Abstract

The fundamental features of third-harmonic generation microscopy are examined both theoretically and experimentally, and the technique is applied to the characterization of layered structures. Measurements and model calculations have been performed of the third-harmonic yield generated from homogeneous layers. Model calculations based on the paraxial approximation show good agreement with the experimental results, despite the conditions of high numerical aperture. The method proposed here allows for the determination of (i) the layer’s third-order susceptibility relative to that of the substrate, (ii) its index of refraction at the third-harmonic frequency relative to that at the fundamental frequency, and (iii) its thickness and for the identification of a gradient region between two adjacent layers.

© 2002 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. R. Eramo and M. Matera, “Third-harmonic generation in positively dispersive gases with a novel cell,” Appl. Opt. 33, 1691–1696 (1994).
    [CrossRef] [PubMed]
  4. A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. J. Squier, K. R. Wilson, M. Müller, and G. J. Brakenhoff, “3D-microscopy using third-harmonic generation at interfaces in biological and non-biological specimens,” in Ultrafast Phenomena XI, T. Elsasser, J. G. Fujimoto, D. Wiersma, and W. Zinth, eds., Vol. 63 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1998), p. 153.
  8. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  9. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  10. W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. R. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).
  11. J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  12. E. O. Potma, W. P. de Boeij, and D. A. Wiersma, “Nonlinear coherent four-wave mixing in optical microscopy,” J. Opt. Soc. Am. B 17, 1678–1684 (2000).
    [CrossRef]
  13. J. J. Stamnes, Waves in Focal Regions (IOP Publishing, Bristol, UK, 1986).

2000 (1)

1998 (2)

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

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]

1997 (1)

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]

1994 (1)

1987 (1)

A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

1969 (1)

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]

1966 (1)

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]

Ashkin, A.

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]

Barad, Y.

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]

Boyd, G. D.

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]

Brakenhoff, G. J.

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

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]

de Boeij, W. P.

Eisenberg, H.

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]

Eramo, R.

Hilber, G.

A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Horowitz, M.

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]

Kleinman, D. A.

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]

Lago, A.

A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Matera, M.

Müller, M.

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]

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

New, G. H. C.

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]

Potma, E. O.

Silberberg, Y.

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]

Squier, J.

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

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]

Wallenstein, R.

A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Ward, J. F.

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]

Wiersma, D. A.

Wilson, K. R.

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]

J. Squier, M. Müller, G. J. Brakenhoff, and K. R. Wilson, “Third harmonic generation microscopy,” Opt. Express 3, 315–324 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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]

J. Microsc. (Oxford) (1)

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]

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

Opt. Express (1)

Phys. Rev. (2)

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]

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]

Phys. Rev. A (1)

A. Lago, G. Hilber, and R. Wallenstein, “Optical frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Other (5)

J. J. Stamnes, Waves in Focal Regions (IOP Publishing, Bristol, UK, 1986).

J. Squier, K. R. Wilson, M. Müller, and G. J. Brakenhoff, “3D-microscopy using third-harmonic generation at interfaces in biological and non-biological specimens,” in Ultrafast Phenomena XI, T. Elsasser, J. G. Fujimoto, D. Wiersma, and W. Zinth, eds., Vol. 63 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1998), p. 153.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. R. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the experimental setup, with two variants for the detection path. An IR beam generated by the optical parametric amplifier (OPA) is apodized by a variable aperture (A) and imaged onto the entrance pupil of the excitation objective by means of two lenses (L1 and L2). L2 and L3 are the tube lenses of the respective microscope objectives. The distance between the two lenses (d) and the sample position (z) can be varied. The total amount of THG intensity is measured with a photomultiplier tube (PMT), with a filter (F) blocking out the fundamental. Alternatively, the numerical aperture of the THG signal is measured by imaging of the output pupil of the collection objective onto a CCD camera (CCD).

Fig. 2
Fig. 2

Two sample geometries used in the experiments: top, with a single interface, also referred to as bulk–bulk, and bottom, with two interfaces, also referred to as bulk-layer–bulk. Media 1 and 2 are characterized by their refractive indices at the fundamental and tripled frequencies, n(ωf) and n(ωth), respectively, and by their third-order susceptibility χ(3).

Fig. 3
Fig. 3

THG dependence on tube-lens position for a glass–air interface, with 1.25-NA excitation at λf=1.2 µm. (a) THG axial profiles measured at three tube lens positions. (b) FWHM and maximum THG intensity of the THG axial profile as a function of the tube-lens position. (The solid and dashed curves are guides to the eye only.)

Fig. 4
Fig. 4

FWHM of THG axial profiles from a glass–air interface as a function of input NA (fundamental). Solid line, prediction from Gaussian theory (no fitting parameters). The data represented by the filled circles were obtained with an air objective in the excitation path; the open triangles, with an oil-immersion objective.

Fig. 5
Fig. 5

Dependence of the output NA (THG) on the input NA (fundamental). Open triangles, data obtained with a 63×/1.25-NA (oil-immersion) objective; filled circles, with a 40×/0.65-NA (air) objective in the excitation path. The excitation beam approximately follows a radially flat intensity distribution (hat-profile excitation) at all input NA values.

Fig. 6
Fig. 6

Typical THG axial profiles for the double-interface configuration with either an air gap (left) or an immersion-oil gap (right). The gap is 8 µm thick and is situated between two K5 glass slides. The axial profiles are recorded at different input NA values of 0.25, 0.30, and 0.35 as indicated.

Fig. 7
Fig. 7

Measured (left) and calculated (right) intensity ratios Rpre, Rmid, and Rpost for a double-interface geometry. Gaps are filled with immersion oil or air, as shown. Experimental conditions are given in the text.

Fig. 8
Fig. 8

Calculated THG conversion efficiencies as a function of NA of the excitation beam for four values of the third-order susceptibility ratio χgap(3)/χglass(3). For all traces, Δngap=-0.022 and Δnglass=-0.032.

Fig. 9
Fig. 9

Visibility of a stack consisting of 100 layers, each 0.5 µm thick, with focusing in the middle. Visibility is defined here as the absolute logarithm of the ratio between the yield for focusing on an interface to that for focusing halfway between the interfaces. The dispersion ratio is defined as Δngap/Δnglass, where Δnglass=-0.032 and the susceptibility ratio is χgap(3)/χglass(3).

Fig. 10
Fig. 10

Calculated gradient sensitivity (width of the THG axial profile at high NA) as a function of gradient extension between two different bulk materials. Two situations are displayed: Dashed curve, the materials have equal third-order susceptibility [χ1(3)=χ2(3)] but unequal dispersion (Δn1=-0.022 and Δn1=-0.032); solid curve, the two materials have equal dispersion (Δn1=Δn2=-0.032) but differ in third-order susceptibility [χ1(3)=4χ2(3)].

Equations (23)

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2ikfz+2x2+2y2Ef (r)
=0,
2ikthz+2x2+2y2Eth(r)
=-4πωthc2χ(3)Ef3(r)exp(iΔkz).
kf=2πn(ωf)λf,
kth=2πn(ωth)λth,
Δk=3kf-kth=6πΔnλf,
E(r, t)=exy{Ef (r)exp[i(kf z-ωf t)]+Eth(r)exp[i(kthz-ωtht)]+c.c.}.
Ef (r)=ηAf exp-ηkf r22zRn,
Eth(r)=ηAth(z)exp-3ηkf r22zRn,
η(z)=11+iz/zRn,
Ath(z)=2πiωthχ(3)Af3S(z)nthc,
S(z)=z η2(ξ)exp(iΔkξ)dξ.
|S(z0)|2=z0 η2(ξ)dξ2=zRn21+(z0/zRn)2,
|S(z0)|2=η2(z0)exp(iΔkz0)z0z0+Δζ dξ2=Δz1+(z0/zRn)22,
Δϕ=Δk1n1(ωf)zif-Δk2n2(ωf)zif.
S(z)=j exp(iΔϕj)qjrj dξexp(iΔkjξ)(1+iξ/zR,j)2,
qj+1nj+1(ωf)=rjnj(ωf),
rj-qj=layerthickness,
Δϕj+1-Δϕj=Δkjrj-Δkj+1qj+1.
Rpre=ITHG(-L/4)ITHG(0),
Rpost=ITHG(+L/4)LTHG(0),
Rmid=ITHG(+L/2)ITHG(0).

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