Abstract

The third-order nonlinear susceptibility (χ(3)) can be measured quantitatively using third-harmonic generation (THG) from two different interfaces. For the first time it is demonstrated both in experiments and theory that the magnitude of the THG signals from the two interfaces is not only determined by material properties (refractive index and χ(3)), but also by optical aberrations. It is found that this method of χ(3) determination can be applied without additional correction factors only for focusing conditions with a numerical aperture (NA) ≤ 0.35. The implications for general application of THG in three-dimensional microscopy are discussed.

© 2006 Optical Society of America

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References

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Appl. Opt. (1)

Appl. Phys. Lett. (4)

C.-K. Sun, S.-W. Chu, S.-P. Tai, S. Keller, U.K. Mishra, S.P. DenBaars, "Scanning second-harmonic/third-harmonic generation microscopy of gallium nitride," Appl. Phys. Lett. 77, 2331-2333 (2000).
[CrossRef]

Y. Barad, H. Eisenberg, M. Horowitz, Y. Silberberg, "Nonlinear Scanning Laser Microscopy by Third Harmonic Generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

D. Yelin, Y. Silberberg, Y. Barad and J. S. Patel, "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," Appl. Phys. Lett. 74, 3107-3109 (1999).
[CrossRef]

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, "Nonlinear optical susceptibility measurements of solutions using third-harmonic generation on the interface," Appl. Phys. Lett. 82, 3982-3984 (2003).
[CrossRef]

J. Chem. Phys. (1)

G. R. Meredith, B. Buchalter, and C. Hanzlik, "Third-order susceptibility determination by third harmonic generation. II," J. Chem. Phys. 78, 1543-1551 (1983).
[CrossRef]

J. Microsc. (2)

S. Hell, G. Reiner, C. Cremer, E.H.K. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

M. Müller, 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] [PubMed]

J. Opt. Soc. Am. B (3)

J. Struct. Biol. (1)

V. Shcheslavskiy, G. I. Petrov, S. Saltiel, and V. V. Yakovlev, "Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy," J. Struct. Biol. 147, 42-49 (2004).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Optik (1)

C. J. R. Sheppard, C.J. Cogswell, "Effects of aberrating layers and tube length on confocal imaging properties," Optik 87, 34-38 (1991).

Phys. Rev. (1)

J. F. Ward, G. H. C. New, "Optical Third Harmonic Generation in Gases by a Focused Laser Beam," Phys. Rev. 185, 57-72 (1969).
[CrossRef]

Phys. Rev. A (1)

F. Kajzar, J. Messier, "Third-harmonic generation in liquids," Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

Phys. Rev. E (1)

R. Barille, L. Canioni, L. Sarger, and G. Rivoire, "Nonlinearity measurements of thin films by third-harmonic-generation microscopy," Phys. Rev. E 66 (2002).
[CrossRef]

PNAS (1)

W. Supatto, D. Débarre, B. Moulia, E. Brouzés, J-L. Martin, E. Farge, E. Beaurepaire, "In vivo modulation of morphogenetic movements in Drosophila embryos with femtosecond laser pulses," PNAS 102, 1047-1052 (2005).
[CrossRef] [PubMed]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic Press, Inc., New York, 1992).

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1993).

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic Press, Inc., Orlando, 1984).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental configuration for (a) quantitative χ(3) measurements and (b) evaluation of the THG signal depth dependence in a refractive index mismatched sample. Regions AB and CD are cover glasses, region BC contains the sample of interest. (c) Schematic of the experimental set-up for the THG measurements. Symbols used: Ln: lens; v.a.: variable aperture; S: sample; O: microscope objective; C: collection lens; F: filter. L4 can be translated along the optical axis, as can the microscope objective (O), which is mounted on a piezo scanner.

Fig. 2.
Fig. 2.

FWHM of the THG z-response as a function of the L4 position. Error bars represent one standard deviation of error and the solid line is a guide to the eye. Representative z-responses -open circles and corresponding fits to the left- and right-hand side (red and blue curves respectively) - are shown for L4 = 11.5, 14 and 16.5.

Fig. 3.
Fig. 3.

(a) Measured ratio IB/IA as a function of NA for G1 (triangles), G2 (circles) and G3 (squares) in a air-glass-air configuration. The solid line represents a numerical calculation for G2. (b) Measured (open symbols) and calculated (solid line) THG z-responses at interfaces A (red) and B (blue) for G2. The measurement error is approximately ±2%.

Fig. 4.
Fig. 4.

Measured χ(3) values for methanol, ethanol and 2-propanol. Red and light blue bars represent direct evaluation of χ(3) based on IB/IA measurements with NA = 0.35 and NA = 0.65 respectively. Dark blue bars represent χ(3) value obtained from the NA = 0.65 measurement after correcting for the effect of aberration. Violet bars denote literature χ(3) values obtained at 1062 nm for methanol and ethanol and at 1910 nm for 2-propanol [24, 26]

Fig. 5.
Fig. 5.

Measured ratio IC/IB as a function of depth in a refractive index mismatched medium (water) for two different microscope objectives: 0.65 NA/40x air-spaced (blue circles) and 1.25 NA/63x oil immersion. Solid lines represent theoretical calculations for NA = 0.65 (blue) with a uniform profile and NA = 1.25 (red) with a Gaussian profile. All measurements and calculations are for G2 glass.

Tables (1)

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Table 1. Properties of glass types used.

Equations (4)

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ϕ = kt [ n 2 ( 1 4 n 1 2 s 2 ( 1 s 2 ) n 2 2 ) 1 2 n 1 ( 1 2 s 2 ) ]
ϕ = k ( t 170 ) [ n 2 ( 1 4 n 1 2 s 2 ( 1 s 2 ) n 2 2 ) 1 2 n 1 ( 1 2 s 2 ) ]
χ mat ( 3 ) = χ glass ( 3 ) J glass ( 1 ± I B I A ) J mat
J = 0 exp ( i Δ kz ) ( 1 + 2 iz b ) 2 dz

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