Abstract

Experimentally measured and theoretically calculated elastic light-scattering spectra from single microparticles illuminated by 100-fs pulses are presented. Although in the theoretical calculation only a single incoming femtosecond laser pulse was used, the spectral behavior of scattered light shows all the features seen in the experimental spectrum from many femtosecond pulses, including morphology-dependent resonances (MDR’s). The good agreement between experimental and theoretical elastic light-scattering data has stimulated a theoretical investigation of the time-dependent behavior of the elastically scattered light from a single microparticle on a femtosecond time scale. Since the spatial pulse length of the incoming laser pulse is smaller than the particle circumference, the temporal behavior of reflection, diffraction, refraction, and coupling into MDR’s can be distinguished. Since the time-dependent scattering is strongly dependent on particle size, refractive index, and pulse chirp, it may be possible to encode several bits of information into a single laser pulse and therefore to increase optical data communication rates.

© 2000 Optical Society of America

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References

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1999 (1)

J. Musick, J. Popp, W. Kiefer, “Raman spectroscopic and elastic light scattering investigations of chemical reactions in single electrodynamically levitated microparticles,” J. Mol. Struct. 480/481, 317–321 (1999).
[CrossRef]

1998 (2)

1997 (1)

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1992 (1)

1989 (1)

1986 (1)

S. X. Qian, R. K. Chang, “Multi-order Stokes emission from micrometer-sized droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

1985 (1)

Barber, P. W.

Bennemann, K. H.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Boutou, V.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Carroll, D.

D. Carroll, X. H. Zheng, “Modelling third harmonic generation from microdroplets,” Pure Appl. Opt. 7, L49–L55 (1998).
[CrossRef]

Chang, R. K.

Cheung, J. L.

Chowdhury, D. Q.

Dewitz, J. P.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Hartings, J. M.

Hill, S. C.

Hübner, W.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Kasparian, J.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Khaled, E. E. M.

Kiefer, W.

J. Musick, J. Popp, W. Kiefer, “Raman spectroscopic and elastic light scattering investigations of chemical reactions in single electrodynamically levitated microparticles,” J. Mol. Struct. 480/481, 317–321 (1999).
[CrossRef]

Krämer, B.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Leach, D. H.

Leisner, T.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Musick, J.

J. Musick, J. Popp, W. Kiefer, “Raman spectroscopic and elastic light scattering investigations of chemical reactions in single electrodynamically levitated microparticles,” J. Mol. Struct. 480/481, 317–321 (1999).
[CrossRef]

Popp, J.

J. Musick, J. Popp, W. Kiefer, “Raman spectroscopic and elastic light scattering investigations of chemical reactions in single electrodynamically levitated microparticles,” J. Mol. Struct. 480/481, 317–321 (1999).
[CrossRef]

Qian, S. X.

Rairoux, P.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Snow, J. B.

Vajda, S.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Vezin, B.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Wolf, J. P.

J. Kasparian, B. Krämer, T. Leisner, P. Rairoux, V. Boutou, B. Vezin, J. P. Wolf, “Size dependence of nonlinear Mie scattering in micro droplets illuminated by ultrashort pulses,” J. Opt. Soc. Am. B 15, 1918–1922 (1998).
[CrossRef]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Wöste, L.

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Zhang, J. Z.

Zheng, X. H.

D. Carroll, X. H. Zheng, “Modelling third harmonic generation from microdroplets,” Pure Appl. Opt. 7, L49–L55 (1998).
[CrossRef]

J. Mol. Struct. (1)

J. Musick, J. Popp, W. Kiefer, “Raman spectroscopic and elastic light scattering investigations of chemical reactions in single electrodynamically levitated microparticles,” J. Mol. Struct. 480/481, 317–321 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Lett. (2)

Phys. Rev. Lett. (2)

S. X. Qian, R. K. Chang, “Multi-order Stokes emission from micrometer-sized droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

