Abstract

For second harmonic generation (SHG) imaging, the specimen is often observed through an immersion medium and a cover glass whose refractive indices are usually different from that of the specimen. However, the currently used theoretical models are based on the assumption that the specimen is situated in a homogeneous medium. The limitation of these models is that they ignore the effects of the refractive index mismatches and the imaging depth. In this paper, we have demonstrated, for the first time to our knowledge, a rigorous model of SHG imaging through stratified media focused by radially polarized beams. Based on the proposed model, the detected SHG intensity patterns excited in a refractive index perfectly matched, aberration-free medium and in mismatched stratified media are compared. The effects of the imaging depth and effective numerical aperture (NA) on the performance of SHG imaging with oil immersion objectives are investigated by the stratified media model. It is found that the full width at half maximum (FWHM) in the axial direction at imaging depth of 80 µm is ~3.1 times as large as that of 10 µm imaging depth. While for the transverse FWHM, the increment is only about 23%. The quality of the SHG intensity distribution can be increased by reducing the NA appropriately at the expense of the detected signal strength. The proposed model is helpful to provide guidelines for the adaptive aberration correction in SHG imaging and can be used to optimize the experimental configuration.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (1)

2015 (5)

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

M. Li, S. Yan, B. Yao, M. Lei, Y. Yang, J. Min, and D. Dan, “Trapping of rayleigh spheroidal particles by highly focused radially polarized beams,” J. Opt. Soc. Am. B 32(3), 468–472 (2015).
[Crossref]

J. M. Bueno, R. Palacios, A. Pennos, and P. Artal, “Second-harmonic generation microscopy of photocurable polymer intrastromal implants in ex-vivo corneas,” Biomed. Opt. Express 6(6), 2211–2219 (2015).
[Crossref] [PubMed]

C. Teulon, I. Gusachenko, G. Latour, and M. C. Schanne-Klein, “Theoretical, numerical and experimental study of geometrical parameters that affect anisotropy measurements in polarization-resolved SHG microscopy,” Opt. Express 23(7), 9313–9328 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (2)

2012 (3)

2011 (1)

2010 (4)

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

Y. Zhang, T. Suyama, and B. Ding, “Longer axial trap distance and larger radial trap stiffness using a double-ring radially polarized beam,” Opt. Lett. 35(8), 1281–1283 (2010).
[Crossref] [PubMed]

A. Ohtsu, “Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations,” Opt. Commun. 283(20), 3831–3837 (2010).
[Crossref]

A. Ohtsu, Y. Kozawa, and S. Sato, “Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams,” Appl. Phys. B 98(4), 851–855 (2010).
[Crossref]

2008 (2)

2007 (3)

2006 (2)

E. Y. S. Yew and C. J. R. Sheppard, “Vectorial approach to studying second harmonic generation in collagen using linearly and radially polarized beams,” Proc. SPIE 6163, 61630L (2006).
[Crossref]

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

2004 (2)

2003 (3)

2000 (2)

1998 (3)

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148(4-6), 300–315 (1998).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

R. Gauderon, P. B. Lukins, and C. J. R. Sheppard, “Three-dimensional second-harmonic generation imaging with femtosecond laser pulses,” Opt. Lett. 23(15), 1209–1211 (1998).
[Crossref] [PubMed]

1997 (2)

1994 (1)

1986 (1)

1962 (1)

D. A. Kleinmann, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126(6), 1977–1979 (1962).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Ai, M.

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

Alfano, R. R.

Alkilani, A.

Amat-Roldan, I.

Ammar, M.

Araki, T.

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Artal, P.

Artigas, D.

Ashida, K.

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Bautista, G.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Beaurepaire, E.

Bertrand-Grenier, A.

Biss, D. P.

Boryskina, O. P.

Boulesteix, T.

Brown, T.

Brown, T. G.

Bueno, J. M.

Campagnola, P. J.

G. Hall, K. B. Tilbury, K. R. Campbell, K. W. Eliceiri, and P. J. Campagnola, “Experimental and simulation study of the wavelength dependent second harmonic generation of collagen in scattering tissues,” Opt. Lett. 39(7), 1897–1900 (2014).
[Crossref] [PubMed]

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

Campbell, K. R.

Chang, S.

Chen, S. Y.

Chen, Y.

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Couture, C. A.

Dan, D.

Deutsch, M.

Dhaka, V.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Ding, B.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Eliceiri, K. W.

Fleury, V.

Freund, I.

Furukawa, H.

Gauderon, R.

Grasso, M.

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Guilbert, T.

Guo, Y.

Gusachenko, I.

Haeberlé, O.

Hall, D. G.

Hall, G.

Harris, D.

Hashimoto, M.

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148(4-6), 300–315 (1998).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

Ho, P. P.

Huhtio, T.

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Huttunen, M. J.

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Jiang, H.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Jordan, R. H.

Kakko, J. P.

Karvonen, L.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Kauppinen, E.

Kauranen, M.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Kleinmann, D. A.

D. A. Kleinmann, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126(6), 1977–1979 (1962).
[Crossref]

Kontio, J. M.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Kowalczuk, L.

Kozawa, Y.

A. Ohtsu, Y. Kozawa, and S. Sato, “Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams,” Appl. Phys. B 98(4), 851–855 (2010).
[Crossref]

Laliberté, M.

Lamarre, I.

Latour, G.

Le Grand, Y.

Légaré, F.

Lei, M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, M.

Lipsanen, H.

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
[Crossref] [PubMed]

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

Liu, F.

Liu, J.

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

Lou, P. J.

Loza-Alvarez, P.

Lukins, P. B.

Mäkitalo, J.

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Meixner, A. J.

Millard, A. C.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

Min, J.

Miri, A. K.

Mohler, W. A.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

Mongeau, L.

Niioka, H.

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Odin, C.

Ohtsu, A.

A. Ohtsu, “Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations,” Opt. Commun. 283(20), 3831–3837 (2010).
[Crossref]

A. Ohtsu, Y. Kozawa, and S. Sato, “Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams,” Appl. Phys. B 98(4), 851–855 (2010).
[Crossref]

Olsen, B. R.

Palacios, R.

Pan, A.

Pennos, A.

Pfeffer, C. P.

Plotnikov, S. V.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

Psilodimitrakopoulos, S.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Recher, G.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Rivard, M.

Rouède, D.

Sacks, P.

Salamin, Y. I.

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

Sato, S.

A. Ohtsu, Y. Kozawa, and S. Sato, “Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams,” Appl. Phys. B 98(4), 851–855 (2010).
[Crossref]

Sauviat, M. P.

Savage, H.

Schanne-Klein, M. C.

Schantz, S.

Shen, S.

Sheppard, C. J. R.

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[Crossref]

E. Y. S. Yew and C. J. R. Sheppard, “Vectorial approach to studying second harmonic generation in collagen using linearly and radially polarized beams,” Proc. SPIE 6163, 61630L (2006).
[Crossref]

R. Gauderon, P. B. Lukins, and C. J. R. Sheppard, “Three-dimensional second-harmonic generation imaging with femtosecond laser pulses,” Opt. Lett. 23(15), 1209–1211 (1998).
[Crossref] [PubMed]

Shieh, D. B.

Simonen, J.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Sun, C. K.

Sun, J.

Suyama, T.

Tan, J.

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

Tan, X.

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

Tenjimbayashi, K.

Teulon, C.

Tiaho, F.

Tilbury, K. B.

Török, P.

Tsai, M. R.

Varga, P.

Wackenhut, F.

Wang, R.

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

Wang, X.

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P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148(4-6), 300–315 (1998).
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B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Yan, S.

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Yao, B.

Yew, E. Y. S.

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[Crossref]

E. Y. S. Yew and C. J. R. Sheppard, “Vectorial approach to studying second harmonic generation in collagen using linearly and radially polarized beams,” Proc. SPIE 6163, 61630L (2006).
[Crossref]

Yoshiki, K.

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Youngworth, K.

Zang, X.

Zeng, M.

Zeng, Z.

Zhadin, N.

Zhan, Q.

Zhang, N.

Zhang, Y.

Zhuang, X.

Appl. Opt. (1)

Appl. Phys. B (1)

A. Ohtsu, Y. Kozawa, and S. Sato, “Calculation of second-harmonic wave pattern generated by focused cylindrical vector beams,” Appl. Phys. B 98(4), 851–855 (2010).
[Crossref]

Appl. Phys. Express (1)

M. Hashimoto, H. Niioka, K. Ashida, K. Yoshiki, and T. Araki, “High-sensitivity and high-spatial-resolution imaging of self-assembled monolayer on platinum using radially polarized beam excited second-harmonic-generation microscopy,” Appl. Phys. Express 8(11), 112401 (2015).
[Crossref]

Biomed. Opt. Express (5)

Biophys. J. (1)

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J. 90(2), 693–703 (2006).
[Crossref] [PubMed]

J. Mod. Opt. (1)

P. Török, P. D. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (2)

G. Bautista, J. Mäkitalo, Y. Chen, V. Dhaka, M. Grasso, L. Karvonen, H. Jiang, M. J. Huttunen, T. Huhtio, H. Lipsanen, and M. Kauranen, “Second-harmonic generation imaging of semiconductor nanowires with focused vector beams,” Nano Lett. 15(3), 1564–1569 (2015).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Opt. Commun. (4)

J. Liu, M. Ai, J. Tan, R. Wang, and X. Tan, “Focusing of cylindrical-vector beams in elliptical mirror based system with high numerical aperture,” Opt. Commun. 305, 71–75 (2013).
[Crossref]

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275(2), 453–457 (2007).
[Crossref]

A. Ohtsu, “Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations,” Opt. Commun. 283(20), 3831–3837 (2010).
[Crossref]

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148(4-6), 300–315 (1998).
[Crossref]

Opt. Express (10)

J. Sun, X. Wang, S. Chang, M. Zeng, S. Shen, and N. Zhang, “Far-field radiation patterns of second harmonic generation from gold nanoparticles under tightly focused illumination,” Opt. Express 24(7), 7477–7487 (2016).
[Crossref] [PubMed]

G. Bautista, J. P. Kakko, V. Dhaka, X. Zang, L. Karvonen, H. Jiang, E. Kauppinen, H. Lipsanen, and M. Kauranen, “Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures,” Opt. Express 25(11), 12463–12468 (2017).
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K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

O. Haeberlé, M. Ammar, H. Furukawa, K. Tenjimbayashi, and P. Török, “The point spread function of optical microscopes imaging through stratified media,” Opt. Express 11(22), 2964–2969 (2003).
[Crossref] [PubMed]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[Crossref] [PubMed]

C. P. Pfeffer, B. R. Olsen, and F. Légaré, “Second harmonic generation imaging of fascia within thick tissue block,” Opt. Express 15(12), 7296–7302 (2007).
[Crossref] [PubMed]

F. Tiaho, G. Recher, and D. Rouède, “Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy,” Opt. Express 15(19), 12286–12295 (2007).
[Crossref] [PubMed]

C. Odin, T. Guilbert, A. Alkilani, O. P. Boryskina, V. Fleury, and Y. Le Grand, “Collagen and myosin characterization by orientation field second harmonic microscopy,” Opt. Express 16(20), 16151–16165 (2008).
[Crossref] [PubMed]

C. Odin, T. Guilbert, A. Alkilani, O. P. Boryskina, V. Fleury, and Y. Le Grand, “Collagen and myosin characterization by orientation field second harmonic microscopy,” Opt. Express 16(20), 16151–16165 (2008).
[Crossref] [PubMed]

C. Teulon, I. Gusachenko, G. Latour, and M. C. Schanne-Klein, “Theoretical, numerical and experimental study of geometrical parameters that affect anisotropy measurements in polarization-resolved SHG microscopy,” Opt. Express 23(7), 9313–9328 (2015).
[Crossref] [PubMed]

Opt. Lett. (10)

Y. Zhang, T. Suyama, and B. Ding, “Longer axial trap distance and larger radial trap stiffness using a double-ring radially polarized beam,” Opt. Lett. 35(8), 1281–1283 (2010).
[Crossref] [PubMed]

T. Boulesteix, E. Beaurepaire, M. P. Sauviat, and M. C. Schanne-Klein, “Second-harmonic microscopy of unstained living cardiac myocytes: measurements of sarcomere length with 20-nm accuracy,” Opt. Lett. 29(17), 2031–2033 (2004).
[Crossref] [PubMed]

D. P. Biss and T. G. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28(11), 923–925 (2003).
[Crossref] [PubMed]

X. Wang, Z. Zeng, X. Zhuang, F. Wackenhut, A. Pan, and A. J. Meixner, “Second-harmonic generation in single CdSe nanowires by focused cylindrical vector beams,” Opt. Lett. 42(13), 2623–2626 (2017).
[Crossref] [PubMed]

G. Hall, K. B. Tilbury, K. R. Campbell, K. W. Eliceiri, and P. J. Campagnola, “Experimental and simulation study of the wavelength dependent second harmonic generation of collagen in scattering tissues,” Opt. Lett. 39(7), 1897–1900 (2014).
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P. Török, “Propagation of electromagnetic dipole waves through dielectric interfaces,” Opt. Lett. 25(19), 1463–1465 (2000).
[Crossref] [PubMed]

I. Freund and M. Deutsch, “Second-harmonic microscopy of biological tissue,” Opt. Lett. 11(2), 94–96 (1986).
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R. H. Jordan and D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution,” Opt. Lett. 19(7), 427–429 (1994).
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Y. Guo, P. P. Ho, H. Savage, D. Harris, P. Sacks, S. Schantz, F. Liu, N. Zhadin, and R. R. Alfano, “Second-harmonic tomography of tissues,” Opt. Lett. 22(17), 1323–1325 (1997).
[Crossref] [PubMed]

R. Gauderon, P. B. Lukins, and C. J. R. Sheppard, “Three-dimensional second-harmonic generation imaging with femtosecond laser pulses,” Opt. Lett. 23(15), 1209–1211 (1998).
[Crossref] [PubMed]

Phys. Rev. (1)

D. A. Kleinmann, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126(6), 1977–1979 (1962).
[Crossref]

Phys. Rev. A (1)

Y. I. Salamin, “Direct particle acceleration by two identical crossed radially polarized laser beams,” Phys. Rev. A 82(1), 013823 (2010).
[Crossref]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Proc. SPIE (1)

E. Y. S. Yew and C. J. R. Sheppard, “Vectorial approach to studying second harmonic generation in collagen using linearly and radially polarized beams,” Proc. SPIE 6163, 61630L (2006).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Focusing of a near-infrared radially polarized beam through a three-layer stratified medium. The origin O of the (x, y, z) reference frame is at the unaberrated Gaussian focal point. (b) SHG radiation imaged through the same medium. The specimen is placed at the origin O’ of the (x’, y’, z’) reference frame. Superscripts 1, 2, 3, and d are for the three media and the detector region. OL: objective lens, DP: detector plane, DL: detector lens.
Fig. 2
Fig. 2 The detected SHG intensity distributions at different depths below a 120 µm cover glass. SHG is obtained at λ = 1060 nm with a NA = 1.2 oil immersion objective, for a specimen located in a watery environment. (a1) The SHG intensity patterns through focus (ϕd = 45° plane) for aberration free medium (n1 = n2 = n3), (a2)-(a6) for mismatched stratified media at different imaging depths. The corresponding SHG intensity patterns in the focal plane (x-y plane) are shown in (b1)-(b6). All the intensity distributions are normalized by the respective maximum value.
Fig. 3
Fig. 3 The normalized SHG intensity line profiles for different imaging depths. (a) The axial intensity line profiles. (b) The transverse intensity line profiles in the focal plane. The scan positions of the transverse intensity line profiles are z = −1.52 µm, −3.70 µm, −6.94 µm, −10.1 µm and −13.18 µm for imaging depth of 10 µm, 20 µm, 40 µm, 60 µm and 80 µm respectively.
Fig. 4
Fig. 4 (a) The transverse FWHM, (b) the axial FWHM, (c) the peak intensity of the detected SHG signal and (d) the PSRM of the SHG intensity distribution in the focal plane, as a function of the imaging depths for different excitation wavelengths. The excitation wavelength is set to 0.82 μm, 0.94 μm, 1.06 μm and 1.23 μm respectively. For each excitation wavelength, the peak intensity is normalized by the value of 10 μm imaging depth.
Fig. 5
Fig. 5 SHG response to an on-axis point object as a function of the effective NA for an oil immersion objective of maximum NA = 1.25. (a) Aberration free, (b) depth = 20 µm, (c) depth = 40 µm, (d) depth = 60 µm, (e) depth = 80 µm.

Tables (1)

Tables Icon

Table 1 The performances of SHG imaging for different imaging depths

Equations (33)

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E Nρ (ρ,z)=A 0 α 1 cos 1/2 θ 1 sin θ 1 l 0 ( θ 1 ) ( T p (N1) cos θ N ) J 1 ( k 1 ρsin θ 1 ) ×exp(i k 0 Ψ i )exp(i k N zcos θ N )d θ 1 ,
E Nz (ρ,z)=iA 0 α 1 cos 1/2 θ 1 sin θ 1 l 0 ( θ 1 ) ( T p (N1) sin θ N ) J 0 ( k 1 ρsin θ 1 ) ×exp(i k 0 Ψ i )exp(i k N zcos θ N )d θ 1 ,
Ψ i = h N1 n N cos θ N h 1 n 1 cos θ 1 ,
[ P x P y P z ]=[ d xxx d xyy d xzz d xyz d xxz d xxy d yxx d yyy d yzz d yyz d yxz d yxy d zxx d zyy d zzz d zyz d zxz d zxy ][ E Nx E Nx E Ny E Ny E Nz E Nz 2 E Ny E Nz 2 E Nx E Nz 2 E Nx E Ny ].
E 1 x = 1 2 [ P x ( T s + T p cos θ N cos θ 1 )2 P z T p sin θ N cos θ 1 cos ϕ 1 ( T s T p cos θ N cos θ 1 )( P x cos2 ϕ 1 + P y sin2 ϕ 1 )],
E 1 y = 1 2 [ P y ( T s + T p cos θ N cos θ 1 )2 P z T p sin θ N cos θ 1 sin ϕ 1 ( T s T p cos θ N cos θ 1 )( P x sin2 ϕ 1 P y cos2 ϕ 1 )],
E 1 z =[ P z T p sin θ N sin θ 1 T p cos θ N sin θ 1 ( P x cos ϕ 1 + P y sin ϕ 1 )].
E= (cos θ 1 ) 1/2 R 1 L 1 1 R E 1 ,
R=[ cos ϕ 1 sin ϕ 1 0 sin ϕ 1 cos ϕ 1 0 0 0 1 ],
L 1 =[ cos θ 1 0 sin θ 1 0 1 0 sin θ 1 0 cos θ 1 ],
E x = (cos θ 1 ) 1/2 { P x ( T p cos 2 ϕ 1 cos θ N + T s sin 2 ϕ 1 ) + P y ( T p cos θ N T s )sin ϕ 1 cos ϕ 1 P z T p sin θ N cos ϕ 1 },
E y = (cos θ 1 ) 1/2 { P x cos ϕ 1 ( T p cos θ N T s )sin ϕ 1 + P y ( T s cos 2 ϕ 1 + T p sin 2 ϕ 1 cos θ N ) P z T p sin ϕ 1 sin θ N },
E z =0.
E 2 = (cos θ d ) 1/2 R 1 L 2 RE,
L 2 =[ cos θ d 0 sin θ d 0 1 0 sin θ d 0 cos θ d ],
E 2x = (cos θ d ) 1/2 (cos θ 1 ) 1/2 { P x [ 1 2 T s (1cos2 ϕ 1 )+ 1 2 T p cos θ d cos θ N (1+cos2 ϕ 1 )] + P y [ 1 2 T p cos θ d cos θ N 1 2 T s ]sin2 ϕ 1 P z T p cos θ d sin θ N cos ϕ 1 },
E 2y = (cos θ d ) 1/2 (cos θ 1 ) 1/2 { P x [ 1 2 ( T s + T p cos θ d cos θ N )sin2 ϕ 1 ] + P y [ 1 2 T s (1+cos2 ϕ 1 )+ 1 2 T p cos θ d cos θ N (1cos2ϕ)] P z T p cos θ d sin θ N sin ϕ 1 },
E 2z = (cos θ d ) 1/2 (cos θ 1 ) 1/2 { P x ( T p sin θ d cos θ N cos ϕ 1 ) + P y ( T p sin θ d cos θ N sin ϕ 1 )+ P z T p sin θ d sin θ N }.
E dx =i A d P x I d01 +i A d P x I d21 cos2 ϕ d +i A d P y I d21 sin2 ϕ d 2 A d P z I d11 cos ϕ d ,
E dy =i A d P x I d21 sin2 ϕ d i A d P y I d01 i A d P y I d21 cos2 ϕ d 2 A d P z I d11 sin ϕ d ,
E dz =2 A d P x I d12 cos ϕ d 2 A d P y I d12 sin ϕ d 2i A d P z I d02 ,
I d01 = 0 α d (cos θ d ) 1/2 (cos θ 1 ) 1/2 ( T s sin θ d + T p sin θ d cos θ d cos θ N ) J 0 ( k d ρ d sin θ d ) ×exp(i k d0 Ψ det )exp(i k d z d cos θ d )d θ d ,
I d02 = 0 α d (cos θ d ) 1/2 (cos θ 1 ) 1/2 ( T p sin 2 θ d sin θ N ) J 0 ( k d ρ d sin θ d ) ×exp(i k d0 Ψ det )exp(i k d z d cos θ d )d θ d ,
I d11 = 0 α d (cos θ d ) 1/2 (cos θ 1 ) 1/2 ( T p cos θ d sin θ d sin θ N ) J 1 ( k d ρ d sin θ d ) ×exp(i k d0 Ψ det )exp(i k d z d cos θ d )d θ d ,
I d12 = 0 α d (cos θ d ) 1/2 (cos θ 1 ) 1/2 ( T p sin 2 θ d cos θ N ) J 1 ( k d ρ d sin θ d ) exp(i k d0 Ψ det )exp(i k d z d cos θ d )d θ d ,
I d21 = 0 α d (cos θ d ) 1/2 (cos θ 1 ) 1/2 ( T s sin θ d + T p sin θ d cos θ d cos θ N ) × J 2 ( k d ρ d sin θ d )exp(i k d0 Ψ det )exp(i k d z d cos θ d )d θ d ,
k d1 sin α 1 k d sin α d = k d1 sin θ 1 k d sin θ d =M,
Ψ det = n 1 h 1 cos θ 1 n N h N1 cos θ N .
I SHG = | E dx | 2 + | E dy | 2 + | E dz | 2 .
l 0 ( θ 1 )=exp[ β 0 2 ( sin θ 1 sin α 1 ) 2 ]J1( 2β0 sin θ 1 sin α 1 ),
P x = d xzz E Nz E Nz + d xyy E Ny E Ny + d xxx E Nx E Nx ,
P y =2 d yyx E Ny E Nx ,
P z =2 d zzx E Nz E Nx .

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