Abstract

We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40° to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by simple two-wave interference models.

© 2003 Optical Society of America

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    [CrossRef]
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  49. T. Fujimura, K. Edamatsu, T. Itoh, R. Shimada, A. Imada, T. Koda, N. Chiba, H. Muramatsu, T. Ataka, “Scanning near-field optical images of ordered polystyrene particle layers in transmission and luminescence excitation modes,” Opt. Lett. 22, 489–491 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
  51. S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
    [CrossRef]
  52. M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
    [CrossRef]
  53. R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
    [CrossRef]
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    [CrossRef]

2002

2001

Y.-L. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Y. Yin, Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

2000

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

H. Miyazaki, Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[CrossRef]

H. Ishikawa, H. Tamaru, K. Miyano, “Microsphere resonators strongly coupled to a plane dielectric substrate: coupling via optical near field,” J. Opt. Soc. Am. A 17, 802–813 (2000).
[CrossRef]

1999

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

H. Yukawa, S. Arnold, K. Miyano, “Microcavity effect of dyes adsorbed on a levitated droplet,” Phys. Rev. A 60, 2491–2496 (1999).
[CrossRef]

H. Ishikawa, H. Tamaru, K. Miyano, “Observation of a modulation effect caused by a microsphere resonator strongly coupled to a dielectric substrate,” Opt. Lett. 24, 643–645 (1999).
[CrossRef]

T. Yamasaki, T. Tsutsui, “Fabrication and optical properties of two-dimensional ordered arrays of silica microspheres,” Jpn. J. Appl. Phys. 38, 5916–5921 (1999).
[CrossRef]

1998

H. Miyazaki, K. Ohtaka, “Near-field images of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 58, 6920–6937 (1998).
[CrossRef]

R. L. Lee, “Mie theory, Airy theory, and the natural rainbow,” Appl. Opt. 37, 1506–1519 (1998).
[CrossRef]

A. Gotoh, K. Kamiya, F. Ikazaki, “Preparation of nano-sized complex particles regulated by the number of particle constituents,” J. Mater. Sci. Lett. 17, 1195–1197 (1998).
[CrossRef]

Y.-L. Xu, R. T. Wang, “Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix,” Phys. Rev. E 58, 3931–3948 (1998).
[CrossRef]

1997

T. Fujimura, K. Edamatsu, T. Itoh, R. Shimada, A. Imada, T. Koda, N. Chiba, H. Muramatsu, T. Ataka, “Scanning near-field optical images of ordered polystyrene particle layers in transmission and luminescence excitation modes,” Opt. Lett. 22, 489–491 (1997).
[CrossRef] [PubMed]

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

1996

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

1995

1991

1988

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

1986

1984

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

1983

1982

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

1981

1980

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

1979

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

K. Ohtaka, “Energy band of photons and low-energy photon diffraction,” Phys. Rev. B 19, 5057–5067 (1979).
[CrossRef]

1977

H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 236, 116–127 (1977).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

1973

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

1971

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part I—multiple expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part II—numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[CrossRef]

1967

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Alexander, D. R.

Arnold, S.

H. Yukawa, S. Arnold, K. Miyano, “Microcavity effect of dyes adsorbed on a levitated droplet,” Phys. Rev. A 60, 2491–2496 (1999).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Ataka, T.

Ausloos, M.

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Barton, J. P.

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Blanco, A.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Bohren, C. F.

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

Borghese, F.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Bruning, J. H.

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part I—multiple expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part II—numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[CrossRef]

Chang, R. K.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Chiba, N.

Chrissoulidis, D. P.

Dean, C. E.

Denti, P.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Edamatsu, K.

Fornes, V.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Fujimura, T.

Fujishima, A.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Fukui, M.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

Fuller, K. A.

Gérardy, J. M.

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

Gotoh, A.

A. Gotoh, K. Kamiya, F. Ikazaki, “Preparation of nano-sized complex particles regulated by the number of particle constituents,” J. Mater. Sci. Lett. 17, 1195–1197 (1998).
[CrossRef]

Greenberg, J. M.

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, Cambridge, UK, 1980).

Gustafson, B. Å. S.

Y.-L. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Haraguchi, M.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

Huffman, D. R.

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

Ikazaki, F.

A. Gotoh, K. Kamiya, F. Ikazaki, “Preparation of nano-sized complex particles regulated by the number of particle constituents,” J. Mater. Sci. Lett. 17, 1195–1197 (1998).
[CrossRef]

Imada, A.

Imhof, A.

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

Ioannidou, M. P.

Ishikawa, H.

Itoh, T.