J. Kasparian, B. Krämer, J. P. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hübner, J. P. Wolf, L. Wöste, K. H. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett. 78, 2952–2955 (1997).
[CrossRef]

Pure Appl. Opt. (1)

D. Carroll, X. H. Zheng, “Modelling third harmonic generation from microdroplets,” Pure Appl. Opt. 7, L49–L55 (1998).
[CrossRef]

Other (3)

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

R. K. Chang, A. J. Campillo, eds., Optical Processes in Microcavities, Vol. 3 of Advanced Series in Applied Physics (World Scientific, Singapore, 1996).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup. The ∼100-fs laser pulses from a Ti:sapphire laser system, operating at 800 nm and at a repetition rate of 78 MHz, are focused onto an ∼20-µm glass sphere. The glass sphere is levitated with an electrodynamic trap. The elastically scattered light is collected at 90° by a 50-mm lens and focused into a fiber that is connected to a spectrometer (Acton, 300 mm). A nitrogen-cooled CCD camera is used as a detection device.

Fig. 2
Fig. 2

Scattered intensity at 90° versus wavelength for the experimental spectrum (lower curve) and the calculated spectrum (upper curve). The theoretical spectrum assumes a glass sphere of radius of 19.68 µm with refractive index m=1.5454,000m-1×(λ-802nm) (normal dispersion), integrating over a solid angle of 10°. The resonances leading to the observed structure are marked TM(n,l).

Fig. 3
Fig. 3

Illustration of reflection, refraction, and diffraction of light at a spherical particle. Reflection and refraction can be calculated by geometrical optics (ray tracing), whereas diffraction cannot.

Fig. 4
Fig. 4

Calculated scattered intensity as a function of the retarded time as defined in Eq. (9) for the exact scattering angle of 90°. Although the incoming laser pulse is only ∼100 fs long, the scattered light reveals intensity peaks for several picoseconds.

Fig. 5
Fig. 5

Same as Fig. 4 but for five different scattering angles. To permit smaller intensity peaks to be recognized more easily, the square root of the intensity is shown.

Fig. 6
Fig. 6

Left, intensity of the first maximum that is recorded at the detector as a function of the scattering angle in a logarithmic scale. The shape of this curve looks very similar to the reflection curves from geometrical optics. The dashed curve from 0° to ∼15° gives the expected behavior for reflection only; the deviation of the calculated solid curve from the dashed curve can be explained by diffraction that occurs in this angle range. Right, the time delay of the first intensity peak in the scattered light that reaches the detector relative to the time that the scattered light needs to arrive at the detector in 180° backscattering. For more details, see text.

Fig. 7
Fig. 7

Magnified view of the square root of the scattered light intensity as a function of the retarded time for the three example scattering angles of 45°, 90°, and 135°, together with schematic drawings useful in explaining the different shapes of the pulses. For more details, see the text.

Fig. 8
Fig. 8

Time-dependent intensity (square root) at 90° for three particles of radius 19.68 µm but slightly different refractive indices. Although those differences are small, the scattered pulse shapes can easily be distinguished. For example, the relative intensities of the second and the third peaks in each pulse could be used as distinguishing criteria: The second peak becomes higher for increasing refractive index, whereas the third peak becomes smaller.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ψn(mx)ψn(mx)-mξn(x)ξn(x)=0,
mψn(mx)ψn(mx)-ξn(x)ξn(x)=0.
Qn,lleak=Re(xn,l)2 Im(xn,l)=ωn,lΔωn,l=ωn,lτn,l.
Einc(z, t)=Eˆ(z, t)exp[-iω0(t-z/c)]ix,
Eˆ(z, t)=E0 exp-12(t-z/c)2σt2.
Einc(z, t)=12π-dωEinc(ω)exp(ikz-iωt).
Einc(ω)=12π-dtEinc(z=0, t)exp(iωt)
=E0σωexp-12(ω-ω0)2σω2.
Eoutτ=t-zc=12π-dωEout(ω)exp(-iωτ).

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