Abstract

Ballistic light, i.e., radiation that propagates undeflected through a turbid medium, undergoes a small change in phase velocity and exhibits unusual dispersion because of its wave nature. We use a novel highly sensitive differential phase optical interferometer to study these previously unmeasurable phenomena. We find that ballistic propagation can be classified into three regimes based on the wavelength-to-size ratio. In the regime in which the scatterer size is comparable with the wavelength, there is an anomalous phase-velocity increase as a result of adding scatterers of higher refractive index. We also observe an anomaly in the relative phase velocity, where red light is slowed more than blue light even though the added scatterers are made of material with normal dispersion.

© 2001 Optical Society of America

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L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

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H. Matsumoto, Rev. Sci. Instrum. 65, 2894 (1994).
[CrossRef]

H. Matsumoto and L. Zeng, Opt. Commun. 104, 241 (1994).
[CrossRef]

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D. A. Benaron and D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

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Acedo, P.

J. Irby, R. Murray, P. Acedo, and H. Lamela, Rev. Sci. Instrum. 70, 699 (1999).
[CrossRef]

Alfano, R. R.

An, K.

Backman, V.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

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[CrossRef] [PubMed]

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Chandrasekhar, S.

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Chen, Z.

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L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Dasari, R. R.

de Boer, J. F.

Drexler, W.

Feld, M. S.

C. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 25, 1526 (2000).
[CrossRef]

C. Yang, K. An, L. T. Perelman, R. R. Dasari, and M. S. Feld, J. Opt. Soc. Am. A 16, 866 (1999).
[CrossRef]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Fujimoto, J. G.

Georgakoudi, I.

Hamamo, T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Hanlon, E. B.

Ippen, E. P.

Irby, J.

J. Irby, R. Murray, P. Acedo, and H. Lamela, Rev. Sci. Instrum. 70, 699 (1999).
[CrossRef]

Itzkan, I.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Kartner, F. X.

Lamela, H.

J. Irby, R. Murray, P. Acedo, and H. Lamela, Rev. Sci. Instrum. 70, 699 (1999).
[CrossRef]

Li, X. D.

Lima, C.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Manohanan, R.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Matsumoto, H.

H. Matsumoto, Rev. Sci. Instrum. 65, 2894 (1994).
[CrossRef]

H. Matsumoto and L. Zeng, Opt. Commun. 104, 241 (1994).
[CrossRef]

Morgner, U.

Murray, R.

J. Irby, R. Murray, P. Acedo, and H. Lamela, Rev. Sci. Instrum. 70, 699 (1999).
[CrossRef]

Nelson, J. S.

Nusrat, A.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Perelman, L. T.

C. Yang, K. An, L. T. Perelman, R. R. Dasari, and M. S. Feld, J. Opt. Soc. Am. A 16, 866 (1999).
[CrossRef]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Pitris, C.

Saxer, C.

Seiler, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Shields, S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Stevenson, D. K.

D. A. Benaron and D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

Van Dam, J.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

Wallace, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Wax, A.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Xiang, S.

Yang, C.

Yoo, K. M.

Zeng, L.

H. Matsumoto and L. Zeng, Opt. Commun. 104, 241 (1994).
[CrossRef]

Zhao, Y.

Zonios, G.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

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

Opt. Commun. (1)

H. Matsumoto and L. Zeng, Opt. Commun. 104, 241 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manohanan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamamo, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, Phys. Rev. Lett. 80, 627 (1998).
[CrossRef]

Rev. Sci. Instrum. (2)

H. Matsumoto, Rev. Sci. Instrum. 65, 2894 (1994).
[CrossRef]

J. Irby, R. Murray, P. Acedo, and H. Lamela, Rev. Sci. Instrum. 70, 699 (1999).
[CrossRef]

Science (1)

D. A. Benaron and D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: M1, M2, mirrors (M1 is the reference mirror); BS, beam splitter; D1, D2, photodetectors; DM, 400-nm–800-nm dichroic mirror; ADC, analog–digital converter.

Fig. 2
Fig. 2

Phase-velocity difference versus scatterer radius. The data points show the measured values. Theoretical fits based on the van de Hulst model and the Mie theory solution are shown.

Fig. 3
Fig. 3

Modeled normalized phase velocity Δv/ηv0 versus normalized scatterer size ρ. The normalized refractive-index difference, m-1, equals 0.2 for this plot.

Equations (6)

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

ΔLk2,k1=Ψ2-2Ψ1k2.
Δv2v0-Δv1v0=-ΔLk2,k1n0L,
EL=E0exp-ikncxL=E0exp-ikn-inL,
n=1+2πNk3 ImS0,
n=2πNk3 ReS0,
Δvv0=1-n=-3η2a3k3ka2sinρρ2-cosρρ,

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