Jimba, Y.

H. Miyazaki, Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Kamiya, K.

A. Gotoh, K. Kamiya, F. Ikazaki, “Preparation of nano-sized complex particles regulated by the number of particle constituents,” J. Mater. Sci. Lett. 17, 1195–1197 (1998).
[CrossRef]

Kattawar, G. W.

Koda, T.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

T. Fujimura, K. Edamatsu, T. Itoh, R. Shimada, A. Imada, T. Koda, N. Chiba, H. Muramatsu, T. Ataka, “Scanning near-field optical images of ordered polystyrene particle layers in transmission and luminescence excitation modes,” Opt. Lett. 22, 489–491 (1997).
[CrossRef] [PubMed]

Komori, Y.

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

Kuwata-Gonokami, M.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Lagendijk, A.

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

Lee, R. L.

Liang, C.

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Lo, Y. T.

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part I—multiple expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part II—numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[CrossRef]

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Lopez, C.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Lynch, D. K.

Ma, W.

Mackowski, D. W.

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[CrossRef]

Matsushita, S. I.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Mayoral, R.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Meseguer, F.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Mifsud, A.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Miguez, H.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Miwa, T.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Miyano, K.

Miyazaki, H.

H. T. Miyazaki, H. Miyazaki, K. Miyano, “Anomalous scattering from dielectric bispheres in the specular direction,” Opt. Lett. 27, 1208–1210 (2002).
[CrossRef]

H. Miyazaki, Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[CrossRef]

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

H. Miyazaki, K. Ohtaka, “Near-field images of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 58, 6920–6937 (1998).
[CrossRef]

Miyazaki, H. T.

H. T. Miyazaki, H. Miyazaki, K. Miyano, “Anomalous scattering from dielectric bispheres in the specular direction,” Opt. Lett. 27, 1208–1210 (2002).
[CrossRef]

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

Mukaiyama, T.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Muramatsu, H.

Nakai, T.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

Nussenzveig, H. M.

Ocana, M.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Ohtaka, K.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

H. Miyazaki, K. Ohtaka, “Near-field images of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 58, 6920–6937 (1998).
[CrossRef]

K. Ohtaka, “Energy band of photons and low-energy photon diffraction,” Phys. Rev. B 19, 5057–5067 (1979).
[CrossRef]

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M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

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B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

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A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

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F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Sato, T.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

Schaub, S. A.

Schuerman, D. W.

Schwartz, P.

Shimada, R.

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

T. Fujimura, K. Edamatsu, T. Itoh, R. Shimada, A. Imada, T. Koda, N. Chiba, H. Muramatsu, T. Ataka, “Scanning near-field optical images of ordered polystyrene particle layers in transmission and luminescence excitation modes,” Opt. Lett. 22, 489–491 (1997).
[CrossRef] [PubMed]

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M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

Sindoni, O. I.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Skaropoulos, N. C.

Spirk, R.

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Ström, S.

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

Takeda, K.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Tamaru, H.

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Tryk, D. A.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Tsutsui, T.

T. Yamasaki, T. Tsutsui, “Fabrication and optical properties of two-dimensional ordered arrays of silica microspheres,” Jpn. J. Appl. Phys. 38, 5916–5921 (1999).
[CrossRef]

van Blaaderen, A.

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

van de Hulst, H. C.

Vazquez, L.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Vos, W. L.

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

Wang, R. T.

Wegdam, G. H.

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

Wiltzius, P.

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Xia, Y.

Y. Yin, Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

Xu, Y.-L.

Y.-L. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Y.-L. Xu, R. T. Wang, “Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix,” Phys. Rev. E 58, 3931–3948 (1998).
[CrossRef]

Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yagi, Y.

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Yamasaki, T.

T. Yamasaki, T. Tsutsui, “Fabrication and optical properties of two-dimensional ordered arrays of silica microspheres,” Jpn. J. Appl. Phys. 38, 5916–5921 (1999).
[CrossRef]

Yin, Y.

Y. Yin, Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

Yukawa, H.

H. Yukawa, S. Arnold, K. Miyano, “Microcavity effect of dyes adsorbed on a levitated droplet,” Phys. Rev. A 60, 2491–2496 (1999).
[CrossRef]

Adv. Mater.

Y. Yin, Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

Aerosol. Sci. Technol.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol. Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part II—numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres, part I—multiple expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971).
[CrossRef]

J. Appl. Phys.

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

J. Mater. Sci. Lett.

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[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transf.

Y.-L. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Jpn. J. Appl. Phys.

