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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 7 — Jul. 1, 2002
  • pp: 1604–1610

Green’s function formulation for third-harmonic generation microscopy

Ji-Xin Cheng and X. Sunney Xie  »View Author Affiliations

JOSA B, Vol. 19, Issue 7, pp. 1604-1610 (2002)

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We report a theoretical study of third-harmonic generation (THG) microscopy by use of a Green’s function formulation. The third-harmonic signal under a tight-focusing condition is calculated for samples with various shapes and sizes. Our results show that THG signals can be efficiently generated at a sizable interface perpendicular or parallel to the optical axis or from a small object with a size comparable to the width of the axial excitation intensity profile. The signal-generation mechanism of THG microscopy is explained by a modified phase-matching condition, |k3-3(k1+Δkg)|lπ, where Δkg is the wave vector mismatch induced by the Gouy phase shift of the focused excitation field. The relation of the THG power and radiation pattern to the orientation of an interface is investigated. A comparison between signal generation in THG microscopy and that in coherent anti-Stokes Raman scattering microscopy is given.

© 2002 Optical Society of America

OCIS Codes
(180.5810) Microscopy : Scanning microscopy
(180.6900) Microscopy : Three-dimensional microscopy
(190.4160) Nonlinear optics : Multiharmonic generation
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

Ji-Xin Cheng and X. Sunney Xie, "Green's function formulation for third-harmonic generation microscopy," J. Opt. Soc. Am. B 19, 1604-1610 (2002)

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  1. R. Gauderon, P. B. Lukins, and C. J. R. Sheppard, “Three-dimensional second-harmonic generation imaging with femtosecond laser pulses,” Opt. Lett. 23, 1209–1211 (1998). [CrossRef]
  2. P. J. Campagnola, M.-D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999). [CrossRef] [PubMed]
  3. L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685–1694 (2000). [CrossRef]
  4. 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]
  5. 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]
  6. J. X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341–1343 (2001). [CrossRef]
  7. 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]
  8. M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, “3D microscopy of transparent objects using third-harmonic generation,” J. Microsc. (Oxford) 191, 266–274 (1998). [CrossRef]
  9. J. A. Squier and M. Muller, “Third-harmonic generation imaging of laser-induced breakdown in glass,” Appl. Opt. 38, 5789–5794 (1999). [CrossRef]
  10. J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org. [CrossRef] [PubMed]
  11. D. Yelin and Y. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express 5, 169–175 (1999), http://www.opticsexpress.org. [CrossRef] [PubMed]
  12. L. Canioni, S. Rivet, L. Sarger, R. Barille, P. Vacher, and P. Voisin, “Imaging Ca2+ intracellular dynamics with a third-harmonic generation microscope,” Opt. Lett. 26, 515–517 (2001). [CrossRef]
  13. D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338–379 (1966). [CrossRef]
  14. 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]
  15. G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975). [CrossRef]
  16. R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470–484 (1973). [CrossRef]
  17. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  18. A. E. Siegman, Lasers (University Science, Mill Valley, Calif. 1986).
  19. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
  20. The effect of distortion is quite small when the laser beam is focused on small features. The discontinuity of χ(1) (refractive index) at a sizable interface provides an additional mechanism for THG signal generation.
  21. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959). [CrossRef]
  22. L. Novotny, Lecture Notes on Nano-Optics (University of Rochester, Rochester, N.Y., 2000).
  23. For a fundamental Gaussian beam, max[Ey2]/max[Ex2]= 0.003 and max[Ez2]/max[Ex2]=0.12 under the tight-focusing (NA=1.4) condition. As THG is a third-order nonlinear process, the contributions from the y and z components are negligible. For the same reason, the azimuth-dependent part of the x-polarized component can be neglected.
  24. W. C. Chew, Waves and Fields in Inhomogeneous Media, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1995).
  25. L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997). [CrossRef]
  26. The effect of index dispersion on the phase mismatch can be neglected because of the small excitation volume under the tight-focusing condition. For example, the refractive index of water is 1.339 at 0.4 μm and 1.324 at 1.2 μm. The corresponding coherence length, π/|k3−3k1|, is calculated to be 13.3 μm, which is much larger than the axial length of the focal volume under the tight-focusing condition.
  27. J. X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity,” J. Phys. Chem. B 105, 1277–1280 (2001). [CrossRef]

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