OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry Van Driel
  • Vol. 26, Iss. 7 — Jul. 1, 2009
  • pp: 1295–1309

Coherent anti-Stokes Raman scattering in a Fabry–Perot cavity: A theoretical study

Franck Billard, David Gachet, and Hervé Rigneault  »View Author Affiliations

JOSA B, Vol. 26, Issue 7, pp. 1295-1309 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (806 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a study of coherent anti-Stokes Raman scattering (CARS) under focused beam excitation in a planar Fabry–Perot cavity using an image-dipole formalism. We give a comprehensive description of forward- and backward-CARS signal generation by introducing the expressions of the nonlinear induced polarization in the cavity as a function of their counterpart in free space. We show that the cavity gives rise to a backward-CARS signal and allows working with low numerical aperture collection objectives. We finally discuss the influence of the scatterer position in the cavity on the detected signal.

© 2009 Optical Society of America

OCIS Codes
(300.6230) Spectroscopy : Spectroscopy, coherent anti-Stokes Raman scattering
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:

Original Manuscript: September 30, 2008
Revised Manuscript: April 20, 2009
Manuscript Accepted: April 22, 2009
Published: June 8, 2009

Franck Billard, David Gachet, and Hervé Rigneault, "Coherent anti-Stokes Raman scattering in a Fabry-Perot cavity: A theoretical study," J. Opt. Soc. Am. B 26, 1295-1309 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. Schrader, Infrared and Raman Spectroscopy (VCH, 1995). [CrossRef]
  2. J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in gallium phosphide,” Phys. Rev. Lett. 22, 60-64 (1969). [CrossRef]
  3. J. J. Wynne, “Nonlinear optical spectroscopy of χ(3) in LiNbO3,” Phys. Rev. Lett. 29, 650-653 (1972). [CrossRef]
  4. P. R. Regnier and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973). [CrossRef]
  5. R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974). [CrossRef]
  6. M. D. Duncan, J. Reintjes, and T. J. Manuccia, “Scanning coherent anti-Stokes Raman scattering microscope,” Opt. Lett. 7, 350-352 (1982). [CrossRef] [PubMed]
  7. A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 82, 4142-4145 (1999). [CrossRef]
  8. J. Cooney and A. Gross, “Coherent anti-Stokes Raman scattering by droplets in the Mie size range,” Opt. Lett. 7, 218-220 (1982). [CrossRef] [PubMed]
  9. S.-X. Qian, J. B. Snow, and R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets,” Opt. Lett. 10, 499-501 (1985). [CrossRef] [PubMed]
  10. H. Chew, D.-S. Wang, and M. Kerker, “Surface enhancement of coherent anti-Stokes Raman scattering by colloidal spheres,” J. Opt. Soc. Am. B 1, 56-66 (1984). [CrossRef]
  11. T.-W. Koo, S. Chan, and A. A. Berlin, “Single-molecule detection of biomolecules by surface-enhanced coherent anti-Stokes Raman scattering,” Opt. Lett. 30, 1024-1026 (2005). [CrossRef] [PubMed]
  12. C. Fabry, “Sur la localisation des franges d'interférences produites par les miroirs de Fresnel,” Acad. Sci., Paris, C. R. 110, 455-457 (1890).
  13. E. M. Purcell, “Spontaneous emission probabilities at radiofrequencies,” Phys. Rev. 69, 681 (1946). [CrossRef]
  14. P. Goy, J. M. Raimond, M. Gross, and S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903-1906 (1983). [CrossRef]
  15. F. de Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955-2958 (1987). [CrossRef] [PubMed]
  16. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233-236 (1981). [CrossRef]
  17. R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibitedspontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137-2140 (1985). [CrossRef] [PubMed]
  18. G. Gabrielse and H. Dehmelt, “Observation of inhibited spontaneous emission,” Phys. Rev. Lett. 55, 67-70 (1985). [CrossRef] [PubMed]
  19. D. J. Heinzen, J. J. Childs, J. E. Thomas, and M. S. Feld, “Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320-1323 (1987). [CrossRef] [PubMed]
  20. D. Meschede, H. Walther, and G. Müller, “One-atom maser,” Phys. Rev. Lett. 54, 551-554 (1985). [CrossRef] [PubMed]
  21. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314-3317 (1992). [CrossRef] [PubMed]
  22. F. Cairo, F. de Martini, and D. Murra, “QED-vacuum confinement of inelastic quantum scattering at optical frequencies: a new perspective in Raman spectroscopy,” Phys. Rev. Lett. 70, 1413-1416 (1993). [CrossRef] [PubMed]
  23. A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Raman scattering enhancement by optical confinement in a semiconductor planar microcavity,” Phys. Rev. Lett. 75, 3764-3767 (1995). [CrossRef] [PubMed]
  24. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002). [CrossRef] [PubMed]
  25. I. V. Soboleva, E. M. Murchikova, A. A. Fedyanin, and O. A. Aktsipetrov, “Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon,” Appl. Phys. Lett. 87, 241110 (2005). [CrossRef]
  26. H. Yang, P. Xie, S. K. Chan, W. Lu, Z.-Q. Zhang, I. K. Sou, G. K. L. Wong, and K. S. Wong, “Simultaneous enhancement of the second- and third-harmonic generations in one-dimensional semiconductor photonic crystals,” IEEE J. Quantum Electron. 42, 447-452 (2006). [CrossRef]