M. Haraguchi, T. Nakai, A. Shinya, T. Okamoto, M. Fukui, T. Koda, R. Shimada, K. Ohtaka, K. Takeda, “Optical modes in two-dimensionally ordered dielectric spheres,” Jpn. J. Appl. Phys. 39, 1747–1751 (2000).
[CrossRef]

T. Yamasaki, T. Tsutsui, “Fabrication and optical properties of two-dimensional ordered arrays of silica microspheres,” Jpn. J. Appl. Phys. 38, 5916–5921 (1999).
[CrossRef]

Langmuir

S. I. Matsushita, Y. Yagi, T. Miwa, D. A. Tryk, T. Koda, A. Fujishima, “Light propagation in composite two-dimensional arrays of polystyrene spherical particles,” Langmuir 16, 636–642 (2000).
[CrossRef]

Mol. Cryst. Liq. Cryst.

R. Shimada, Y. Komori, T. Koda, T. Fujimura, T. Itoh, K. Ohtaka, “Photonic band effect in ordered polystyrene particle layers,” Mol. Cryst. Liq. Cryst. 349, 5–8 (2000).
[CrossRef]

Nature

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. A

H. Yukawa, S. Arnold, K. Miyano, “Microcavity effect of dyes adsorbed on a levitated droplet,” Phys. Rev. A 60, 2491–2496 (1999).
[CrossRef]

Phys. Rev. B

W. L. Vos, R. Spirk, A. van Blaaderen, A. Imhof, A. Lagendijk, G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16231–16235 (1996).
[CrossRef]

H. Miyazaki, K. Ohtaka, “Near-field images of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 58, 6920–6937 (1998).
[CrossRef]

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25, 4204–4229 (1982).
[CrossRef]

K. Ohtaka, “Energy band of photons and low-energy photon diffraction,” Phys. Rev. B 19, 5057–5067 (1979).
[CrossRef]

H. Miyazaki, Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000).
[CrossRef]

Phys. Rev. D

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3678 (1973).
[CrossRef]

Phys. Rev. E

Y.-L. Xu, R. T. Wang, “Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix,” Phys. Rev. E 58, 3931–3948 (1998).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
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[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

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D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
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Speaking exactly, E1and E2are true caustics for n≤1.50but not caustics for n>1.50.However, since dθ/dbhas a value close to zero, and a large number of rays about b=0contribute to this trajectory, obvious structures can still be seen at n=1.58[Figs. 2(f) and (g) ]. Moreover, each E1and E2is generally composed of two finer structures at n<1.50.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

gmm01f.f at www.astro.ufl.edu/~xu .

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

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

In Refs. 15-18the ratio of the rigorous solution to the NIS solution was used to show the magnitude of specular resonance. However, in this paper we discuss their difference rather than their ratio. This is because the ratio can have a meaninglessly large value when the NIS amplitude is very small and is not a good measure of the magnitude of the specular resonance, in which the brightness of the ray rather than the degree of enhancement is important.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (13)

Fig. 1
Fig. 1

Coordinate system of a bisphere. Two spheres with a common refractive index n are aligned along the z axis. The wave vector of the incident light lies in the xz plane (incidence plane) and makes an angle α with the z axis. The incident light first strikes the lower (first) sphere at z0 and then enters the upper (second) sphere at z0. The polarization perpendicular and parallel to the incidence plane is defined as s and p, respectively. Note that the scattering angle θ is defined as the angle between the scattered light and the z axis.

Fig. 2
Fig. 2

Incidence angle α dependence of the scattering intensity distribution (αθ diagrams) from bispheres in the resonance and geometrical-optics regimes for typical refractive indices n: (a)–(d) results of rigorous calculations for S=15; (e)–(h) results of geometrical-optics calculations; (a), (e) n=1.44, s polarization; (b), (f) n=1.58, s polarization; (c), (g) n=1.58, p polarization; (d), (h) n=1.84, s polarization. AG2 indicate characteristic structures: A, forward scattering; B, specular resonance (divided into substructures B1B3); C, backward scattering; D1G2 are discussed in Section 4.

Fig. 3
Fig. 3

Size S and incidence angle α dependence of the scattering intensity in the specular direction (θ=-α) for typical refractive indices n: n=(a) 1.44, (b) 1.58, (c) 1.84, for s-polarized incident light. Lower panels are the results of the rigorous calculations. Upper panels are the results of the geometrical-optics calculations (S). P denotes the peak of the scattering intensity in the specular direction in the limit of the geometrical optics. The light curves in the upper panels show the magnified intensity to emphasize the structure Q around the backscattering.

Fig. 4
Fig. 4

Refractive index n and incidence angle α dependence of the scattering intensity in the specular direction in the resonance and geometrical-optics regimes for s-polarized incident light: (a) results of rigorous calculations for S=15, (b) results of geometrical-optics calculations.

Fig. 5
Fig. 5

Size S, refractive index n, and incidence angle α dependence of the specular resonance intensity from bispheres. The difference between the rigorous solution of the scattering in the specular direction and the NIS solution in the same direction is plotted. The contours show that both solutions have equal values. Panels (a), (b), and (c) show S dependence for s-polarized incident light for n=1.44, 1.58, and 1.84, respectively [corresponding to Figs. 3(a), 3(b), and 3(c) ]. Panels (d) and (e) show n dependence for s-polarized incident light for S=15 and the geometrical-optics limit, respectively [corresponding to Figs. 4(a) and 4(b) ]. These figures are plotted in a linear scale and in a reversed contrast.

Fig. 6
Fig. 6

Important structures observed in the incidence angle α dependence of the scattering intensity distribution from bispheres (αθ diagrams). Typical trajectory of light that yields each structure is schematically illustrated.

Fig. 7
Fig. 7

(a) Schematic illustration to explain the impact parameter b. The impact parameter is the ratio of the distance between the incident ray and the center of the first sphere to the sphere’s radius R. (b)–(f) Relationship between the impact parameter b and the scattering angle θ for various refractive indices n and incidence angles α: α=(b) 0°, (c) 10°, (d) 20°, (e) 25°, (f) 30°. When dθ/db=0, the trajectory for this b forms a caustic. The dashed horizontal lines in the lower panels are the specular directions.

Fig. 8
Fig. 8

Incidence angle α dependence of the scattering intensity distribution (αθ diagram) from two identical cylinders in contact in the geometrical-optics regime for n=1.58 and s polarization.  

Fig. 9
Fig. 9

(a) Size S and incidence angle α dependence of the internal intensity for n=1.58 and s polarization, (b) corresponding far-field intensity of the specular resonance. Modes written in (a) follow the notation in Ref. 21. For example, 21TE1 means a transverse electric mode with an angular momentum number of 21 and a radial mode number of 1.

Fig. 10
Fig. 10

(a) Schematic illustration to explain the interference of the specular-resonance wave and a reflected wave from the surface of the sphere, (b)–(d) comparison between the rigorous solution of the specular resonance shown in Fig. 3 and the two-wave interference model. Superimposed curves show the maxima of the interference. Refractive index n=(b) 1.44, (c) 1.58, (d) 1.84, for s polarization. (e) Comparison between the exact solution of the specular resonance shown in Fig. 4 and the two-wave interference model. Agreement between the bright fringes of the exact solution and the curves of the interference model is good, especially at α40°.    

Fig. 11
Fig. 11

(a) Schematic illustration to explain the interference of scattered waves from two point scatterers, (b)–(e) incidence angle α dependence of the scattering intensity distribution (αθ diagrams) from bispheres for n=1.58 and s polarization. Maxima of the interference model are superimposed: S=(b) 2, (c) 4, (d) 10, (e) 25.

Fig. 12
Fig. 12

Incidence angle α dependence of the scattering intensity distribution (αθ diagrams) from bispheres with a finite gap between the spheres for n=1.58 and s polarization. (a)–(c) Results of rigorous calculations for S=15, (d)–(f) results of geometrical-optics calculations: Dg=(a), (d) 0.5R; (b), (e) R; (c), (f) 1.5R.

Fig. 13
Fig. 13

(a)–(f) Incidence angle α dependence of the scattering intensity distribution (αθ diagrams) from bispheres made of spheres with different sizes for n=1.58 and s polarization. (a)–(c) Results of rigorous calculations. Size of the spheres was determined so that average diameter corresponds to S=15. (d)–(f) Results of geometrical-optics calculations. (a), (d) R1:R2=3:1; (b), (e) R1:R2=1:1, same as Figs. 2(b) and 2(f), respectively; (c), (f) R1:R2=1:3. (g) Schematic illustration to explain the spherical-lens model; (h) schematic illustration to show the maximum incidence angle α0 that yields the specular resonance. The relationships between θ and α based on the spherical-lens model are superimposed in (d)–(f). Critical angle α0 is also shown by arrows on the right.

Tables (1)

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Table 1 Size Ranges Yielding Conspicuous Structures B1 through G2 and Scattering Intensity by Geometrical-Optics Theory

Equations (2)

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2S(2n-1-cos α+sin α)=2mπ,
S(cos α-cos θ)=mπ,

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