Abstract

An analytic model is developed to describe the influence of coherent vibrational motion on optical third harmonic generation. The vibrational coherence is prepared and probed by a pair of collinear optical pulses, focused at the interface of a crystal that has vibrational modes that are accessible to impulsive Raman scattering. Under these conditions, the probe pulse generates a third harmonic signal that is perturbed by the vibrational coherence through three mechanisms uncovered by this model: (1) coherent second hyper-Raman scattering, (2) cascaded amplitude modulation, and (3) perturbation of Fresnel transmission and reflection at the interface. Upon scanning the optical pulse delay and translating the crystal through the focal plane, these three contributions exhibit key differences, which may be observed experimentally.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
    [CrossRef]
  2. J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
    [CrossRef]
  3. J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
    [CrossRef]
  4. Y. R. Shen, “Surface nonlinear optical spectroscopy,” Solid State Commun. 84, 171–172 (1992).
    [CrossRef]
  5. Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
    [CrossRef]
  6. T. Nomoto and H. Onishi, “Fourth-order coherent Raman spectroscopy in a time domain: applications to buried interfaces,” Phys. Chem. Chem. Phys. 9, 5515–5521 (2007).
    [CrossRef]
  7. D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
    [CrossRef]
  8. J. W. Wilson and R. A. Bartels, “Rapid birefringent delay scanning for coherent multiphoton impulsive Raman pump–probe spectroscopy,” IEEE J. Sel. Top. Quantum Electron. PP, 1–10 (2012).
  9. In transforming to the group frame, a new symbol, ζ, is introduced (even though z=ζ) as a reminder that ∂/∂ζ≠∂/∂z. In fact, ∂/∂t=∂/∂tpr, ∂/∂z=−upr−1∂/∂tpr+∂/∂ζ.
  10. J. Chesnoy and A. Mokhtari, “Resonant impulsive-stimulated Raman scattering on malachite green,” Phys. Rev. A 38, 3566–3576 (1988).
    [CrossRef]
  11. L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
    [CrossRef]
  12. G. Herzberg, Molecular Spectra and Molecular Structure(Krieger, 1989).
  13. E. Wilson, J. Decius, and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, 1955).
  14. D. A. Long and L. Stanton, “Studies of nonlinear phenomena. I. Theory of the hyper Raman effect,” Proc. R. Soc. A 318, 441–457 (1970).
    [CrossRef]
  15. J. H. Christie and D. J. Lockwood, “Selection rules for three- and four-photon Raman interactions,” J. Chem. Phys. 54, 1141–1154 (1971).
    [CrossRef]
  16. T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
    [CrossRef]
  17. P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
    [CrossRef]
  18. J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
    [CrossRef]
  19. R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
    [CrossRef]
  20. K. Hartinger and R. A. Bartels, “Pulse polarization splitting in a transient wave plate,” Opt. Lett. 31, 3526–3528 (2006).
    [CrossRef]
  21. K. Hartinger and R. A. Bartels, “Analytical model of the effective transient optical response of symmetric-top molecules in the presence of a rotational coherence,” J. Opt. Soc. Am. B 25, 407–413 (2008).
    [CrossRef]
  22. K. Hartinger and R. A. Bartels, “Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization,” Appl. Phys. Lett. 92, 021126 (2008).
    [CrossRef]
  23. R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102, 207–220 (1997).
    [CrossRef]
  24. In the Fresnel perturbation discussion, we depart from the usual notation (uppercase T for the power transmission coefficient and lowercase t for the field transmission coefficient). We denote the field transmission coefficient with an uppercase T=2ni/(nt+ni), where ni is the incident index and nt is the transmitted index, in order to avoid ambiguity with the time variable t.
  25. Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
    [CrossRef]
  26. D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
    [CrossRef]
  27. J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
    [CrossRef]
  28. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).
  29. J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
    [CrossRef]
  30. R. S. Tasgal and Y. B. Band, “Third-harmonic generation in isotropic media by focused pulses,” Phys. Rev. A 70, 053810 (2004).
    [CrossRef]
  31. When solving for E0,th, we divide out Mth. This modulation term is reintroduced in Eq. (30).
  32. Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
    [CrossRef]
  33. P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
    [CrossRef]
  34. A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).
  35. D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
    [CrossRef]
  36. A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
    [CrossRef]
  37. M. B. Raschke and Y. R. Shen, “Nonlinear optical spectroscopy of solid interfaces,” Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).
    [CrossRef]
  38. Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
    [CrossRef]
  39. N. Bloembergen, “Surface nonlinear optics: a historical overview,” Appl. Phys. B 68, 289–293 (1999).
    [CrossRef]
  40. P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
    [CrossRef]
  41. Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
    [CrossRef]
  42. S. Mukamel, Principles of Nonlinear Optical Spectroscopy(Oxford University, 1995).
  43. R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1979).
    [CrossRef]
  44. U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
    [CrossRef]
  45. A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses.,” Rev. Mod. Phys 50, 607–665 (1978).
    [CrossRef]

2012

J. W. Wilson and R. A. Bartels, “Rapid birefringent delay scanning for coherent multiphoton impulsive Raman pump–probe spectroscopy,” IEEE J. Sel. Top. Quantum Electron. PP, 1–10 (2012).

2011

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

2010

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

2009

P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
[CrossRef]

2008

J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Analytical model of the effective transient optical response of symmetric-top molecules in the presence of a rotational coherence,” J. Opt. Soc. Am. B 25, 407–413 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization,” Appl. Phys. Lett. 92, 021126 (2008).
[CrossRef]

2007

T. Nomoto and H. Onishi, “Fourth-order coherent Raman spectroscopy in a time domain: applications to buried interfaces,” Phys. Chem. Chem. Phys. 9, 5515–5521 (2007).
[CrossRef]

2006

K. Hartinger and R. A. Bartels, “Pulse polarization splitting in a transient wave plate,” Opt. Lett. 31, 3526–3528 (2006).
[CrossRef]

2005

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
[CrossRef]

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

2004

M. B. Raschke and Y. R. Shen, “Nonlinear optical spectroscopy of solid interfaces,” Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).
[CrossRef]

R. S. Tasgal and Y. B. Band, “Third-harmonic generation in isotropic media by focused pulses,” Phys. Rev. A 70, 053810 (2004).
[CrossRef]

2002

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

2001

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

1999

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

N. Bloembergen, “Surface nonlinear optics: a historical overview,” Appl. Phys. B 68, 289–293 (1999).
[CrossRef]

1997

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102, 207–220 (1997).
[CrossRef]

Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[CrossRef]

1996

T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
[CrossRef]

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

1995

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

1994

L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
[CrossRef]

1992

Y. R. Shen, “Surface nonlinear optical spectroscopy,” Solid State Commun. 84, 171–172 (1992).
[CrossRef]

1989

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

1988

J. Chesnoy and A. Mokhtari, “Resonant impulsive-stimulated Raman scattering on malachite green,” Phys. Rev. A 38, 3566–3576 (1988).
[CrossRef]

1987

P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

1985

Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

1979

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1979).
[CrossRef]

1978

A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses.,” Rev. Mod. Phys 50, 607–665 (1978).
[CrossRef]

1971

J. H. Christie and D. J. Lockwood, “Selection rules for three- and four-photon Raman interactions,” J. Chem. Phys. 54, 1141–1154 (1971).
[CrossRef]

1970

D. A. Long and L. Stanton, “Studies of nonlinear phenomena. I. Theory of the hyper Raman effect,” Proc. R. Soc. A 318, 441–457 (1970).
[CrossRef]

1969

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

1957

U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
[CrossRef]

Bagayev, S. N.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Band, Y. B.

R. S. Tasgal and Y. B. Band, “Third-harmonic generation in isotropic media by focused pulses,” Phys. Rev. A 70, 053810 (2004).
[CrossRef]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Bartels, R. A.

J. W. Wilson and R. A. Bartels, “Rapid birefringent delay scanning for coherent multiphoton impulsive Raman pump–probe spectroscopy,” IEEE J. Sel. Top. Quantum Electron. PP, 1–10 (2012).

