Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Spatial Phase Coherence in Femtosecond Coherent Raman Scattering

Ali Hosseinnia1,2,*, Michele Marrocco3,†, Francesco Vergari3,4, Meena Raveesh5, Sebastian Riewer1, Ashutosh Jena1, Abhishek Kushwaha1, Francesco Mazza1, Mark Linne6 et al.

Joakim Bood5 and Isaac Boxx1

  • *Contact author: ali.hosseinnia@list.lu
  • Contact author: michele.marrocco@enea.it

Phys. Rev. Lett. 136, 163801 – Published 22 April, 2026

DOI: https://doi.org/10.1103/r98z-7bwj

Abstract

Conventional femtosecond coherent laser spectroscopy predominantly focuses on the temporal phase coherence through time- or frequency-resolved methods. In this Letter, we suggest an alternative experimental framework based on spatial phase coherence. The intrinsic spectral dispersion of wave vectors in femtosecond pulses and sample dimensions exceeding the laser wavelength creates a compelling basis to establish spatial phase coherence as a novel approach to femtosecond laser spectroscopy. Using rotational Raman coherence in air as a case study, we analyze the transverse spatial distribution of the third-order signal generated by the rotational wave packet. Our findings reveal apparent temporal shifts and distortions in time-resolved signals that arise in conventional measurements lacking sensitivity to spatial phase coherence. Moreover, we demonstrate that spatial phase coherence can serve as a useful tool for thermometric applications, showcasing its sensitivity to temperature variations. These discoveries open new avenues in femtosecond laser spectroscopy, including an alternative single-shot detection scheme, a new form of Raman coherence imaging, and molecular species quantification during overlapping fractional revivals.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. V. L. Ginzburg and L. D. Landau, On the theory of superconductivity, Zh. Eksp. Teor. Fiz. 20, 1064 (1950); Reprinted in Collected Papers of L. D. Landau (Pergamon Press, Oxford, 1965), 10.1016/C2013-0-01806-3.
  2. A. L. Schawlow and C. H. Townes, Infrared and optical masers, Phys. Rev. 112, 1940 (1958).
  3. T. H. Maiman, Stimulated optical radiation in ruby, Nature (London) 187, 493 (1960).
  4. R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130, 2529 (1963).
  5. A. T. Winfree, Biological rhythms and the behavior of populations of coupled oscillators, J. Theor. Biol. 16, 15 (1967).
  6. M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57, 1761 (1986).
  7. A. Abramovici et al., LIGO: The laser interferometer gravitational-wave observatory, Science 256, 325 (1992).
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).
  9. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
  10. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, Amsterdam, 1996).
  11. J. D. Schultz et al., Coherence in chemistry: Foundations and frontiers, Chem. Rev. 124, 11641 (2024).
  12. J. D. Monnier, Optical interferometry in astronomy, Rep. Prog. Phys. 66, 789 (2003).
  13. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999).
  14. A. Zumbusch, G. R. Holtom, and X. S. Xie, Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering, Phys. Rev. Lett. 82, 4142 (1999).
  15. D. Pestov et al., Optimizing the laser-pulse configuration for coherent Raman spectroscopy, Science 316, 265 (2007).
  16. S. Roy, J. R. Gord, and A. Patnaik, Recent advances in coherent anti-Stokes Raman scattering spectroscopy: Fundamental developments and applications in reacting flows, Prog. Energy Combust. Sci. 36, 280 (2010).
  17. H. U. Stauffer, J. D. Miller, M. N. Slipchenko, T. R. Meyer, B. D. Prince, S. Roy, and J. R. Gord, Time- and frequency-dependent model of time-resolved coherent anti-Stokes Raman scattering (CARS) with a picosecond-duration probe pulse, J. Chem. Phys. 140, 024316 (2014).
  18. C. H. Camp Jr and M. T. Cicerone, Chemically sensitive bioimaging with coherent Raman scattering, Nat. Photonics 9, 295 (2015).
  19. D. R. Dietze and R. A. Mathies, Femtosecond stimulates Raman spectroscopy, Chem. Phys. Chem. 17, 1224 (2016).
  20. R. Righini, Ultrafast optical Kerr effect in liquids and solids, Science 262, 1386 (1993).
  21. H. Stapelfeldt and T. Seideman, Aligning molecules with strong laser pulses, Rev. Mod. Phys. 75, 543 (2003).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/r98z-7bwj for detailed description of the simulation, as well as effects of slits on signal sampling, and possible applications for thermometry, which includes Refs. [23–32].
  23. R. Bluhm, V. A. Kostelecký, and J. A. Porter, The evolution and revival structure of localized quantum wave packets, Am. J. Phys. 64, 944 (1996).
  24. J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Determination of the time dependence of n2 in air, Opt. Commun. 135, 310 (1997).
  25. I. Sh. Averbukh and N. F. Perelman, Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics, Phys. Lett. A 139, 449 (1989).
  26. M. Raveesh, A. Dominguez, M. Linne, J. Bood, and A. Hosseinnia, Interferometric quantum control (IQC) by fs/ns rotational coherent anti-Stokes Raman spectroscopy (RCARS), Opt. Express 31, 38064 (2023).
  27. L. Martnisson, P.-E. Bengtsson, M. Aldén, and S. Kröll, A test of different rotational Raman linewidth models: Accuracy of rotational coherent anti-Stokes Raman scattering thermometry in nitrogen from 295 to 1850 K, J. Chem. Phys. 99, 2466 (1993).
  28. A. Bohlin, P.-E. Bengtsson, and M. Marrocco, On the sensitivity of rotational CARS N2 thermometry to the Herman-Wallis factor, J. Raman Spectrosc. 42, 1843 (2011).
  29. A. Bohlin, E. Nordström, P.-E. Bengtsson, and M. Marrocco, On the sensitivity of rotational CARS O2 thermometry to the Herman-Wallis factor, J. Raman Spectrosc. 43, 599 (2012).
  30. L. Martnisson, P.-E. Bengtsson, and M. Aldén, Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent anti-Stokes Raman spectroscopy, Appl. Phys. B 62, 29 (1996).
  31. M. Marrocco, Time-domain coherent anti-Stokes Raman scattering in terms of the time-delayed Yuratich equation, Opt. Lett. 39, 4831 (2014).
  32. T. Vieillard, F. Chaussard, F. Billard, D. Sugny, O. Faucher, S. Ivanov, J. M. Hartmann, C. Boulet, and B. Lavorel, Field-free molecular alignment for probing collisional relaxation dynamics, Phys. Rev. A 87, 023409 (2013).
  33. M. Schmitt, G. Knopp, A. Materny, and W. Kiefer, The application of femtosecond time-resolved coherent anti-Stokes Raman scattering for the investigation of ground and excited state molecular dynamics of molecules in the gas phase, J. Phys. Chem. A 102, 4059 (1998).
  34. H.-M. Frey, P. Beaud, T. Gerber, B. Mischler, P. P. Radi, and A. P. Tzannis, Femtosecond nonresonant degenerate four-wave mixing at atmospheric pressure and in a free jet, Appl. Phys. B 68, 735 (1999).
  35. T. Lang, K.-L. Kompa, and M. Motzkus, Femtosecond CARS on H2, Chem. Phys. Lett. 310, 65 (1999).
  36. P. Beaud, H.-M. Frey, T. Lang, and M. Motzkus, Flame thermometry by femtosecond CARS, Chem. Phys. Lett. 344, 407 (2001).
  37. V. Renard, M. Renard, S. Guerin, Y. T. Pashayan, B. Lavorel, O. Faucher, and H. R. Jauslin, Postpulse molecular alignment measured by a weak field polarization technique, Phys. Rev. Lett. 90, 153601 (2003).
  38. F. Chaussard, B. Lavorel, E. Hertz, and O. Faucher, Optical diagnostics with ultrafast and strong field Raman techniques, in Ultrafast Phenomena in Molecular Sciences, edited by R. de Nalda and L. Bañares (Springer, Heidelberg, 2014), Chap. 11.
  39. S. P. Kearney, Hybrid   fs/ps rotational CARS temperature and oxygen measurements in the product gases of canonical flat flames, Combust. Flame 162, 1748 (2015).
  40. R. W. Robinett, Quantum wave packet revivals, Phys. Rep. 392, 1 (2004).
  41. J. Yang et al., Diffractive imaging of a rotational wavepacket in nitrogen molecules with femtosecond megaelectronvolt electron pulses, Nat. Commun. 7, 11232 (2016).
  42. F. Vergari, F. Mazza, M. Marrocco, and A. Hosseinnia, Geometrical control of spatio–temporal coherence in femtosecond rotational coherent Raman scattering, Opt. Lett. 51, 604 (2026).
  43. D. R. Richardson, R. P. Lucht, W. D. Kulatilaka, S. Roy, and J. R. Gord, Theoretical modeling of single-laser-shot, chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering thermometry, Appl. Phys. B 104, 699 (2011).
  44. B. Lavorel, O. Faucher, M. Morgen, and R. Chaux, Analysis of femtosecond Raman-induced polarization spectroscopy (RIPS) in N2 and CO2 by fitting and scaling laws, J. Raman Spectrosc. 31, 77 (2000).
  45. A. Hosseinnia, M. Raveesh, A. Dominguez, M. Ruchkina, M. Linne, and J. Bood, Single-shot coherent control of molecular rotation by fs/ns rotational coherent anti-Stokes Raman spectroscopy, Opt. Express 30, 32204 (2022).
  46. G. Batignani, E. Mai, M. Martinati, M. M. Neethish, S. Mukamel, and T. Scopigno, Temperature dependence of coherent versus spontaneous Raman scattering, Phys. Rev. Lett. 133, 206902 (2024).
  47. M. Raveesh, A. Hosseinnia, A. Padhiary, X. Wei, V. Kornienko, E. Kristensson, A. Ehn, B. Peterson, M. Linne, and J. Bood, Exploring time-domain femtosecond rotational coherent Raman scattering for diagnostics, J. Raman Spectrosc. 56, 666 (2025).
  48. C. C. Hayden and D. W. Chandler, Femtosecond time-resolved studies of coherent vibrational Raman scattering in large gas-phase molecules, J. Chem. Phys. 103, 10465 (1995).
  49. L. Dhar, J. A. Rogers, and K. A. Nelson, Time-resolved vibrational spectroscopy in the impulsive limit, Chem. Rev. 94, 157 (1994).
  50. A. Volkmer, L. D. Book, and X. S. Xie, Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay, Appl. Phys. Lett. 80, 1505 (2002).
  51. D. Oron, N. Dudovich, and Y. Silberberg, Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy, Phys. Rev. Lett. 90, 213902 (2003).
  52. S. Yampolsky, D. A. Fishman, S. Dey, E. Hulkko, M. Banik, E. O. Potma, and V. A. Apkarian, Seeing a single molecule vibrate through time-resolved coherent anti-Stokes Raman scattering, Nat. Photonics 8, 650 (2014).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation