Abstract

We report results of scattering measurements using femtosecond pulses to collect a wealth of infor mation in a single experiment. Potential issues with particle scattering, such as variation in particle size, were avoided by using 9 and 50μm diameter glass fibers. We first establish an angular scattering intensity baseline, and we show that the spectral width of very short pulses leads to smoothing of the angular scattering pattern, consistent with continuous broadband illumination. We then measure the angular scattering pattern from short pulses with a spectrometer and reveal an underlying spectral periodicity of broadband scattered light that is consistent with narrowband cw scattering. Our experimental results compare well with existing theory. We show that such two-dimensional experimental data and derived analytic solution can provide robust characterization of scattering objects even in the presence of noise.

© 2009 Optical Society of America

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References

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  1. A. Jones, “Some calculations on the scattering efficiencies of a sphere illuminated by an optical pulse,” J. Phys. D 40, 7306-7312 (2007).
    [CrossRef]
  2. K. S. Shifrin and I. G. Zolotov, “Nonstationary scattering of electromagnetic pulses by spherical particles,” Appl. Opt. 34, 552-558 (1995).
    [CrossRef] [PubMed]
  3. S. Bakic, C. Heinisch, N. Damaschke, T. Tschudi, and C. Tropea, “Time integrated detection of femtosecond laser pulses scattered by small droplets,” Appl. Opt. 47, 523-530 (2008).
    [CrossRef] [PubMed]
  4. H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses- numerical simulation,” Optik (Jena) 115, 205-217(2004).
    [CrossRef]
  5. H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations--A numerical study,” Optik (Jena) 117, 40-47(2006).
    [CrossRef]
  6. Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
    [CrossRef]
  7. W. Bickel, W. Gilliar, and B. Bell, “Light scattering from fibers: a closer look with a new twist,” Appl. Opt. 19, 3671-3675(1980).
    [CrossRef] [PubMed]
  8. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  9. G. Videen and W. Bickel, “Scattering from geometrically perturbed perfect quartz fibers,” Appl. Opt. 26, 471-474 (1987).
    [CrossRef] [PubMed]
  10. W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
    [CrossRef]
  11. B. Bell and W. Bickel, “Single fiber light scattering matrix: an experimental determination,” Appl. Opt. 20, 3874-3879(1981).
    [CrossRef] [PubMed]
  12. O. Svelto, Principles of Lasers (Plenum, 1989).

2008

Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
[CrossRef]

S. Bakic, C. Heinisch, N. Damaschke, T. Tschudi, and C. Tropea, “Time integrated detection of femtosecond laser pulses scattered by small droplets,” Appl. Opt. 47, 523-530 (2008).
[CrossRef] [PubMed]

2007

A. Jones, “Some calculations on the scattering efficiencies of a sphere illuminated by an optical pulse,” J. Phys. D 40, 7306-7312 (2007).
[CrossRef]

2006

H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations--A numerical study,” Optik (Jena) 117, 40-47(2006).
[CrossRef]

2004

H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses- numerical simulation,” Optik (Jena) 115, 205-217(2004).
[CrossRef]

1995

1987

G. Videen and W. Bickel, “Scattering from geometrically perturbed perfect quartz fibers,” Appl. Opt. 26, 471-474 (1987).
[CrossRef] [PubMed]

W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
[CrossRef]

1981

1980

Apeksimov, D.

Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
[CrossRef]

Bakic, S.

Bech, H.

H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations--A numerical study,” Optik (Jena) 117, 40-47(2006).
[CrossRef]

H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses- numerical simulation,” Optik (Jena) 115, 205-217(2004).
[CrossRef]

Bell, B.

Bickel, W.

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Damaschke, N.

Geints, Y.

Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
[CrossRef]

Gilliar, W.

W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
[CrossRef]

W. Bickel, W. Gilliar, and B. Bell, “Light scattering from fibers: a closer look with a new twist,” Appl. Opt. 19, 3671-3675(1980).
[CrossRef] [PubMed]

Heinisch, C.

Hoar, D.

W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
[CrossRef]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jones, A.

A. Jones, “Some calculations on the scattering efficiencies of a sphere illuminated by an optical pulse,” J. Phys. D 40, 7306-7312 (2007).
[CrossRef]

Leder, A.

H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations--A numerical study,” Optik (Jena) 117, 40-47(2006).
[CrossRef]

H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses- numerical simulation,” Optik (Jena) 115, 205-217(2004).
[CrossRef]

Shifrin, K. S.

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, 1989).

Tropea, C.

Tschudi, T.

Videen, G.

W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
[CrossRef]

G. Videen and W. Bickel, “Scattering from geometrically perturbed perfect quartz fibers,” Appl. Opt. 26, 471-474 (1987).
[CrossRef] [PubMed]

Zemlyanov, A.

Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
[CrossRef]

Zolotov, I. G.

Am. J. Phys.

W. Gilliar, W. Bickel, G. Videen, and D. Hoar, “Light scattering from fibers: an extension of a single-slit diffraction experiment,” Am. J. Phys. 55, 555-559 (1987).
[CrossRef]

Appl. Opt.

J. Phys. D

A. Jones, “Some calculations on the scattering efficiencies of a sphere illuminated by an optical pulse,” J. Phys. D 40, 7306-7312 (2007).
[CrossRef]

Opt. Commun.

Y. Geints, D. Apeksimov, and A. Zemlyanov, “Efficiency of frequency-pulsed excitation of a micron-sized spherical microcavity by chirped ultrashort laser radiation,” Opt. Commun. 281, 5372-5376 (2008).
[CrossRef]

Optik (Jena)

H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses- numerical simulation,” Optik (Jena) 115, 205-217(2004).
[CrossRef]

H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations--A numerical study,” Optik (Jena) 117, 40-47(2006).
[CrossRef]

Other

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

O. Svelto, Principles of Lasers (Plenum, 1989).

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Figures (6)

Fig. 1
Fig. 1

Angular scattering pattern of 800 nm light ( 100 nm bandwidth (solid line with circles), 25 nm bandwidth (solid line with triangles), and cw (solid line) from (a)  9 μm and (b)  50 μm diameter glass fibers. Simulation with 1001 modes for both 100 and 25 nm bandwidths.

Fig. 2
Fig. 2

Optical spectra of (a) the Micra laser at 100 (solid line) and 25 nm (dotted line) bandwidths measured with the Ocean Optics spectrometer, and (b) the 815 nm laser diode measured with two spectrometers: Ocean Optics (dotted line) and Ando 6317B (solid line).

Fig. 3
Fig. 3

Angular scattering pattern of (a)  9 μm and (b)  50 μm diameter glass fibers when excited by 100 nm bandwidth (solid line with circles), 25 nm bandwidth (solid line with triangles), and cw (solid line) sources.

Fig. 4
Fig. 4

Optical spectrum versus angle for the scattering pattern of a 100 nm bandwidth source from (a)  9 μm and (b)  50 μm diameter glass fibers. Simulated optical spectrum versus angle for the scattering pattern of a uniform amplitude, 100 nm bandwidth source from (c)  9 μm and (d)  50 μm diameter glass fibers.

Fig. 5
Fig. 5

Comparison of the scattering pattern of 815 nm light from a 50 μm diameter glass fiber. Experimental measurements with a 815 nm , cw laser diode (solid line with circles) and a broadband mode-locked source through a spectrometer set at 815 nm (solid line with triangles) are compared with a simulation (solid line) as described in Section 2.

Fig. 6
Fig. 6

Two-dimensional scattering pattern of a 9 μm diameter glass fiber using the analytic expression from the p = 0 , 1 Debye series ray trace solution.

Equations (8)

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E ( t ) = A ( t ) e i ω 0 t ,
A ( t ) = n = N N E n e in ( Δ ω t + ϕ ) .
Δ τ p = 0.441 2 π ( 2 N + 1 ) Δ ω .
E s ( ϕ , k ) = e i 3 π / 4 2 π k b e i k b T 2 ( ϕ , k ) E i ,
T 2 ( ϕ , k ) = a 0 + 2 n = 1 a n cos ( n ( π ϕ ) ) ,
a n ( k ) = m J n ( k r ) J n ( m k r ) J n ( k r ) J n ( m k r ) m J n ( m k r ) H n ( 1 ) ( k r ) J n ( m k r ) H n ( 1 ) ( k r ) .
70 °
Δ ϕ = 2 π R λ [ n cos ( θ 1 ) 2 cos ( ϕ 1 ) cos ( ϕ 1 + θ i ) 2 cos ( ϕ 2 ) cos ( ϕ 2 + θ i ) ] ,

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