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Analytical model of the effective transient optical response of symmetric-top molecules in the presence of a rotational coherence,” J. Opt. Soc. Am. B 25, 407–413 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization,” Appl. Phys. Lett. 92, 021126 (2008).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Pulse polarization splitting in a transient wave plate,” Opt. Lett. 31, 3526–3528 (2006).
[CrossRef]

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Becker, M. F.

D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
[CrossRef]

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

Bloembergen, N.

N. Bloembergen, “Surface nonlinear optics: a historical overview,” Appl. Phys. B 68, 289–293 (1999).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

Chang, Y. M.

Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[CrossRef]

Chekina, S. N.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Chen, Z.

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

Chesnoy, J.

J. Chesnoy and A. Mokhtari, “Resonant impulsive-stimulated Raman scattering on malachite green,” Phys. Rev. A 38, 3566–3576 (1988).
[CrossRef]

Christie, J. H.

J. H. Christie and D. J. Lockwood, “Selection rules for three- and four-photon Raman interactions,” J. Chem. Phys. 54, 1141–1154 (1971).
[CrossRef]

Conrad, D. C.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Cross, P.

E. Wilson, J. Decius, and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, 1955).

Cundiff, S. T.

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

Day, G. W.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

DeCamp, M. F.

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

Decius, J.

E. Wilson, J. Decius, and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, 1955).

Dhar, L.

L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
[CrossRef]

Downer, M. C.

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

Duppen, K.

T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
[CrossRef]

Eichler, H. J.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Elsaesser, T.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

Fahy, S.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Fano, U.

U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
[CrossRef]

Fernandez, J.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Fourkas, J. T.

T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
[CrossRef]

Frenkel, A.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Gad, G. M. A.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Gamble, J.

Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Gao, Y.

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

Garrett, G. A.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
[CrossRef]

Hale, P. D.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Hanuza, J.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Hartinger, K.

K. Hartinger and R. A. Bartels, “Analytical model of the effective transient optical response of symmetric-top molecules in the presence of a rotational coherence,” J. Opt. Soc. Am. B 25, 407–413 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization,” Appl. Phys. Lett. 92, 021126 (2008).
[CrossRef]

K. Hartinger and R. A. Bartels, “Pulse polarization splitting in a transient wave plate,” Opt. Lett. 31, 3526–3528 (2006).
[CrossRef]

Hellwarth, R.

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1979).
[CrossRef]

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure(Krieger, 1989).

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Hunt, J. H.

P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
[CrossRef]

Ivannikova, N. I.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Kaiser, W.

A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses.,” Rev. Mod. Phys 50, 607–665 (1978).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Kapteyn, H. C.

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Keto, J. W.

D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
[CrossRef]

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

Korn, G.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

Kravstov, N. V.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Kupka, D.

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

Laubereau, A.

A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses.,” Rev. Mod. Phys 50, 607–665 (1978).
[CrossRef]

Lee, K. S.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Leone, S. R.

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Li, X. Q.

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

Liu, Y.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Lockwood, D. J.

J. H. Christie and D. J. Lockwood, “Selection rules for three- and four-photon Raman interactions,” J. Chem. Phys. 54, 1141–1154 (1971).
[CrossRef]

Long, D. A.

D. A. Long and L. Stanton, “Studies of nonlinear phenomena. I. Theory of the hyper Raman effect,” Proc. R. Soc. A 318, 441–457 (1970).
[CrossRef]

Martinez, O. E.

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

Masihzadeh, O.

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

Merlin, R.

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102, 207–220 (1997).
[CrossRef]

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Minch, B. C.

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

Mokhtari, A.

J. Chesnoy and A. Mokhtari, “Resonant impulsive-stimulated Raman scattering on malachite green,” Phys. Rev. A 38, 3566–3576 (1988).
[CrossRef]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Mukamel, S.

S. Mukamel, Principles of Nonlinear Optical Spectroscopy(Oxford University, 1995).

Murnane, M. M.

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Nazarkin, A.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

Nelson, K. A.

L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
[CrossRef]

Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

New, G. H. C.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Nomoto, T.

T. Nomoto and H. Onishi, “Fourth-order coherent Raman spectroscopy in a time domain: applications to buried interfaces,” Phys. Chem. Chem. Phys. 9, 5515–5521 (2007).
[CrossRef]

Onishi, H.

T. Nomoto and H. Onishi, “Fourth-order coherent Raman spectroscopy in a time domain: applications to buried interfaces,” Phys. Chem. Chem. Phys. 9, 5515–5521 (2007).
[CrossRef]

Raschke, M. B.

M. B. Raschke and Y. R. Shen, “Nonlinear optical spectroscopy of solid interfaces,” Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).
[CrossRef]

Reiche, P.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Rogers, J. A.

L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
[CrossRef]

Rose, A. H.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Schlup, P.

P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
[CrossRef]

Shen, Y. R.

M. B. Raschke and Y. R. Shen, “Nonlinear optical spectroscopy of solid interfaces,” Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).
[CrossRef]

Y. R. Shen, “Surface nonlinear optical spectroscopy,” Solid State Commun. 84, 171–172 (1992).
[CrossRef]

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
[CrossRef]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Stanton, L.

D. A. Long and L. Stanton, “Studies of nonlinear phenomena. I. Theory of the hyper Raman effect,” Proc. R. Soc. A 318, 441–457 (1970).
[CrossRef]

Steffen, T.

T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
[CrossRef]

Stoker, D.

D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
[CrossRef]

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

Tasgal, R. S.

R. S. Tasgal and Y. B. Band, “Third-harmonic generation in isotropic media by focused pulses,” Phys. Rev. A 70, 053810 (2004).
[CrossRef]

Tom, H. W. K.

Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[CrossRef]

Ueda, K.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Uher, C.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Wahlstrand, J. K.

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

Ward, J. F.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Weinacht, T. C.

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Whitaker, J. F.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

Williams, P. A.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Wilson, E.

E. Wilson, J. Decius, and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, 1955).

Wilson, J. W.

J. W. Wilson and R. A. Bartels, “Rapid birefringent delay scanning for coherent multiphoton impulsive Raman pump–probe spectroscopy,” IEEE J. Sel. Top. Quantum Electron. PP, 1–10 (2012).

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
[CrossRef]

Wittmann, M.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

Xu, L.

Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[CrossRef]

Yan, Y. X.

Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Yasiliev, Y. V.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Annu. Rev. Phys. Chem.

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

Appl. Opt.

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
[CrossRef]

Appl. Phys. B

N. Bloembergen, “Surface nonlinear optics: a historical overview,” Appl. Phys. B 68, 289–293 (1999).
[CrossRef]

Appl. Phys. Lett.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

K. Hartinger and R. A. Bartels, “Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization,” Appl. Phys. Lett. 92, 021126 (2008).
[CrossRef]

Chem. Phys. Lett.

J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. 463, 300–304 (2008).
[CrossRef]

D. Kupka, J. W. Wilson, O. Masihzadeh, and R. A. Bartels, “Distinguishing bulk and interface modulation of optical third harmonic generation due to coherent optical phonon excitation,” Chem. Phys. Lett. 490, 97–101 (2010).
[CrossRef]

Chem. Rev.

L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994).
[CrossRef]

Curr. Opin. Solid State Mater. Sci.

M. B. Raschke and Y. R. Shen, “Nonlinear optical spectroscopy of solid interfaces,” Curr. Opin. Solid State Mater. Sci. 8, 343–352 (2004).
[CrossRef]

IEEE J. Quantum Electron.

P. Schlup, J. W. Wilson, and R. A. Bartels, “Sensitive and selective detection of low-frequency vibrational modes through a phase-shifting Fourier transform spectroscopy.,” IEEE J. Quantum Electron. 45, 777–782 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. W. Wilson and R. A. Bartels, “Rapid birefringent delay scanning for coherent multiphoton impulsive Raman pump–probe spectroscopy,” IEEE J. Sel. Top. Quantum Electron. PP, 1–10 (2012).

J. Chem. Phys.

Y. X. Yan, J. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

J. H. Christie and D. J. Lockwood, “Selection rules for three- and four-photon Raman interactions,” J. Chem. Phys. 54, 1141–1154 (1971).
[CrossRef]

T. Steffen, J. T. Fourkas, and K. Duppen, “Time resolved four- and six-wave mixing in liquids. I. Theory,” J. Chem. Phys. 105, 7364–7382 (1996).
[CrossRef]

J. Opt. Soc. Am. B

K. Hartinger and R. A. Bartels, “Analytical model of the effective transient optical response of symmetric-top molecules in the presence of a rotational coherence,” J. Opt. Soc. Am. B 25, 407–413 (2008).
[CrossRef]

J. Phys. Condens. Matter

Z. Chen, Y. Gao, B. C. Minch, and M. F. DeCamp, “Coherent optical phonon generation in Bi3Ge4O12,” J. Phys. Condens. Matter 23, 385402 (2011).
[CrossRef]

Laser Phys.

A. A. Kaminskii, S. N. Bagayev, N. V. Kravstov, S. N. Chekina, Y. V. Yasiliev, N. I. Ivannikova, K. Ueda, H. J. Eichler, G. M. A. Gad, J. Hanuza, J. Fernandez, and P. Reiche, “Spectroscopy and cw laser action, magnetooptics and nonlinear optical frequency conversion in Ln3+ doped and undoped Bi4Ge3O12 and Bi4Si3O12 crystals,” Laser Phys. 11, 897–918 (2001).

Opt. Lett.

K. Hartinger and R. A. Bartels, “Pulse polarization splitting in a transient wave plate,” Opt. Lett. 31, 3526–3528 (2006).
[CrossRef]

J. W. Wilson, P. Schlup, and R. A. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. 33, 2116–2118 (2008).
[CrossRef]

J. K. Wahlstrand, R. Merlin, X. Q. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
[CrossRef]

Phys. Chem. Chem. Phys.

T. Nomoto and H. Onishi, “Fourth-order coherent Raman spectroscopy in a time domain: applications to buried interfaces,” Phys. Chem. Chem. Phys. 9, 5515–5521 (2007).
[CrossRef]

Phys. Rev.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Phys. Rev. A

R. S. Tasgal and Y. B. Band, “Third-harmonic generation in isotropic media by focused pulses,” Phys. Rev. A 70, 053810 (2004).
[CrossRef]

D. Stoker, M. F. Becker, and J. W. Keto, “Optical third-harmonic generation using ultrashort laser pulses,” Phys. Rev. A 71, 061802 (2005).
[CrossRef]

J. Chesnoy and A. Mokhtari, “Resonant impulsive-stimulated Raman scattering on malachite green,” Phys. Rev. A 38, 3566–3576 (1988).
[CrossRef]

Phys. Rev. B

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[CrossRef]

Phys. Rev. Lett.

Y. Liu, A. Frenkel, G. A. Garrett, J. F. Whitaker, S. Fahy, C. Uher, and R. Merlin, “Impulsive light scattering by coherent phonons in LaAlO3: disorder and boundary effects,” Phys. Rev. Lett. 75, 334–337 (1995).
[CrossRef]

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83, 2560–2563 (1999).
[CrossRef]

P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, “Sum-frequency vibrational spectroscopy of a Langmuir film: study of molecular orientation of a two-dimensional system,” Phys. Rev. Lett. 59, 1597–1600 (1987).
[CrossRef]

R. A. Bartels, T. C. Weinacht, S. R. Leone, H. C. Kapteyn, and M. M. Murnane, “Nonresonant control of multimode molecular wave packets at room temperature,” Phys. Rev. Lett. 88, 033001 (2002).
[CrossRef]

Y. M. Chang, L. Xu, and H. W. K. Tom, “Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation,” Phys. Rev. Lett. 78, 4649–4652 (1997).
[CrossRef]

Phys. Status Solidi C

D. Stoker, M. C. Downer, M. F. Becker, and J. W. Keto, “Optical third-harmonic surface microscopy using ultra-short laser pulses,” Phys. Status Solidi C 2, 3978–3982 (2005).
[CrossRef]

Proc. R. Soc. A

D. A. Long and L. Stanton, “Studies of nonlinear phenomena. I. Theory of the hyper Raman effect,” Proc. R. Soc. A 318, 441–457 (1970).
[CrossRef]

Prog. Quantum Electron.

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1979).
[CrossRef]

Rev. Mod. Phys

A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses.,” Rev. Mod. Phys 50, 607–665 (1978).
[CrossRef]

Rev. Mod. Phys.

U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957).
[CrossRef]

Solid State Commun.

Y. R. Shen, “Surface nonlinear optical spectroscopy,” Solid State Commun. 84, 171–172 (1992).
[CrossRef]

R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102, 207–220 (1997).
[CrossRef]

Other

In the Fresnel perturbation discussion, we depart from the usual notation (uppercase T for the power transmission coefficient and lowercase t for the field transmission coefficient). We denote the field transmission coefficient with an uppercase T=2ni/(nt+ni), where ni is the incident index and nt is the transmitted index, in order to avoid ambiguity with the time variable t.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

When solving for E0,th, we divide out Mth. This modulation term is reintroduced in Eq. (30).

In transforming to the group frame, a new symbol, ζ, is introduced (even though z=ζ) as a reminder that ∂/∂ζ≠∂/∂z. In fact, ∂/∂t=∂/∂tpr, ∂/∂z=−upr−1∂/∂tpr+∂/∂ζ.

G. Herzberg, Molecular Spectra and Molecular Structure(Krieger, 1989).

E. Wilson, J. Decius, and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, 1955).

S. Mukamel, Principles of Nonlinear Optical Spectroscopy(Oxford University, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Time-resolved vibrational spectroscopy detected via THG of the probe pulse.

Fig. 2.
Fig. 2.

Coherence-modulated signals of various orders in a BGO12 crystal. Left column: recorded signal as a function of pump-probe delay. Right column: Fourier transform with respect to τ, normalized to the 90cm1 peak. (a) Linear δχ(1) coherence modulation of phase measured with spectral interferometry [3]; (b) coherence-modulated SHG, a combination of δχ(1) and δχ(2) effects; (c) CM-THG signal [7], a combination of δχ(1) and δχ(3) effects.

Fig. 3.
Fig. 3.

Integral of each contribution with respect to interface placement ξi: gcshrs(ξi), gcasc(ξi), gfrnl(ξi) (shown with unperturbed THG for comparison).

Fig. 4.
Fig. 4.

(a) Measured interface scan amplitude A(ξi) of Raman signal (blue crosses) and model fit (red line); (b) measured phase ϕ(ξi) of Raman signal (blue circles) and model fit (red line); (c) model fit, extrapolated beyond interface scan range: Kcshrsgchsrs (red dash line), Kcascgcasc (green solid line), and Kfrnlgfrnl (blue dash-dot line). Shaded regions on right correspond to focal plane in the bulk, while the region on the left is the focal plane in air. Adapted from [7].

Fig. 5.
Fig. 5.

Simulated THG from a thin piece of sapphire scanned through the focal plane. THG in air accounts for the asymmetry between the peaks.

Fig. 6.
Fig. 6.

Simulated THG interface scan of a thick sapphire sample. Scans are shown for the CW case (no mismatch), and the pulse case with group and phase match taken into account. A CW case with narrowed Rayleigh range is also shown for comparison.

Fig. 7.
Fig. 7.

Simulated CSHRS and cascade interface scan behavior, taking into account GVM effects.

Equations (61)

Equations on this page are rendered with MathJax. Learn more.

Scmthg(τ,zizw)=Kcshrsfcshrs(τ,zizw)+Kcascfcasc(τ,zizw)+Kfrnlffrnl(τ,zizw),
Epu=12E¯pu(x,y,ζ,tpr+τ)ei(ω1tk1z)+c.c.,
E¯pu=E0,puUpu(x,y,ζ)Epu(tpr+τ).
Upu=1A(ζ)exp[x2+y2w12A(ζ)],
A=1i(ζzwzR).
|Upu|21|A(ζ)|2Φ(ζ),
Dpu(Ωv)eiθpu(Ωv)=|Epu(t)|2eiΩvtdt,
Q(ζ,tpr)=Φ(ζ)Q0sin[Ωv(tpr+τ)+ϕ0].
δχ(n)(ζ,tpr)=NFnϵ0Q(ζ,tpr)Φ(ζ)δχ˜(n)(tpr+τ),
δχ˜(n)=δχ0(n)sin[Ωv(tpr+τ)+ϕ0],
Epr=12E¯pr(x,y,ζ,tpr)ei(ω1tk1z)+c.c.
E¯pr=E0,prUpr(x,y,ζ)Epr(tpr)Mpr(ζ,τ).
Upr=1A(ζ)exp[x2+y2w12A(ζ)],
{i2k12+ζ}Upr=0.
{i2k12+ζ}E¯pr=iωpr2cn1(1iωprtpr)δχ(1)E¯pr.
{i2k12+ζ}E¯pr=iδkE¯pr,
δk(τ)=ω12n1cΦ(ζ)δχ0(1)sin(Ωvτ+ϕ0),
δk(τ)=Ωv2n1cΦ(ζ)δχ0(1)cos(Ωvτ+ϕ0).
Mpr(τ,ζ)=exp[iδk˜(Γζ)],
Γ(ζ)ζΦ(ζ)dζ=zRatan(ζzwzR)+π2zR.
uprζ=14cnϵ0[E¯prE¯pr*ζ+E¯pr*E¯prζ]dt.
uprζ=12cnϵ0δk(τ)E¯prE¯pr*dt.
δT1=δnT1ni=δT0,1δχ0(1)Φ(zizw)sin(Ωvτ+ϕ0),
δT0,1=12n1T1n1=1n1(n1+1)2.
Eth=12E¯th(x,y,ζ,tpr)ei(3ω1tk3z)+c.c.
E¯th=E0,th(τ,ζ)Uth(x,y,ζ)Eth(tpr)Mth(τ,ζ),
Uth=1A(ζ)exp[x2+y2w32A(ζ)].
{i2k32+ζ}E¯th=iω38cn3[χ0(3)+δχ(3)]E¯pr3.
E0,thζ=iC1A2(ζ)[χ0,c(3)+δχ˜(3)Φ(ζ)]eiΔδk˜(Γζ),
iE0,thCzR=T0,3δχ˜(3)ξiΦ(ξ)A2(ξ)dξ+[T0,3+δT3˜Φ(ξi)]χ0,c(3)ξieΔδk˜Γ(ξ)A2(ξ)dξ+[T0,13+3T0,12δT1˜Φ(ξi)]χ0,a(3)ξi1A2(ξ)dξ,
E0,th=iCzR[T0,3δχ˜(3)I1(ξi)+T0,3χ0,c(3)Δδk˜I2(ξi)+Δχ˜eff(3)Φ(ξi)I3(ξi)+Δχeff(3)I3(ξi)],
I1=ξiΦ(ξ)A2(ξ)dξ=atan(ξi)4+ξi4(ξi2+1)+ξii2(ξi2+1)2+π8,
I2=ξiΓ(ξ)A2(ξ)dξ=zRξiatanξi+π2ξi+12ξi2+1+izR(12atanξi+π4atanξi12ξi+π2ξi2+1),
I3=ξi1A2(ξ)dξ=ξiξi2+1iξi2+1.
S3=12n3,acϵ0|MthE0,th|2Sthg+Scshrs+Scasc+Sfrnl
Sthg=12CΔχeff(3)|I3|2=12CΔχeff(3)11+ξi2,
Scshrs=CT0,3δχ˜(3){I1I3*}=Kcshrsgcshrs(ξi)sin(Ωvτ),
Kcshrs=CT0,3δχ0(3),
gcshrs(ξi)=2ξiatan(ξi)+πξi+28(ξi2+1)+14(ξi2+1)2.
Scasc=CΔχeff(3)δk˜3{ΓI3I3*}+CT0,3χ0,c(3)Δδk˜{I2I3*}=Kcascgcasc(ξi)cos(Ωvτ).
gcasc(ξi)=1zR{ΓI3I3*}=1zR{I2I3*}=atanξi+π22(ξi2+1).
Kcasc=32CT0,3χ0,c(3)Ωvcn1δχ0(1)zR.
Sfrnl=12CΔχ˜eff(3)Φ(ξi)|I3|2=Kfrnlgfrnl(ξi)sin(Ωvτ),
Kfrnl=12C[χ0,c(3)n3(n3+1)2]δχ0(1)
gfrnl=Φ(ξi)|I3|2=1(ξi2+1)2.
Scmthg(τ,ξi)=[Kcshrsgcshrs(ξi)Kfrnlgfrnl(ξi)]sin(Ωvτ+ϕ0)+Kcascgcasc(ξi)cos(Ωvτ+ϕ0)=A(ξi)sin[Ωvτ+ϕ0+ϕ(ξi)],
ϕ(ξi)=arctan{Kcshrsgcshrs(ξi)Kfrnlgfrnl(ξi)Kcascgcasc(ξi)}.
{i2k32+ζ}E¯th(tth,ζ)=iω38cn3χ(3)E¯pr3(ζ,tth+Δu1ζ)eiΔkζ.
Eth(tth)E0,thζ=iCχ0(3)E0,pr3Epr3(tth+Δu1ζ)A2(ζ)eiΔkζ
E0,th(ζ)Eth(tth)=iCχ0(3)E0,pr3Epr3(tth+Δu1ζ)A2(ζ)eiΔkζdζ
E0,th=iCχ0,c(3)E0,pr3ζiEpr3(tth+Δu1ζ)A2(ζ)eiΔkζdζiCχ0,a(3)E0,pr3ζiEpr3(tth)A2(ζ)dζ,
Scshrs,GVM{[0Lsin[Ω(τ+Δu1z)]Φ(z)A(z)2dz]×[0L1A(z)2dz]*}.
Scasc,GVM{[0Lsin[Ω(τ+Δu1z)]Γ(z)A(z)2dz]×[0L1A(z)2dz]*}.
{i2k12+ζ}E¯pr(x,y,ζ,tpr)=iω12cn1ϵ0(1iω1tpr)δP(x,y,ζ,tpr).
δP(ζ,tpr)=ϵ02E¯prE0,pu2|Upu(ζ)|2×0R(3)(t)|Epu(tpr+τt)|2dt.
R(3)(t)=iN2ϵ0(α)2[Q˜(t),Q˜(0)]ρ0.
[Q˜(t),Q˜(0)]ρ0=i4Ωvsin(Ωvt).
Q(ζ,tpr)=αΩvE0,pu2Φ(ζ)0sin(Ωvt)Epu2(tpr+τt)dt=Q0Φ(ζ)sin[Ωv(tpr+τ)+ϕ0],
[T0,3+δT3˜Φ(ξi)]χ0,c(3)ξi1A2(ξ)dξ+T0,3Δδk˜χ0,c(3)ξiΓ(ξ)A2(ξ)dξ
iE0,thCzR=T0,3δχ˜(3)ξiΦ(ξ)A2(ξ)dξ+T0,3Δδk˜χ0,c(3)ξiΓ(ξ)A2(ξ)dξ+3T0,12δT1˜Φ(ξi)χ0,a(3)ξi1A2(ξ)dξ+δT3˜Φ(ξi)χ0,c(3)ξi1A2(ξ)dξ+T0,13χ0,a(3)ξi1A2(ξ)dξ+T0,3χ0,c(3)ξi1A2(ξ)dξ.
iE0,thCzR=T0,3δχ˜(3)ξiΦ(ξ)A2(ξ)dξ+T0,3Δδk˜χ0,c(3)ξiΓ(ξ)A2(ξ)dξ+Δχ˜eff(3)Φ(ξi)ξi1A2(ξ)dξ+Δχeff(3)ξi1A2(ξ)dξ.

Metrics