Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions

Journal of Chemical Physics

Volumn 111, Issue 24, 1999, Pages 10934-10956

  Albrecht, Allison W ^a   Hybl, John D ^a   Gallagher Faeder, Sarah M ^a   Jonas, David M ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001097952     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.480457     Document Type: Article

References (161)

1. D. J. Tannor, R. Kosloff, and S. A. Rice, J. Chem. Phys. 85, 5805 (1986).
2. D. J. Tannor and S. A. Rice, Adv. Chem. Phys. 70, 441 (1988).
3. P. Brumer and M. Shapiro, Acc. Chem. Res. 22, 407 (1989).
4. W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
5. M. Shapiro and P. Brumer, Int. Rev. Phys. Chem. 13, 187 (1994).
6. R. J. Gordon and S. A. Rice, Annu. Rev. Phys. Chem. 48, 601 (1997).
7. L. Zhu, K. Suto, J. A. Fiss, R. Wada, T. Seideman, and R. J. Gordon, Phys. Rev. Lett. 79, 4108 (1997).
8. R. N. Zare, J. Chem. Phys. 279, 1875 (1998).
9. W. S. Warren and A. H. Zewail, J. Chem. Phys. 78, 2279 (1983).
10. F. Spano, M. Haner, and W. S. Warren, Chem. Phys. Lett. 135, 97 (1987).
11. N. F. Scherer, A. J. Ruggiero, M. Du, and G. R. Fleming, J. Chem. Phys. 93, 856 (1990).
12. N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, J. Chem. Phys. 95, 1487 (1991).
13. N. F. Scherer, A. Matro, L. D. Ziegler, M. Du, R. J. Carlson, J. A. Cina, and G. R. Fleming, J. Chem. Phys. 96, 4180 (1992).
14. M. Cho, N. F. Scherer, G. R. Fleming, and S. Mukamel, J. Chem. Phys. 96, 5618 (1992).
15. L. D. Ziegler and N. F. Scherer, J. Chem. Phys. 7, 4704 (1992).
16. W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).
17. W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Chem. Phys. Lett. 247, 264 (1995).
18. W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Chem. Phys. 233, 287 (1998).
19. C. J. Kennedy, Appl. Opt. 15, 2623 (1976).
20. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, MA, 1990).
21. F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).
22. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).
23. N. A. Ramsey, Rev. Mod. Phys. 62, 541 (1990).
24. J. K. M. Sanders and B. K. Hunter, Modern NMR Spectroscopy: A Guide for Chemists (Oxford University Press, Oxford, 1987).
25. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1987).
26. C. Leichtle, W. P. Schleich, I. S. Averbukh, and M. Shapiro, J. Chem. Phys. 108, 6057 (1998).
27. S. Mukamel, Annu. Rev. Phys. Chem. 41, 647 (1990).
28. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
29. X.-P. Jiang and P. Brumer, J. Chem. Phys. 94, 5833 (1991).
30. X.-P. Jiang, M. Shapiro, and P. Brumer, J. Chem. Phys. 104, 607 (1996).
31. H. Tang, R. Kosloff, and S. A. Rice, J. Chem. Phys. 104, 5457 (1996).
32. D. G. Abrashkevich, M. Shapiro, and P. Brumer, J. Chem. Phys. 108, 3585 (1998).
33. A. Brown and W. J. Meath, J. Chem. Phys. 109, 9351 (1998).
34. L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, Opt. Lett. 21, 2008 (1996).
35. The magnitude and sign of the momentum impulse imparted to a free charge by a short optical pulse should depend on the absolute phase of the pulse.
36. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1986).
37. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).
38. A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry: a User's Handbook (Elsevier, New York, 1990).
39. D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, Phys. Rev. B 50, 8439 (1994).
40. J.-P. Likforman, M. Joffre, and V. Thierry-Mieg, Opt. Lett. 22, 1104 (1997).
41. M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 1338 (1997).
42. 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).
43. J. D. Hybl, A. W. Albrecht, S. M. Gallagher Faeder, and D. M. Jonas, Chem. Phys. Lett. 297, 307 (1998).
44. A. M. Weiner, S. De Silvestri, and E. P. Ippen, J. Opt. Soc. Am. B 2, 654 (1985).
45. W. M. Zhang, V. Chernyak, and S. Mukamel, J. Chem. Phys. 110, 5011 (1999).
46. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).
47. The envelope phase of the above quasimonochromatic approximation to a pulse thus varies as the pulse propagates through the sample. At a single point in space, the quasimonochromatic field given above also has a constant carrier wave phase as the delay is varied (hence an envelope phase-shift).
48. M. Schubert and B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley-Interscience, New York, 1986).
49. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
50. T. W. Mossberg, R. Kachru, S. R. Hartmann, and A. M. Flusberg, Phys. Rev. A 20, 1976 (1979).
51. Y.-X. Yan, E. B. Gamble, and K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
52. K. A. Nelson and E. P. Ippen, Adv. Chem. Phys. 75, 1 (1989).
53. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
54. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
55. F. Reynaud, F. Salin, and A. Barthelmy, Opt. Lett. 14, 275 (1989).
56. E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 17, 1131 (1992).
57. E. Tokunaga, A. Terasaki, and T. Kobayashi, J. Opt. Soc. Am. B 12, 753 (1995).
58. L. Lepetit, G. Chériaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
59. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 884 (1996).
60. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 1313 (1996).
61. S. Mukamel and R. F. Loring, J. Opt. Soc. Am. B 3, 595 (1986).
62. Y. J. Yan and S. Mukamel, J. Chem. Phys. 89, 5160 (1988).
63. Y. J. Yan and S. Mukamel, J. Chem. Phys. 94, 179 (1991).
64. Y. Tanimura and S. Mukamel, J. Chem. Phys. 99, 9496 (1993).
65. V. Chernyak, W. M. Zhang, and S. Mukamel, J. Chem. Phys. 109, 9587 (1998).
66. S. M. Gallagher Faeder and D. M. Jonas, J. Phys. Chem. A (in press).
67. S. M. Gallagher Faeder, Ph.D. thesis, University of Colorado, 1999.
68. L. Lepetit and M. Joffre, Opt. Lett. 21, 564 (1996).
69. A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, Phys. Rev. Lett. 79, 2702 (1997).
70. I. Levy, M. Shapiro, and P. Brumer, J. Chem. Phys. 93, 2493 (1990).
71. K. Okumura and Y. Tanimura, Chem. Phys. Lett. 295, 298 (1998).
72. M. Takeda, Jpn. J. Opt. 13, 55 (1984).
73. C. Dorrer, J. Opt. Soc. Am. B 16, 1160 (1999).
74. D. A. Wiersma and K. Duppen, Science 237, 1147 (1987).
75. Y. Nagasawa, J.-Y. Yu, and G. R. Fleming, J. Chem. Phys. 109, 6175 (1998).
76. M. Kujawinska, in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, edited by D. W. Robinson and G. T. Reid (Institute of Physics, Philadelphia, 1993), pp. 141-193.
77. Selected Papers on Interference, Interferometry, and Interferometric Metrology, edited by P. Hariharan and D. Malacara (SPIE Optical Engineering, Bellingham, WA, 1995), Vol. MS 110.
78. This result can be derived by inserting a phase-shift φ in the derivation of the electric field diffracted by a sound wave given in Ch. 12 of A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, New York, 1997). This result also holds for absorption coefficient gratings.
79. H. Petek and S. Ogawa. Prog. Surf. Sci. 56, 239 (1997).
80. W. Nessler, S. Ogawa, H. Nagano, H. Petek, J. Shimoyama, Y. Nakayama, and K. Kishio, J. Electron Spectrosc. Relat. Phenom. 88-91, 495 (1998).
81. S. Ogawa, H. Nagano, H. Petek, and A. P. Heberle, Phys. Rev. Lett. 78, 1339 (1997).
82. A. P. Heberle, J. J. Baumberg, and K. Köhler, Phys. Rev. Lett. 75, 2598 (1995).
83. H. Petek, A. P. Heberle, W. Nessler, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
84. H. Kawashima, M. M. Wefers, and K. A. Nelson, Annu. Rev. Phys. Chem. 46, 627 (1995).
85. N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
86. D. Marcuse, Principles of Quantum Electronics (Academic, New York, 1980).
87. K. Creath, in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, edited by D. W. Robinson and G. T. Reid (Institute of Physics, Philadelphia, 1993), pp. 95-140.
88. V. Nagarajan, E. Johnson, J. C. Williams, and W. W. Parson, J. Phys. Chem. B 103, 2297 (1999).
89. T. Radhakrishan, Proc.-Indian Acad. Sci., Sect. A 33, 22 (1951).
90. Properties of Optical and Laser-Related Materials: a Handbook, edited by D. N. Nikogosyan (Wiley, Chichester, 1997).
91. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927).
92. G. D. Goodno, G. Dadusc, and R. J. Dwayne Miller, J. Opt. Soc. Am. B 15, 1791 (1998).
93. R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, Phys. Rev. Lett. 71, 2575 (1993).
94. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
95. C. Spielmann, L. Xu, and F. Krausz, Appl. Opt. 36, 2523 (1997).
96. M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, Opt. Lett. 19, 572 (1994).
97. M. Wefers and K. A. Nelson, Opt. Lett. 18, 2032 (1993).
98. W. Yang, D. Keusters, D. Goswami, and W. S. Warren, Opt. Lett. 23, 1843 (1998).
99. J. X. Tull, M. A. Dugan, and W. S. Warren, Adv. Magn. Opt. Reson. 20, 1 (1997).
100. M. M. Salour and C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
101. M. M. Salour, Rev. Mod. Phys. 50, 667 (1978).
102. J. C. Bergquist, S. A. Lee, and J. L. Hall, Phys. Rev. Lett. 38, 159 (1977).
103. J. T. Fourkas, W. L. Wilson, G. Wäckerle, A. E. Frost, and M. D. Fayer, J. Opt. Soc. Am. B 6, 1905 (1989).
104. Random optical path length variations lead to random delay variations and not random variation of the constant term in the spectral phase which is called the phase of a pulse here.
105. d + φ) in the argument of the cosine in Eq. (4.35) of Ref. 12 and Eq. (3.6) of Ref. 13 identically zero (mod 2π) in the phase-locked pulse pair experiments.
106. E. J. Heller, in Ultrafast Phenomena VII, edited by C. B. Harris, E. P. Ippen, G. A. Mourou, and A. H. Zewail (Springer-Verlag, Berlin, 1990).
107. R. Bavli, V. Engel, and H. Metiu, J. Chem. Phys. 96, 2600 (1992).
108. G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. A 52, 2016 (1995).
109. R. R. Jones, D. W. Schumacher, T. F. Gallagher, and P. H. Bucksbaum, J. Phys. B 28, L405 (1995).
110. V. Blanchet, M. A. Bouchène, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
111. A. G. Marshall, Chemom. Intell. Lab. Syst. 3, 261 (1988).
112. E. Bartholdi and R. R. Ernst, J. Magn. Reson. 11, 9 (1973).
113. L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw-Hill, New York, 1968).
114. E. C. Kemble, The Fundamental Principles of Quantum Mechanics, 1st ed. (McGraw-Hill, New York, 1937).
115. M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
116. L. D. Landau, E. M. Lifschitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
117. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
118. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, New York, 1997).
119. M. L. Forman, W. H. Steel, and G. A. Vanasse, J. Opt. Soc. Am. 56, 59 (1966).
120. J. A. Cina (personal communication, 1999).
121. V. Volterra, Theory of Functional (Blackie, London, 1930).
122. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, New York, 1991).
123. C. P. Slichter, Principles of Magnetic Resonance, 3rd ed. (Springer, New York, 1990).
124. Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
125. D. Lee and A. C. Albrecht, Adv. Chem. Phys. 83, 43 (1993).
126. Y. Tanimura and S. Mukamel, Phys. Rev. E 47, 118 (1993).
127. R. Trebino and D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
128. J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
129. K. W. DeLong and R. Trebino, J. Opt. Soc. Am. A 11, 2429 (1994).
130. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, J. Opt. Soc. Am. B 11, 2206 (1994).
131. J. T. Fourkas, L. Dhar, K. A. Nelson, and R. Trebino, J. Opt. Soc. Am. B 12, 155 (1995).
132. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, IEEE J. Quantum Electron. 32, 1253 (1996).
133. G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Top. Quantum Electron. 2, 575 (1996).
134. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
135. Some discussions of FROG do not distinguish electric field from complex envelope. References 127 and 132-134 use the word "field" (often with complex conjugate notation) for complex envelope, while Refs. 128 through 131 explicitly use the complex envelope to calculate FROG signals. The equations for transient grating and self diffraction FROG signals in Ref. 134 are equal to the nonlinear polarization given by Eq. (13) when the response is instantaneous (i.e., the response function is a product of delta functions). Extensions of Eq. (14) may be useful for inverting interferometric FROG traces.
136. T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang, and G. R. Fleming, J. Chem. Phys. 104, 6089 (1996).
137. W. P. de Boeij. M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Chem. Phys. Lett. 224, 243 (1994).
138. A. M. Weiner, IEEE J. Quantum Electron. QE-19, 1276 (1983).
139. Y. R. Shen, Phys. Rev. B 9, 622 (1974).
140. L. D. Ziegler, Acc. Chem. Res. 27, 1 (1994).
141. As for linear experiments with phase-locked pulse pairs, a time domain analysis leads to the same conclusion if each member of both pulse pairs is treated symmetrically (e.g., pulse c should be included once as an excitation field in calculating the nonlinear polarization with pulse d as heterodyne field, and once as a heterodyne field when pulse d acts as a nonlinear excitation field).
142. D. W. Phillion, D. J. Kuizenga, and A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
143. K. A. Nelson, R. Casalegno, R. J. Dwayne Miller, and M. D. Fayer, J. Chem. Phys. 77, 1144 (1982).
144. M. D. Levenson and G. L. Eesley, Appl. Phys. 19, 1 (1979).
145. D. S. Alavi, R. S. Hartman, and D. H. Waldeck, J. Chem. Phys. 92, 4055 (1990).
146. P. Brumer and M. Shapiro, Chem. Phys. 139, 221 (1989).
147. J. Cao and K. R. Wilson, J. Chem. Phys. 107, 1441 (1997).
148. J. L. Herek, A. Materny, and A. H. Zewail, Chem. Phys. Lett. 228, 15 (1994).
149. C. J. Bardeen, J. Che, K. R. Wilson, V. Yakovlev, P. Cong, J. Krause, and M. Messina, J. Phys. Chem. A 101, 3815 (1997).
150. R. Uberna, M. Khalil, R. M. Williams, J. M. Papanikolas, and S. R. Leone, J. Chem. Phys. 108, 9259 (1998).
151. M. Shapiro and P. Brumer, J. Chem. Soc., Faraday Trans. 93, 1263 (1997).
152. J. A. Fiss, L. Zhu, and R. J. Gordon, Phys. Rev. Lett. 82, 65 (1999).
153. Dephasing can prevent molecules from seeing the global phase relationship between long or widely separated pulses. Harmonics have a locally periodic phase relationship which repeats every period of the lowest harmonic so that the global phase relationship is apparent on a very short time scale.
154. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. (Oxford University Press, London, 1959).
155. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985).
156. For a causal impulse response [e.g., χ(t) in Eq. (A2)], the unique even and odd extensions of that response are equal for positive times and may be substituted one for the other in truncated Fourier sine and cosine transforms to formally derive the Kramers-Kronig relations based only on linear response and causality (see Ref. 157). Subtleties associated with poles of χ(ω) in the complex analytic derivation of the Kramers-Kronig relations are hidden in the impulse response at t = O.
157. C. W. Peterson and B. W. Knight, J. Opt. Soc. Am. 63, 1238 (1973).
158. H. Dym and H. P. McKean, Fourier Series and Integrals (Academic, New York, 1972).
159. M. G. Sceats and G. C. Morris, Phys. Status Solidi A 14, 643 (1972).
160. J. A. Bardwell and M. J. Dignam, J. Chem. Phys. 83, 5468 (1985).
161. C. P. Williams and A. G. Marshall, Anal. Chem. 64, 916 (1992).