Abstract

Resonant scattering from dielectric bispheres in the specular direction (the so-called specular resonance), previously known only in the microwave range, has been observed at the optical wavelength. Systematic experiments with micrometer-sized dielectric bispheres assembled by micromanipulation, together with rigorous numerical calculations, reveal that this scattering is a precursor of the classical rainbow and is a general phenomenon observed in the wide range of size parameters (>5 for n=1.59) for various refractive indices.

© 2002 Optical Society of America

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References

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  1. R. T. Wang, J. M. Greenberg, and D. W. Schuerman, Opt. Lett. 6, 543 (1981).
    [CrossRef] [PubMed]
  2. G. W. Kattawar and C. E. Dean, Opt. Lett. 8, 48 (1983).
    [CrossRef] [PubMed]
  3. K. A. Fuller, G. W. Kattawar, and R. T. Wang, Appl. Opt. 25, 2521 (1986).
    [CrossRef]
  4. Y.-L. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
    [CrossRef]
  5. H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
    [CrossRef]
  6. H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
    [CrossRef]
  7. H. M. Nussenzveig, Sci. Am. 236, 116 (1977).
    [CrossRef]

2000

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

1998

Y.-L. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

1986

1983

1981

1977

H. M. Nussenzveig, Sci. Am. 236, 116 (1977).
[CrossRef]

Dean, C. E.

Fuller, K. A.

Greenberg, J. M.

Jimba, Y.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Kattawar, G. W.

Miyazaki, H.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

Miyazaki, H. T.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

Nussenzveig, H. M.

H. M. Nussenzveig, Sci. Am. 236, 116 (1977).
[CrossRef]

Ohtaka, K.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

Sato, T.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

Schuerman, D. W.

Wang, R. T.

Xu, Y.-L.

Y.-L. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, J. Appl. Phys. 87, 7152 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. B

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Phys. Rev. E

Y.-L. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

Sci. Am.

H. M. Nussenzveig, Sci. Am. 236, 116 (1977).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Observation of light scattering by bispheres. (a) Scanning electron microscope image of a typical bisphere D=2.02 µm,n=1.58. The substrate is coated with a 90-nm-thick conductive indium tin oxide layer. (b) Coordinate system of the scattering measurement. The spheres are aligned along the z axis, and the surface of the substrate coincides with the xz plane. The wave vector of the incident light lies in the xz plane (the incidence plane) and makes an angle α with the z axis. The polarization perpendicular and parallel to the incidence plane is defined as s and p, respectively. (c) Scattering pattern when an s-polarized beam strikes the bisphere shown in (a) with α=25°. The scale underneath the figure indicates scattering angle θ. The honeycomb pattern is an artifact generated by the interference in the CCD, which is of little significance in the intensity profile. (d) Intensity profile of (c) along the x axis.

Fig. 2
Fig. 2

Incidence angle dependence of the scattering intensity distribution from bispheres for typical S and n. (a)–(d) Experimental results for micrometer-sized bispheres with n=1.59. (g)–(j) Corresponding results of calculation by wave optics. (a), (g) S=2.34; (b), (h) S=5.41; (c), (i) S=13.9; (d) S=50.7; and (j) S=40.0. As the calculation for S=50.7 did not reach sufficient numerical convergence, the result for S=40 is shown instead. (e) Experimental result for a single sphere on the substrate for S=13.9 and n=1.59. (k) Result of calculation by geometrical optics for a bisphere with n=1.59. (f), (l) Experimental result for a millmeter-sized bisphere with S=24,800 and n=1.52 and the corresponding calculation by use of geometrical optics, respectively.

Fig. 3
Fig. 3

Light propagation in the incidence plane for bispheres with various S for n=1.59 and α=25°. The incident light is s polarized. (a)–(c) Poynting vectors of the scattered field obtained by wave-optical calculation. The color indicates the magnitude of the Poynting vector. Red is large, and blue is small. (a) S=2.34, (b) S=5.41, and (c) S=40.0. (d) Rays calculated by means of ray tracing. Poynting vectors and rays with intensities larger than half the incident intensity are shown. I, F, and S are the directions of incidence, forward scattering, and specular reflection, respectively.

Fig. 4
Fig. 4

Relation between impact parameter b and scattering angle θ for bispheres with various n for α=25°. Only the rays that strike the first sphere and emerge from the second are considered.

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