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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 3 — Apr. 4, 2013

Numerical second- and third-harmonic generation microscopy

Daaf Sandkuijl, Adam E. Tuer, Danielle Tokarz, J. E. Sipe, and Virginijus Barzda  »View Author Affiliations


JOSA B, Vol. 30, Issue 2, pp. 382-395 (2013)
http://dx.doi.org/10.1364/JOSAB.30.000382


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Abstract

A full numerical description of second- and third-harmonic generation (SHG and THG) at the focus of a nonlinear microscope is presented. The numerical implementation takes into account reflections and refraction by an arbitrary number of interfaces perpendicular to the optical axis in the focal region. The calculation of the second- and third-harmonic far-field radiation pattern is based on a Green function approach and is presented for any collection direction. The calculations are sped up by using the chirp-z transform for the focusing fields as well as for the far-field radiation calculation. Numerical evidence is presented for deviations in the measurement of the second-order nonlinear susceptibility ratio ρχyyy(2)/χyxx(2) of collagen fibers in SHG microscopy at high excitation numerical aperture. When interface reflections are taken into account, significant direct backward THG is demonstrated from interfaces and multilayer structures.

© 2013 Optical Society of America

OCIS Codes
(180.6900) Microscopy : Three-dimensional microscopy
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4160) Nonlinear optics : Multiharmonic generation
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Microscopy

History
Original Manuscript: September 27, 2012
Revised Manuscript: December 13, 2012
Manuscript Accepted: December 14, 2012
Published: January 22, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Daaf Sandkuijl, Adam E. Tuer, Danielle Tokarz, J. E. Sipe, and Virginijus Barzda, "Numerical second- and third-harmonic generation microscopy," J. Opt. Soc. Am. B 30, 382-395 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josab-30-2-382


