Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Predissociation of the Na2 4 3 Sigma<sub>g</sub><sup>+</sup> state
The Na2 4 3g+" align="middle"/> state dissociates adiabatically to the 3s + 4p atomic limit. The vibrational levels of the 4 3g+" align="middle"/> state below the 3s + 3d atomic limit were observed pr...
Next Article
Calculating the Keldysh adiabaticity parameter for atomic, diatomic, and polyatomic molecules
A numerical model is presented to determine the Keldysh adiabaticity parameter for the interaction of an intense laser with a polyatomic molecule. The adiabaticity parameter is a guide to determining ...

Degenerate four-wave mixing spectroscopy as a probe of orientation and alignment in molecular systems

J. Chem. Phys. 108, 7713 (1998); doi:10.1063/1.476207

Issue Date: 8 May 1998

You are not logged in to this journal. Log in

Thierry A. W. Wasserman and Patrick H. Vaccaro
Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107

Bruce R. Johnson
Department of Chemistry and Rice Quantum Institute, Rice University, MS 102, Houston, Texas 77251-1892
Degenerate four-wave mixing (DFWM) spectroscopy is shown to provide a facile means for probing angular momentum (or rotational) anisotropy in nonequilibrated ensembles of gaseous molecules, with judicious selection of experimental conditions permitting quantitative determination of population distributions and Zeeman coherences for magnetic sublevels of the target species. A theoretical description of the nonlinear response induced under such circumstances is obtained by incorporating a state multipole expansion of the zero-order density operator into a perturbative (weak-field) treatment for the DFWM interaction. Aside from allowing the effects of incident field polarizations and phase-matching geometries to be considered in detail, this compact spherical tensor formalism provides guidelines for the extraction of spatial information from rovibronically resolved spectral data. Furthermore, these analyses have identified unusual polarization schemes that lead to signal generation only in the presence of rotational anisotropy, thereby suggesting a new class of four-wave mixing measurements that permit the selective detection of molecular orientation and alignment. ©1998 American Institute of Physics.
History: Received 9 September 1997; accepted 13 January 1998
Permalink: http://link.aip.org/link/?JCPSA6/108/7713/1
BUY THIS ARTICLE   (US$28)
Download PDF (529 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 42.65.Hw
    Optics Nonlinear optics Phase conjugation, optical mixing, and photorefractive effect
  • 33.80.-b
    Molecular properties and interactions with photons Photon interactions with molecules
  • YEAR: 1998

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (66)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, in Optical Phase Conjugation, edited by R. A. Fisher (Academic Press, San Diego, California, 1983), p. 211.
  2. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
  3. R. L. Farrow and D. J. Rakestraw, Science 257, 1894 (1992).
  4. P. H. Vaccaro, in Nonlinear Spectroscopy for Molecular Structure Determination, edited by E. Hirota, R. W. Field, J. P. Maier, and S. Tsuchiya (Blackwell Scientific Publications, London, 1997).
  5. S. A. J. Druet and J. P. Taran, Prog. Quantum Electron. 7, 1 (1981).
  6. H. Bervas, B. Attal-Trétout, L. Labrunie, and S. Le Boiteux, Nuovo Cim. 14, 1043 (1992).
  7. B. Attal-Trétout, P. Monot, and K. Müller-Dethlefs, Mol. Phys. 73, 1257 (1991).
  8. H. Bervas, S. Le Boiteux, L. Labrunie, and B. Attal-Trétout, Mol. Phys. 79, 911 (1993).
  9. I. Aben, W. Ubachs, G. van der Zwan, and W. Hogervorst, Chem. Phys. 169, 113 (1993).
  10. S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 101, 1072 (1994);
    11. 101, 1093 (1994).
  11. C. H. Greene and R. N. Zare, Annu. Rev. Phys. Chem. 33, 119 (1982);
    12. C. H. Greene and R. N. Zare, J. Chem. Phys. 78, 6741 (1983).
  12. P. L. Houston, J. Phys. Chem. 91, 5388 (1987);
    13. G. E. Hall and P. L. Houston, Annu. Rev. Phys. Chem. 40, 375 (1989);
    P. L. Houston, Acc. Chem. Res. 22, 309 (1989).
  13. C. Maltz, N. D. Weinstein, and D. R. Herschbach, Mol. Phys. 24, 133 (1972).
  14. J. P. Simons, J. Phys. Chem. 91, 5378 (1987);
    15. 88, 1287 (1984).
  15. A. J. Orr-Ewing and R. N. Zare, Annu. Rev. Phys. Chem. 45, 315 (1994).
  16. T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, J. Chem. Phys. 106, 6314 (1997).
  17. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1996).
  18. A. J. Bain, A. J. McCaffery, M. J. Proctor, and B. J. Whitaker, Chem. Phys. Lett. 110, 663 (1984).
  19. R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988).
  20. T. A. W. Wasserman, P. H. Vaccaro, and B. R. Johnson, J. Chem. Phys. (submitted).
  21. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1990).
  22. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, New York, 1984).
  23. P. H. Vaccaro, in Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping, edited by H.-L. Dai and R. W. Field (World Scientific, Singapore, 1995), p. 1.
  24. R. L. Vander Wal, B. E. Holmes, J. B. Jeffries, P. M. Danehy, R. L. Farrow, and D. J. Rakestraw, Chem. Phys. Lett. 191, 251 (1992);
    25. G. J. Germann, A. McIlroy, T. Drier, R. L. Farrow, and D. J. Rakestraw, Ber. Bunsenges. Phys. Chem. 97, 1630 (1993);
    G. J. Germann, R. L. Farrow, and D. J. Rakestraw, J. Opt. Soc. Am. B 12, 25 (1995).
  25. H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
  26. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer-Verlag, Berlin, 1996).
  27. A. C. Eckbreth, Appl. Phys. 32, 421 (1978).
  28. R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971);
    29. L. Solyman and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).
  29. N. Georgiev, U. Westblom, and M. Aldén, Opt. Commun. 94, 99 (1992);
    30. N. Georgiev and M. Aldén, Appl. Phys. B 56, 281 (1993);
    E. Konz, G. Marowsky, and H.-G. Rubahn, Opt. Commun. 134, 75 (1997).
  30. T. A. W. Wasserman, A. A. Arias, S. A. Kandel, D. Hsu, and P. H. Vaccaro, SPIE 2548, 220 (1995);
    31. T. A. W. Wasserman, A. A. Arias, T. Müller, and P. H. Vaccaro, Chem. Phys. Lett. 262, 329 (1996).
  31. T. K. Yee and T. K. Gustafson, Phys. Rev. A 18, 1597 (1978);
    32. J. P. Uyemura, IEEE J. Quantum Electron. 13, 472 (1980);
    Y. Prior, 20, 37 (1984).
  32. J. L. Oudar and Y. R. Shen, Phys. Rev. A 22, 1141 (1980).
  33. P. Ye and Y. R. Shen, Phys. Rev. A 25, 2183 (1982).
  34. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  35. S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).
  36. P. R. Berman, Phys. Rev. A 5, 927 (1972).
  37. D. A. Case, G. M. McClelland, and D. R. Herschbach, Mol. Phys. 35, 541 (1978).
  38. A. J. McCaffery, in Gas Kinetics and Energy Transfer, Vol. 4 (The Royal Society of Chemistry, London, 1980), p. 47;
    39. A. J. McCaffery, M. J. Proctor, and B. J. Whitaker, Annu. Rev. Phys. Chem. 37, 223 (1986).
  39. The temporal independence of rho(0)(etagJg) is in keeping with the steady-state treatment appropriate for monochromatic (continuous wave) incident fields. More generally, the known zero-order density operator at reference time t0, rho(0)(etagJg;t0), evolves under field-free conditions until the first DFWM interaction, rho(0)(etagJg;t1) = U0(t1,t0)rho(0)(etagJg;t0)U<sub>0</sub><sup>[dagger]</sup>(t1,t0), where the prescription of Eq. (8) requires that the corresponding density matrix elements have the form: rho<sub>gg[sup [double-prime]]</sub><sup>(0)</sup>(etagJg;t1) = rho<sub>gg[sup [double-prime]]</sub><sup>(0)</sup>(etagJg;t0)e<sub>0</sub><sup>-i Omega[sub gg[sup [double-prime]]](t[sub 1] - t[sub 0])</sup>. This quantity must be substituted into Eq. (6) with the lower limits of integration now extending from t0 rather than minus infinity. The resulting induced signal polarization [cf. Eqs. (10) and (11)] will contain additional terms in both the resonant denominator and exponential phase factors.
  40. S. Mukamel and R. F. Loring, J. Opt. Soc. Am. B 3, 595 (1986).
  41. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1994).
  42. This implies that the following conditions hold true independent of magnetic quantum number labels: <g|[script V]i(t)|g> = <e|[script V]i(t)|e> = 0 and <e|U0(tn,tn – 1)|g> = <g|U0(tn,tn – 1)|e> = 0.
  43. R. Loudon, The Quantum Theory of Light (Oxford University Press, Oxford, 1990).
  44. For target media that fail to satisfy the magnetic sublevel restrictions imposed by the present analyses, the induced DFWM signal polarization can still be evaluated through discrete summations over Malpha quantum numbers [cf. Eqs. (12) and (13)]. Although computationally less efficient than our tensor recoupling scheme and unable to take full advantage of the state multipole formalism, this direct calculation procedure might provide the only viable approach for treating systems that exhibit Malpha-dependent energy splittings (e.g., as induced by the Stark and Zeeman effects) or anisotropic relaxation processes (e.g., as incurred by strong resonance fluorescence).
  45. S. Williams, J. D. Tobiason, J. R. Dunlop, and E. A. Rohlfing, J. Chem. Phys. 102, 8342 (1995);
    46. S. Williams, E. A. Rohlfing, L. A. Rahn, and R. N. Zare, 106, 3090 (1997).
  46. This follows from the normalization condition imposed upon the zero-order density operator: Tr[rho(0)(etagJg)] = 1.
  47. R. C. Hillborn, Am. J. Phys. 50, 982 (1982).
  48. T. Müller, P. Dupré, Q. Zhang, and P. H. Vaccaro, (in preparation).
  49. S. Williams, L. A. Rahn, and R. N. Zare, J. Chem. Phys. 104, 3947 (1996).
  50. R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, Laser Polarization Spectroscopy, SPIE Conference on Advances in Laser Spectroscopy I (San Diego, CA, 1977), p. 88.
  51. P. H. Vaccaro, Ph.D., Massachusetts Institute of Technology, 1986;
    52. P. H. Vaccaro, F. Temps, S. Halle, J. L. Kinsey, and R. W. Field, J. Chem. Phys. 88, 4819 (1988).
  52. A. J. Bain and A. J. McCaffery, J. Chem. Phys. 80, 5883 (1984).
  53. T. Müller, T. A. W. Wasserman, B. R. Johnson, and P. H. Vaccaro, J. Chem. Phys. 108, 4 (1998).
  54. S. M. Wandzura, Opt. Lett. 4, 208 (1979).
  55. M. Ducloy and D. Bloch, Phys. Rev. A 30, 3107 (1984).
  56. J. L. Skinner and W. E. Moerner, J. Phys. Chem. 100, 13251 (1996).
  57. J. R. Dunlop and E. A. Rohlfing, J. Chem. Phys. 100, 856 (1993).
  58. V. Sick, M. N. Bui-Pham, and R. L. Farrow, Opt. Lett. 20, 2036 (1995).
  59. A. A. Arias, T. A. W. Wasserman, and P. H. Vaccaro, J. Chem. Phys. 107, 5617 (1997).
  60. E. J. Friedman-Hill, L. A. Rahn, and R. L. Farrow, J. Chem. Phys. 100, 4065 (1994).
  61. R. P. Lucht, R. Trebino, and L. A. Rahn, Phys. Rev. A 45, 8209 (1992);
    62. R. P. Lucht, R. L. Farrow, and D. J. Rakestraw, J. Opt. Soc. Am. B 10, 1508 (1993);
    M. Nakano and K. Yamaguchi, Chem. Phys. Lett. 234, 323 (1995).
  62. M. A. Buntine, D. W. Chandler, and C. C. Hayden, J. Chem. Phys. 97, 707 (1992);
    63. T. J. Butenhoff and E. A. Rohlfing, 97, 1595 (1992);
    J. D. Tobiason, J. R. Dunlop, and E. A. Rohlfing, 103, 1448 (1995).
  63. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, Boston, Massachusetts, 1990).
  64. U. Fano and G. Racah, Irreducible Tensorial Sets (Academic, New York, 1959);
    65. U. Fano and A. R. P. Rau, Symmetries in Quantum Physics (Academic, San Diego, California, 1996).
  65. D. M. Brink and G. R. Satchler, Angular Momentum (Clarendon, Oxford, 1993).
  66. M. Bouten, Physica (Amsterdam) 42, 572 (1969).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics