Abstract

Scattering of femtosecond laser pulses by small droplets has been measured and compared with predictions, yielding some interesting new applications for time integrated detection of the scattered field. The scattering intensity of integrated detection becomes monotonic with droplet size over large regions of scattering angle and morphology dependent resonances are surpressed, opening the way for particle sizing using the scattered intensity. Furthermore, the ripple structure no longer appears in the rainbow region of scattering, simplifying rainbow refractometry significantly. These scattering proporties of femtosecond laser pulses have been demonstrated in the laboratory using a novel Paul trap for levitating single droplets.

© 2008 Optical Society of America

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References

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  1. A. Frohn and N. Roth, Dynamics of Droplets (Springer-Verlag, 2000).
  2. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).
  3. M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry (Springer-Verlag, 1998).
  4. N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, "Multi-dimensional particle sizing techniques," Exp. Fluids 39, 336-350 (2005).
    [CrossRef]
  5. N. Fujisawa, A. Hosokawa, and S. Tomimatsu, "Simultaneous measurement of droplet size and velocity field by an interferometric imaging technique in spray combustion," Meas. Sci. Technol. 14, 1341-1349 (2003).
    [CrossRef]
  6. J. P. A. J. van Beeck and M. L. Riethmuller, "Nonintrusive measurements of temperature and size of single falling raindrops," Appl. Opt. 34, 1633-1639 (1995).
    [CrossRef] [PubMed]
  7. P. J. Wyatt, K. L. Schehrer, S. D. Phillips, C. Jackson, Y. J. Chang, R. G. Parker, D. T. Phillips, and J. R. Bottinger, "Aerosol particle analyzer," Appl. Opt. 27, 217-221 (1988).
    [CrossRef] [PubMed]
  8. M. Peil, I. Fischer, W. Elsäer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, "Rainbow refractometry with a tailored incoherent semiconductor laser source," Appl. Phys. Lett. 89, 091106 (2006).
    [CrossRef]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  10. A. H. Zewail, "Laser femtochemistry," Science 242, 1645-1653 (1988).
    [CrossRef] [PubMed]
  11. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  12. L. Mees, G. Gouesbet, and G. Grehan, "Scattering of laser pulses (plane wave and focused Gaussian beam) by spheres," Appl. Opt. 40, 2546-2550 (2001).
    [CrossRef]
  13. H. Bech and A. Leder, "Particle sizing by ultrashort laser pulses--numerical simulation," Optik 115, 205-217 (2004).
    [CrossRef]
  14. J. P. A. J. van Beeck, Rainbow Phenomena: Development of a Laser Based, Non-Intrusive Technique for Measuring Droplet Size Temperature and Velocity (Technische Universiteit Eindhoven, 1997).
    [PubMed]
  15. J. P. A. J. van Beeck, L. Zimmer, and M. L. Riethmuller, "Global rainbow thermometry for mean temperature and size measurement of spray droplets," Part. Part. Syst. Charact. 18, 196-204 (2001).
    [CrossRef]
  16. R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
    [CrossRef]
  17. E. A. Hovenac and J. A. Lock, "Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series," J. Opt. Soc. Am. A 9, 781-795 (1992).
    [CrossRef]
  18. G. Gouesbet and G. Grehan, "Generalized Lorenz-Mie theories, from past to future," Atomization Sprays 10, 277-333 (2000).
  19. N. Damaschke, "Light scattering theories and their use for single particle characterization," in Fachgebiet Strömungslehre und Aerodynamik (Technische Universität Darmstadt, 2003).
  20. T. Siebert, O. Sbanski, M. Schmitt, V. Engel, W. Kiefer, and J. Popp, "The mechanism of light storage in spherical microcavities explored on a femtosecond time scale," Opt. Commun. 216, 321-327 (2003).
    [CrossRef]
  21. J. P. Wolf, Y. L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, "Ballistic trajectories of optical wave packets within microcavities," Phys. Rev. A 64, 023808 (2001).
    [CrossRef]
  22. C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J. P. Wolf, "White-light nanosource with directional emission," Phys. Rev. Lett. 89, 035002 (2002).
    [CrossRef] [PubMed]
  23. S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, Y. L. Pan, S. Holler, and R. K. Chang, "Enhanced backward-directed multiphoton-excited flourescence from dielectric microcavities," Phys. Rev. Lett. 85, 54-57 (2000).
    [CrossRef] [PubMed]
  24. H. M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, "Evaporation and condensation rates of liquid droplets deduced from structure resonances in fluorescence spectra," Opt. Lett. 9, 273-275 (1984).
    [CrossRef] [PubMed]
  25. J. Wilms, "Evaporation of multicomponent droplets," in Institut für Thermodynamik der Luft- und Raumfahrt (Universität Stuttgart, 2005), p. 157.
  26. K. Heukelbach, J. Hom, and N. Chigier, "Capabilities and limitations of the rainbow refractometer, determined with temperature measurements of water droplets," presented at the ILASS-Americas 11th Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17-21 May 1998.

2006 (1)

M. Peil, I. Fischer, W. Elsäer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, "Rainbow refractometry with a tailored incoherent semiconductor laser source," Appl. Phys. Lett. 89, 091106 (2006).
[CrossRef]

2005 (1)

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, "Multi-dimensional particle sizing techniques," Exp. Fluids 39, 336-350 (2005).
[CrossRef]

2004 (1)

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

2003 (3)

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

T. Siebert, O. Sbanski, M. Schmitt, V. Engel, W. Kiefer, and J. Popp, "The mechanism of light storage in spherical microcavities explored on a femtosecond time scale," Opt. Commun. 216, 321-327 (2003).
[CrossRef]

N. Fujisawa, A. Hosokawa, and S. Tomimatsu, "Simultaneous measurement of droplet size and velocity field by an interferometric imaging technique in spray combustion," Meas. Sci. Technol. 14, 1341-1349 (2003).
[CrossRef]

2002 (1)

C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J. P. Wolf, "White-light nanosource with directional emission," Phys. Rev. Lett. 89, 035002 (2002).
[CrossRef] [PubMed]

2001 (3)

J. P. Wolf, Y. L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, "Ballistic trajectories of optical wave packets within microcavities," Phys. Rev. A 64, 023808 (2001).
[CrossRef]

J. P. A. J. van Beeck, L. Zimmer, and M. L. Riethmuller, "Global rainbow thermometry for mean temperature and size measurement of spray droplets," Part. Part. Syst. Charact. 18, 196-204 (2001).
[CrossRef]

L. Mees, G. Gouesbet, and G. Grehan, "Scattering of laser pulses (plane wave and focused Gaussian beam) by spheres," Appl. Opt. 40, 2546-2550 (2001).
[CrossRef]

2000 (2)

G. Gouesbet and G. Grehan, "Generalized Lorenz-Mie theories, from past to future," Atomization Sprays 10, 277-333 (2000).

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, Y. L. Pan, S. Holler, and R. K. Chang, "Enhanced backward-directed multiphoton-excited flourescence from dielectric microcavities," Phys. Rev. Lett. 85, 54-57 (2000).
[CrossRef] [PubMed]

1995 (1)

1992 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1988 (2)

1984 (1)

Appl. Opt. (3)

Appl. Phys. Lett. (1)

M. Peil, I. Fischer, W. Elsäer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, "Rainbow refractometry with a tailored incoherent semiconductor laser source," Appl. Phys. Lett. 89, 091106 (2006).
[CrossRef]

Atomization Sprays (1)

G. Gouesbet and G. Grehan, "Generalized Lorenz-Mie theories, from past to future," Atomization Sprays 10, 277-333 (2000).

Exp. Fluids (1)

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, "Multi-dimensional particle sizing techniques," Exp. Fluids 39, 336-350 (2005).
[CrossRef]

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

Meas. Sci. Technol. (1)

N. Fujisawa, A. Hosokawa, and S. Tomimatsu, "Simultaneous measurement of droplet size and velocity field by an interferometric imaging technique in spray combustion," Meas. Sci. Technol. 14, 1341-1349 (2003).
[CrossRef]

Opt. Commun. (1)

T. Siebert, O. Sbanski, M. Schmitt, V. Engel, W. Kiefer, and J. Popp, "The mechanism of light storage in spherical microcavities explored on a femtosecond time scale," Opt. Commun. 216, 321-327 (2003).
[CrossRef]

Opt. Lett. (1)

Optik (1)

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

Part. Part. Syst. Charact. (2)

J. P. A. J. van Beeck, L. Zimmer, and M. L. Riethmuller, "Global rainbow thermometry for mean temperature and size measurement of spray droplets," Part. Part. Syst. Charact. 18, 196-204 (2001).
[CrossRef]

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

Phys. Rev. A (1)

J. P. Wolf, Y. L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, "Ballistic trajectories of optical wave packets within microcavities," Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J. P. Wolf, "White-light nanosource with directional emission," Phys. Rev. Lett. 89, 035002 (2002).
[CrossRef] [PubMed]

S. C. Hill, V. Boutou, J. Yu, S. Ramstein, J. P. Wolf, Y. L. Pan, S. Holler, and R. K. Chang, "Enhanced backward-directed multiphoton-excited flourescence from dielectric microcavities," Phys. Rev. Lett. 85, 54-57 (2000).
[CrossRef] [PubMed]

Science (2)

A. H. Zewail, "Laser femtochemistry," Science 242, 1645-1653 (1988).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (8)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

A. Frohn and N. Roth, Dynamics of Droplets (Springer-Verlag, 2000).

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, 2003).

M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry (Springer-Verlag, 1998).

J. Wilms, "Evaporation of multicomponent droplets," in Institut für Thermodynamik der Luft- und Raumfahrt (Universität Stuttgart, 2005), p. 157.

K. Heukelbach, J. Hom, and N. Chigier, "Capabilities and limitations of the rainbow refractometer, determined with temperature measurements of water droplets," presented at the ILASS-Americas 11th Annual Conference on Liquid Atomization and Spray Systems, Sacramento, Calif., 17-21 May 1998.

J. P. A. J. van Beeck, Rainbow Phenomena: Development of a Laser Based, Non-Intrusive Technique for Measuring Droplet Size Temperature and Velocity (Technische Universiteit Eindhoven, 1997).
[PubMed]

N. Damaschke, "Light scattering theories and their use for single particle characterization," in Fachgebiet Strömungslehre und Aerodynamik (Technische Universität Darmstadt, 2003).

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Figures (9)

Fig. 1
Fig. 1

Numerically obtained angular intensity distributions in the far field of a spherical, homogeneous droplet ( d = 94 μ m , n = 1.333 ). (a) Individual scattering orders, namely reflection and diffraction (dashed curve), first-order refraction (dashed and dotted curves), second-order refraction with first rainbow (solid line), and third-order refraction with second rainbow (dotted curve). (b) The Mie sum is a result of interfering scattering orders for continuous illumination at λ = 780   nm . (c) Simulated 70   fs pulses at a central wavelength of λ = 780   nm yield a Mie sum that follows from added intensities of different scattering orders.

Fig. 2
Fig. 2

Numerically obtained intensity distribution in the far field for a range of diameters of a spherical, homogeneous droplet ( n = 1.333 , ϑ = 70 ° ). (a) cw illumination with λ = 780   nm and (b) pulsed illumination with t pulse = 200   fs , λ = 780   nm .

Fig. 3
Fig. 3

Numerically obtained intensity distribution in the far field for a range of diameters of a spherical, homogeneous droplet ( n = 1.333 , ϑ = 7 0 ° ). (a) For cw illumination ( λ = 780   nm ) the contribution of MDRs becomes apparent on a nanometer scale. (b) For pulsed illumination ( t pulse = 200   fs , λ = 780   nm ) the intensity distribution is free of MDRs and scattering lobes.

Fig. 4
Fig. 4

For discrete angles ϑ of the intensity distribution of an illuminated spherical droplet with a refractive index n ray paths of scattering orders are given by geometrical optics. For the second-order refraction, two rays paths a and b exist. In the case of a sufficient coherence length they interfere with each other and with the reflection ray c in the far field. The resulting intensity can be observed with a camera.

Fig. 5
Fig. 5

Numerically obtained angular intensity distribution for (a) cw and (b) pulsed illumination ( t pulse = 200   fs , λ = 780   nm ) with regard to a spherical droplet ( d = 94 μ m , n = 1.333 ). (a) The Mie sum (full curve) follows from interference between surface reflection and second-order refraction, which obscures the underlying oscillations of the rainbow (dashed curve). (b) The intensity of the surface reflection adds to the intensity of the rainbow, leaving the position of its local maxima.

Fig. 6
Fig. 6

Experimentally obtained angular intensity distribution for (a) cw and (b) pulsed illumination ( t pulse = 200   fs , λ = 780   nm ) with regard to a monodisperse stream of spherical droplets ( d = 94 μ m and n = 1.333 ).

Fig. 7
Fig. 7

(a) Experimental setup for measuring MDRs: (1) Ti:sapphire laser, (2) electrodynamic trap, (3) lens, (4) segmented photodiode, (5) computer with DA–AD card, (6) high voltage amplifier, (7) lens, (8) photodiode. (b) cross section of the electrodes of the electrodynamic trap.

Fig. 8
Fig. 8

Experimentally obtained temporal intensity distributions for (a) cw and (b) pulsed illumination ( t pulse = 200   fs , λ = 780   nm ) with regard to levitated droplets ( n = 1.333 ) and a receiver angle of 70°.

Fig. 9
Fig. 9

Enlarged representation of the temporal intensity distributions of Fig. 8 emphasizing the contribution of MDRs for (a) cw and (b) pulsed illumination ( t pulse = 200   fs , λ = 780   nm ) with regard to levitated droplets ( n = 1.333 ) and a receiver angle of 70°.

Equations (4)

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E ( z , t ) = E 0 ( x , y , z ) exp [ j ω 0 ( t k z 0 z ) ] × exp [ 8 t pulse 2 ( t k z 0 z ) ] ,
A i = E 0 1 2 T π 2  exp { [ ( ω 0 i Δ ω ) t pulse ] 2 32 } ,
ω 0 Δ ω ( 1 32 L ω 0 t pulse ) i ω 0 Δ ω ( 1 32 L ω 0 t pulse ) .
E s ( t ) = i min i max E s ( i ) exp ( j i Δ ω t ) .

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