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References

  1. S. W. Chu, S. Y. Chen, G. W. Chern, T. H. Tsai, Y. C. Chen, B. L. Lin, and C. K. Sun, “Studies of x(2)/x(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J. 86, 3914–3922 (2004). [CrossRef]
  2. I. Freund, M. Deutsch, and A. Sprecher, “Connective tissue polarity. Optical second-harmonic microscopy, crossed-beam summation, and small-angle scattering in rat-tail tendon,” Biophys. J. 50, 693–712 (1986). [CrossRef]
  3. P. Stoller, P. M. Celliers, K. M. Reiser, and A. M. Rubenchik, “Quantitative second-harmonic generation microscopy in collagen,” Appl. Opt. 42, 5209–5219 (2003). [CrossRef]
  4. R. Cisek, N. Prent, C. Greenhalgh, D. Sandkuijl, A. Tuer, A. Major, and V. Barzda, “Multicontrast nonlinear imaging microscopy,” in Biochemical Applications of Nonlinear Optical Spectroscopy, V. V. Yakovlev, ed. (CRC, 2009).
  5. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J. 82, 493–508 (2002). [CrossRef]
  6. A. E. Tuer, S. Krouglov, N. Prent, R. Cisek, D. Sandkuijl, K. Yasufuku, B. C. Wilson, and V. Barzda, “Nonlinear optical properties of type I collagen fibers studied by polarization dependent second harmonic generation microscopy,” J. Phys. Chem. B 115, 12759–12769 (2011). [CrossRef]
  7. W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. USA 100, 7075–7080 (2003). [CrossRef]
  8. 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]
  9. M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, “3D microscopy of transparent objects using third-harmonic generation,” J. Microsc. 191, 266–274 (1998). [CrossRef]
  10. Y. R. Shen, “Surface-properties probed by second-harmonic and sum-frequency generation,” Nature 337, 519–525 (1989). [CrossRef]
  11. L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17, 1685–1694 (2000). [CrossRef]
  12. 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]
  13. R. M. Williams, W. R. Zipfel, and W. W. Webb, “Interpreting second-harmonic generation images of collagen I fibrils,” Biophys. J. 88, 1377–1386 (2005). [CrossRef]
  14. 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]
  15. D. Debarre, N. Olivier, and E. Beaurepaire, “Signal epidetection in third-harmonic generation microscopy of turbid media,” Opt. Express 15, 8913–8924 (2007). [CrossRef]
  16. H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20, 6042–6051 (2012). [CrossRef]
  17. V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: a numerical investigation,” J. Opt. Soc. Am. A 24, 1138–1147 (2007). [CrossRef]
  18. L. R. Rabiner, R. W. Schafer, and C. M. Rader, “Chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17, 86–92(1969). [CrossRef]
  19. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291 (2006). [CrossRef]
  20. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  21. X. Y. Deng, E. D. Williams, E. W. Thompson, X. Gan, and M. Gu, “Second-harmonic generation from biological tissues: effect of excitation wavelength,” Scanning 24, 175–178 (2002). [CrossRef]
  22. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  23. J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
  24. J. J. Saarinen and J. E. Sipe, “A Green function approach to surface optics in anisotropic media,” J. Mod. Opt. 55, 13–32 (2008). [CrossRef]
  25. University of Toronto, “Welcome to T-Space,” https://tspace.library.utoronto.ca .
  26. J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998). [CrossRef]
  27. V. Barzda, “Visualization of mitochondria in cardiomyocytes by simultaneous harmonic generation and fluorescence microscopy,” Opt. Express 13, 8263–8276 (2005). [CrossRef]
  28. This ratio is often defined in literature for a cylindrically symmetric structure oriented along the z axis [27], taking the y axis as the optical axis. In this article, however, the z axis is the optical axis, and the cylindrical structures will be oriented in the xy plane (as is common in numerical modeling of the focal volume). Therefore, we opt to define the ratio with respect to the fibril coordinate frame: ρ≡χyyy(2)/χyxx(2), where y refers to the axis along the cylindrical structure.
  29. B. Dick, “Irreducible tensor analysis of sum-frequency and difference-frequency-generation in partially oriented samples,” Chem. Phys. 96, 199–215 (1985). [CrossRef]
  30. F. Tiaho, G. Recher, and D. Rouede, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15, 12286–12295 (2007). [CrossRef]
  31. A. E. Tuer, M. K. Akens, S. Krouglov, D. Sandkuijl, B. C. Wilson, C. M. Whyne, and V. Barzda, “Hierarchical model of fibrillar collagen organization for interpreting the second-order susceptibility tensors in biological tissue,” Biophys. J. 103, 2093–2105 (2012). [CrossRef]
  32. C. F. Chang, H. C. Chen, M. J. Chen, W. R. Liu, W. F. Hsieh, C. H. Hsu, C. Y. Chen, F. H. Chang, C. H. Yu, and C. K. Sun, “Direct backward third-harmonic generation in nanostructures,” Opt. Express 18, 7397–7406 (2010). [CrossRef]
  33. S. Y. Chen, H. C. Yu, I. J. Wang, and C. K. Sun, “Infrared-based third and second harmonic generation imaging of cornea,” J. Biomed. Opt. 14, 044012 (2009). [CrossRef]
  34. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, 1984).
  35. M. J. Farrar, F. W. Wise, J. R. Fetcho, and C. B. Schaffer, “In vivo imaging of myelin in the vertebrate central nervous system using third harmonic generation microscopy,” Biophys. J. 100, 1362–1371 (2011). [CrossRef]
  36. C. A. Greenhalgh, “Nonlinear multicontrast microscopy for structural and dynamic investigations of myocytes,” in Physics (University of Toronto, 2009).
  37. G. S. Gotterer, T. E. Thompson, and A. L. Lehninger, “Angular light-scattering studies on isolated mitochondria,” J. Biophys. Biochem. Cytol. 10, 15–21 (1961). [CrossRef]
  38. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1997).

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