  27. C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett. 89, 131122 (2006). [CrossRef]
  28. H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction--Part I: basic concepts and analytical trend,” IEEE J. Quantum Electron. 34, 1612-1631 (1998). [CrossRef]
  29. H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction--Part II: selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632-1643 (1998). [CrossRef]
  30. H. Rigneault and S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356-2368 (1996). [CrossRef] [PubMed]
  31. H. Benisty, R. Stanley, and M. Mayer, “Method of source terms for dipole emission modification in modes of arbitrary planar structures,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 15, 1192-1201 (1998). [CrossRef]
  32. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques,” J. Opt. Soc. Am. B 6, 910-916 (1989). [CrossRef]
  33. L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Comptes Rendus Acad. Sci. (Paris) 110, 1251-1253 (1890).
  34. L. G. Gouy, “Sur la propagation anormale des ondes,” Acad. Sci., Paris, C. R. 111, 33-35 (1890).
  35. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  36. H. Morawitz, “Self-coupling of a two-level system by a mirror,” Phys. Rev. 187, 1792-1796 (1969). [CrossRef]
  37. P. W. Milonni and P. L. Knight, “Spontaneous emission between mirrors,” Opt. Commun. 9, 119-122 (1973). [CrossRef]
  38. J. P. Dowling, M. O. Scully, and F. de Martini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415-419 (1991). [CrossRef]
  39. D. Gachet, N. Sandeau, and H. Rigneault, “Influence of the Raman depolarisation ratio on far-field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Eur. Opt. Soc. Rapid Publ. 1, 06013 (2006). [CrossRef]
  40. M. Marrocco, “Coherent anti-Stokes Raman scattering microscopy in the presence of electromagnetic confinement,” Laser Phys. 17, 935-941 (2007). [CrossRef]
  41. D. Gachet, F. Billard, and H. Rigneault, “Coherent anti-Stokes Raman scattering in a microcavity,” Opt. Lett. 34, 1789-1791 (2009). [CrossRef] [PubMed]
  42. H. Lotem, R. T. Lynch, Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976). [CrossRef]
  43. D. Gachet, F. Billard, and H. Rigneault, “Background-free coherent anti-Stokes Raman spectroscopy near transverse interfaces: a vectorial study,” J. Opt. Soc. Am. B 25, 1655-1666 (2008). [CrossRef]
  44. L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685-1694 (2000). [CrossRef]
  45. J.-X. Cheng and X. S. Xie, “Green's function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1604-1610 (2002). [CrossRef]
  46. J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002). [CrossRef]
  47. A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001). [CrossRef]
  48. M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibility tensor in centrosymmetric media,” Phys. Rev. B 10, 4447-4463 (1974). [CrossRef]
  49. A. Volkmer, “Vibrational imaging and microspectrometries based on coherent anti-Stokes Raman scattering microscopy,” J. Phys. D 38, R59-R81 (2005). [CrossRef]
  50. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959). [CrossRef]
  51. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).
  52. The mirrors considered here made of a succession of high (H) and low (L) refractive index hafnium oxide HfO2(n=2.207) and silica SiO2(n=1.456) layers deposed on a silica substrate. The thicknesses (in nanometers) of the different layers are given by (H) 107; (L) 272; (H) 88; (L) 109; (H) 206; (L) 119; (H) 64; (L) 298; (H) 314; (L) 36; (H) 374; (L) 201; (H) 127; (L) 212; (H) 111; (L) 209; (H) 128; (L) 95.
  53. The orientation of the nonlinear induced dipoles is fixed by the excitation beams and the Raman depolarization ratio following Eq. .
  54. A. Kastler, “Atomes à l'intérieur d'un interféromètre Perot-Fabry,” Appl. Opt. 1, 17-24 (1962). [CrossRef]
  55. This is in good agreement with our medium reflectivity mirrors that alter marginally the emitter lifetime inside the cavity.
  56. G. Björk and Y. Yamamoto, “Spontaneous emission in dielectric planar microcavities,” in Spontaneous Emission and Laser. Oscillation in Microcavities, H.Yokoyama and K.Ujihara, eds. (Academic, 1995).
  57. D. Gachet, N. Sandeau, and H. Rigneault, “Far-field radiation pattern in coherent anti-Stokes Raman scattering (CARS) microscopy,” in Biomedical Vibrational Spectroscopy III: Advances in Research and Industry, A.Mahadevan-Jansen and W.H.Peetrich, eds., Proc. SPIE 6093, 609309 (2006). [CrossRef]
  58. Computing two-dimensional patterns such as the ones plotted in Fig. takes about 30 days with a PC working with a 2.5 GHz processor.
  59. Note that, as pointed out previously, because the ring structure does not rigorously follow a revolution symmetry (see Fig. ), the undergone jumps are smoother than in Fig. .
  60. M. Marrocco and E. Nichelatti, “Coherent anti-Stokes Raman scattering microscopy within a microcavity with parallel mirrors,” J. Raman Spectrosc. (to be published).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited