T. Mancal, I. V. Stiopkin, and G. R. Fleming, J. Chem. Phys. 121, 4221 (2004).
52. M. L. Cowan, B. D. Bruner, N. Huse, J. R. Dwyer, B. Chugh, E. T. J. Nibbering, T. Elsaesser, and R. J. D. Miller, Nature (London) 434, 199 (2005).
53. T. Hornung, J. C. Vaughan, T. Feurer, and K. A. Nelson, Opt. Lett. 29, 2052 (2004).
54. W. Wagner, C. Li, J. Semmlow, and W. S. Warren, Opt. Express 13, 3697 (2005).
55. M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003).
56. X. Li, T. Zhang, C. N. Borca, and S. T. Cundiff, Phys. Rev. Lett. 96, 057406 (2006).
57. J. B. Asbury, T. Steinel, and M. D. Fayer, J. Lumin. 107, 271 (2004).
58. S. M. Gallagher, A. W. Albrecht, J. D. Hybl, B. L. Landin, B. Rajaram, and D. M. Jonas, J. Opt. Soc. Am. B 15, 2338 (1998).
59. J. B. Asbury, T. Steinel, C. Stromberg, K. J. Gaffney, I. R. Piletic, A. Goun, and M. D. Fayer, Phys. Rev. Lett. 91, 237402 (2003).
60. M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.140227997 97, 8219 (2000); O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 86, 2154 (2001).
61. M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.140227997 97, 8219 (2000); O. Golonzka, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 86, 2154 (2001).
62. K. A. Nelson, R. Casalegno, R. J. Dwayne Miller, and M. D. Fayer, J. Chem. Phys. 0021-9606 10.1063/1.443979 77, 1144 (1982); R. F. Loring and S. Mukamel, J. Chem. Phys. 83, 4353 (1985).
63. K. A. Nelson, R. Casalegno, R. J. Dwayne Miller, and M. D. Fayer, J. Chem. Phys. 0021-9606 10.1063/1.443979 77, 1144 (1982); R. F. Loring and S. Mukamel, J. Chem. Phys. 83, 4353 (1985).
64. J. D. Hybl, Y. Christophe, and D. M. Jonas, Chem. Phys. 266, 295 (2001).
65. S. Mukamel, Annu. Rev. Phys. Chem. 41, 647 (1990).
66. S. M. Gallagher Faeder and D. M. Jonas, Phys. Rev. A 62, 033820 (2000).
67. A. Albrecht Ferro, J. D. Hybl, and D. M. Jonas, J. Chem. Phys. 114, 4649 (2001).
68. F. C. Spano and W. S. Warren, J. Chem. Phys. 93, 1546 (1990).
69. A. E. Siegman, Lasers, (University Science Books, Mill Valley, CA, 1986).
70. The electronic transition dipole can be calculated from the absorption spectrum using Eq. (22) of S. J. Strickler and R. A. Berg, J. Chem. Phys. 0021-9606 10.1063/1.1733166 37, 814 (1962) to find the Einstein A coefficient and Eq. (30) of R. C. Hilborn, Am. J. Phys. 0002-9505 10.1119/1.12937 50, 982 (1982) to obtain μeg. In condensed phases, Eq. (30) of Hilborn must be modified by replacing = n2 0 for 0 and cn for c. [We self consistently omit the local field correction for both the transition dipole (a reduction) and the field (a compensating increase).] An IR144 peak molar extinction coefficient of 143 000M cm at ∼750 nm was taken from U. Brackmann, Lamdachrome Laser Dyes (Lambda Physik GmbH, Gottingen, 1986). The center frequency and FWHM bandwidth for IR144 in methanol were taken from A. Yu, C. A. Tolbert, and D. M. Jonas, J. Phys. Chem. A 106, 9407 (2002).
71. The electronic transition dipole can be calculated from the absorption spectrum using Eq. (22) of S. J. Strickler and R. A. Berg, J. Chem. Phys. 0021-9606 10.1063/1.1733166 37, 814 (1962) to find the Einstein A coefficient and Eq. (30) of R. C. Hilborn, Am. J. Phys. 0002-9505 10.1119/1.12937 50, 982 (1982) to obtain μeg. In condensed phases, Eq. (30) of Hilborn must be modified by replacing = n2 0 for 0 and cn for c. [We self consistently omit the local field correction for both the transition dipole (a reduction) and the field (a compensating increase).] An IR144 peak molar extinction coefficient of 143 000M cm at ∼750 nm was taken from U. Brackmann, Lamdachrome Laser Dyes (Lambda Physik GmbH, Gottingen, 1986). The center frequency and FWHM bandwidth for IR144 in methanol were taken from A. Yu, C. A. Tolbert, and D. M. Jonas, J. Phys. Chem. A 106, 9407 (2002).
