Abstract

We study and demonstrate the technique of simultaneous spatial and temporal focusing of femtosecond pulses, with the aim to improve the signal-to-background ratio in multiphoton imaging. This concept is realized by spatially separating spectral components of pulses into a “rainbow beam” and recombining these components only at the spatial focus of the objective lens. Thus, temporal pulse width becomes a function of distance, with the shortest pulse width confined to the spatial focus. We developed analytical expressions to describe this method and experimentally demonstrated the feasibility. The concept of simultaneous spatial and temporal focusing of femtosecond pulses has the great potential to significantly reduce the background excitation in multiphoton microscopy, which fundamentally limits the imaging depth in highly scattering biological specimens.

© 2005 Optical Society of America

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References

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J. Microsc. (1)

G.J. Brakenhoff, J. Squier, T. Norris, A.C. Bliton W.H. Wade and B. Athey, �??Real-time two-photon confocal microscopy using a femtosecond amplified Ti:sapphire system,�?? J. Microsc. 181, 253-259 (1996).
[CrossRef] [PubMed]

J. Neuroscience Methods (1)

W. Denk, K. R. Delaney, A. Gelperin, D. Kleinfeld, B. W. Strawbridge, D. W. Tank, and R. Yuste, �??Anatomical and functional imaging of neurons using 2-photon laser microscopy,�?? J. Neuroscience Methods, 54, 161-162 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

O. E. Martinez, �??Grating and prism compressor in the case of finite beam size,�?? J. Opt. Soc. Am. 3, 929-934, 1986.
[CrossRef]

Nature Biotechnol. (1)

J. M. Squirrell, D. L. Wokosin, J. G. White, and B. D. Bavister, �??Long-term two-photon fluorescence imaging of mammalian embryos without compromising viability,�?? Nature Biotechnol. 17, 763-767 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. (1)

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, �??Live tissue intrinsic emission microscopy using multi-photon intrinsic fluorescence and second harmonic generation,�?? Proc. Natl. Acad. Sci. 100, 7075-7080 (2003).
[CrossRef] [PubMed]

Other (1)

H. A. Haus, Waves and fields in optoelectronics, (Prentice-Hall, Englewood Cliffs, NJ, 1984), Chap 4.

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Figures (4)

Fig. 1.
Fig. 1.

Schematics for the proposed simultaneous temporal and spatial focusing technique. The system input is a rainbow-like superposition of many parallel optical beams of which the center positions are linearly displaced according to their wavelengths. The spectrum of the input is assumed to be chirp-free. After passing through a regular objective lens, the rainbow beam is then focused and recombined in space. Temporal focusing is achieved because of the reduced spatial overlapping and the non-zero geometric dispersion outside the focal volume.

Fig. 2.
Fig. 2.

Experimental setup for simultaneous temporal and spatial focusing and measurement of the pulse width dependence by second order auto-correlation. BS: beam splitter. DM: dichroic mirror. The input pulse train at 800nm center wavelength was generated by a mode-locked Ti:Saphire laser (Tsunami, Spectra-Physics). An isolator was used to overcome the instability caused by optical feedback. To spatially separate the spectral components, a reflective grating (1200 lines/mm) was used. The distances between the optical components are indicated. The insets show the cross section profiles of the laser beam impinging on the grating (d), at the back aperture of the cylindrical lens (c), at the back aperture of the objective (b), and at the focal plane of the objective (a). Note that the y-axis is pointing perpendicularly into the paper.

Fig. 3.
Fig. 3.

Auto-correlation traces of the measured pulse at different sample positions: (a) at the focal plane of the objective, (b) when moved 275 µm away from focal plane. The inset inside trace (a) shows the interference fringes at the vicinity of zero time delay.

Fig. 4.
Fig. 4.

Measured (solid square) and theoretically fitted (line) pulse width as a function of sample position. The location of the focal plane of the objective lens is set to be zero.

Equations (12)

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A 1 ( x , t ) = + exp [ ( x α · Δ ω ) 2 s 2 ] · exp [ Δ ω 2 Ω 2 + i Δ ω t ] · d Δ ω ,
M ( x , z , Δ ω ) = s 2 a · ( 1 i k s 2 2 f ) exp [ ( x b ) 2 4 a + i · k · α · Δ ω f x + c ] ,
a = f 1 2 k 2 s 2 i . z f 1 2 f 2 k ,
b = α · Δ ω · ( 1 z f ) ,
c = i · k · α 2 Δ ω 2 2 f 2 ( z f ) ,
f 1 2 = f 2 · k 2 s 4 4 f 2 + k 2 s 4 .
A 2 ( x , z , t ) = + M ( x , z , Δ ω ) · exp ( Δ ω 2 Ω 2 + i Δ ω t ) · d Δ ω
s · Ω 2 π m · a k = k 0 · ( 1 ik 0 s 2 2 f ) · exp [ x 2 4 a k = k 0 ( Ω · t + n · x ) 2 4 m ] ,
m = 1 + α 2 Ω 2 · ( z f ) 2 4 f 2 · a k = k 0 i · k 0 · α 2 Ω 2 · ( z f ) 2 f 2 ,
n = k 0 · α Ω f + i · α Ω · ( z f ) 2 f · a k = k 0 .
τ ( z ) = 1 Re [ 1 m ] · 2 2 ln 2 Ω .
PWSF = 1 + α 2 Ω 2 s 2 α · Ω s α · Ω s .

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