72. The electronic transition dipole can be calculated from the absorption spectrum using Eq. (22) of S. J. Strickler and R. A. Berg, J. Chem. Phys. 0021-9606 10.1063/1.1733166 37, 814 (1962) to find the Einstein A coefficient and Eq. (30) of R. C. Hilborn, Am. J. Phys. 0002-9505 10.1119/1.12937 50, 982 (1982) to obtain μeg. In condensed phases, Eq. (30) of Hilborn must be modified by replacing = n2 0 for 0 and cn for c. [We self consistently omit the local field correction for both the transition dipole (a reduction) and the field (a compensating increase).] An IR144 peak molar extinction coefficient of 143 000M cm at ∼750 nm was taken from U. Brackmann, Lamdachrome Laser Dyes (Lambda Physik GmbH, Gottingen, 1986). The center frequency and FWHM bandwidth for IR144 in methanol were taken from A. Yu, C. A. Tolbert, and D. M. Jonas, J. Phys. Chem. A 106, 9407 (2002).
73. The electronic transition dipole can be calculated from the absorption spectrum using Eq. (22) of S. J. Strickler and R. A. Berg, J. Chem. Phys. 0021-9606 10.1063/1.1733166 37, 814 (1962) to find the Einstein A coefficient and Eq. (30) of R. C. Hilborn, Am. J. Phys. 0002-9505 10.1119/1.12937 50, 982 (1982) to obtain μeg. In condensed phases, Eq. (30) of Hilborn must be modified by replacing = n2 0 for 0 and cn for c. [We self consistently omit the local field correction for both the transition dipole (a reduction) and the field (a compensating increase).] An IR144 peak molar extinction coefficient of 143 000M cm at ∼750 nm was taken from U. Brackmann, Lamdachrome Laser Dyes (Lambda Physik GmbH, Gottingen, 1986). The center frequency and FWHM bandwidth for IR144 in methanol were taken from A. Yu, C. A. Tolbert, and D. M. Jonas, J. Phys. Chem. A 106, 9407 (2002).
74. D. M. Jonas, M. J. Lang, Y. Nagasawa, T. Joo, and G. R. Fleming, J. Phys. Chem. 100, 12660 (1996).
75. S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 0021-9606 10.1063/1.467805 101, 1093 (1994); C. Burda, S. Link, M. B. Mohamed, and M. El-Sayed, J. Chem. Phys. 116, 3828 (2002).
76. S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 0021-9606 10.1063/1.467805 101, 1093 (1994); C. Burda, S. Link, M. B. Mohamed, and M. El-Sayed, J. Chem. Phys. 116, 3828 (2002).
77. D. Bedeaux and N. Bloembergen, Physica (Amsterdam) 0031-8914 10.1016/0031-8914(73)90200-0 69, 57 (1973); G. R. Meredith, J. Chem. Phys. 77, 5863 (1982); N. Belabas, doctoral thesis, Ecole Polytechnique, 2002.
78. D. Bedeaux and N. Bloembergen, Physica (Amsterdam) 0031-8914 10.1016/0031-8914(73)90200-0 69, 57 (1973); G. R. Meredith, J. Chem. Phys. 77, 5863 (1982); N. Belabas, doctoral thesis, Ecole Polytechnique, 2002.
79. D. Bedeaux and N. Bloembergen, Physica (Amsterdam) 0031-8914 10.1016/0031-8914(73)90200-0 69, 57 (1973); G. R. Meredith, J. Chem. Phys. 77, 5863 (1982); N. Belabas, doctoral thesis, Ecole Polytechnique, 2002.
80. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, New York, 1991).
81. R. Wortmann and D. M. Bishop, J. Chem. Phys. 108, 1001 (1998).
82. S. Mukamel, Z. Deng, and J. Grad, J. Opt. Soc. Am. B 5, 804 (1988).
83. H. A. Lorentz, The Theory of Electrons (Dover, New York, 1952).
84. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1977), Vol. 1.
85. V. V. Lozovoy, I. Pastirk, M. G. Comstock, and M. Dantus, Chem. Phys. 266, 205 (2001).
86. S. T. Cundiff (private communication).
87. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, IEEE J. Quantum Electron. 35, 459 (1999).
88. T. J. Butenhoff and E. A. Rohlfing, J. Chem. Phys. 98, 5460 (1993).
89. S. Akturk, X. Gu, P. Gabolde, and R. Trebino, Opt. Express 13, 8642 (2005).
90. K. M. Murdoch, D. E. Thompson, K. A. Meyer, and J. C. Wright, Appl. Spectrosc. 54, 1495 (2000). Our treatment assumes no nonlinear optical response from the windows. Wright and co-workers have used approximate solutions of the wave equation to treat window nonlinearities neglected here.
91. J. D. Hybl, A. Yu, D. Farrow, and D. M. Jonas, J. Phys. Chem. A 106, 7651 (2002).
92. J. Park and R. M. Hochstrasser, Chem. Phys. 323, 78 (2006).
93. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).