Abstract

After a historical review of previous research into cooperative scattering, a theoretical investigation of the effects of interparticle coupling on morphology-dependent resonances of spheres is conducted. Bispheres composed of identical, slightly dissimilar, and very different monomers are considered. Calculations are presented of resonance spectra for selected orientations of the bispheres relative to the incident wave vector along with spectra that should prove useful in describing the scattering properties of a monodisperse ensemble of randomly oriented bispheres. (The bispheres in this dispersion may be constituted from dissimilar monomers.) Normalized source functions for regions inside and near the scatterers are also provided. Finally a numerical simulation of an interesting experiment is carried out in which a resonating aerosol passes through the focal volume of a relatively large, spherical microlens.

© 1991 Optical Society of America

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    [Crossref]
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    [Crossref]
  7. K. Germey, “Die Beugung einer ebenen elektromagnetische Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,” Ann. Phys. 13, 237–251 (1964).
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  19. B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).
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  21. O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).
  22. C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).
  23. J. H. Bruning, Y. T. Lo, “Multiple scattering of em waves by spheres. I. Multiple expansion and ray-optics solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971) II.“Multiple scattering of em waves by spheres. II. Numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
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  24. B. Peterson, S. Ström, “T matrix for eletromagnetic scattering from an arbitrary number of scatterers and representations of E(3),” Phys. Rev. D 8, 3661–3678 (1973).
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    [Crossref]
  31. R. T. Wang, “Extinction signatures of nonspherical/nonisotropic particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980).
  32. R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental results of dependent light scattering by two spheres,” Opt. Lett. 6, 543–545 (1981).
    [Crossref] [PubMed]
  33. G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980).
    [Crossref]
  34. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [Crossref]
  35. S. B. Singham, C. F. Bohren, “Hybrid method in light scattering by an arbitrary particle,” Appl. Opt. 28, 517–522 (1989).
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    [Crossref] [PubMed]
  38. K. A. Fuller, Ph.D. dissertation (Department of Physics, Texas A&M University, College Station, Tex., 1987).
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    [Crossref] [PubMed]
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    [Crossref]
  42. R. Thurn, W. Kiefer, “Structural resonances in the Raman spectra of optically levitated liquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
    [Crossref] [PubMed]
  43. K. A. Fuller, “Some novel features of morphology dependent resonances of bispheres,” Appl. Opt. 28, 3788–3790 (1989).
    [Crossref] [PubMed]
  44. J. P. Barton, D. R. Alexander, S. A. Shaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [Crossref]
  45. M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometric optics,” Appl. Opt. 28, 4962–4965 (1989).
    [Crossref] [PubMed]
  46. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
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  48. M. F. R. Cooray, I. R. Ciric, “Electromagnetic wave scattering by a system of two spheroids of arbitrary orientation,” IEEE Trans. Antennas Propag. 37, 608–619 (1989).
    [Crossref]
  49. D. L. Gresh, “Voyager radio occultation by the Uranian rings: structure, dynamics, and particle sizes,” Sci. Rep. D845-1990-1 (Center for Radar Astronomy, Stanford Electronics Laboratory, Standford University, Stanford, Calif. 94305-4055).

1989 (6)

1988 (3)

1987 (2)

1986 (3)

1985 (2)

SeeM. Inoue, K. Ohtaka, “Enhanced Raman scattering by a two-dimensional array of dielectric spheres,” Phys. Rev. B 26, 3487–3490 (1985) and references contained therein.
[Crossref]

R. Thurn, W. Kiefer, “Structural resonances in the Raman spectra of optically levitated liquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
[Crossref] [PubMed]

1983 (1)

1981 (1)

1978 (1)

1975 (1)

J. W. Young, J. C. Bertrand, “Multiple scattering by two cylinders,” J. Acoust. Soc. Am. 58, 1190–1195 (1975).
[Crossref]

1973 (2)

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

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

1971 (1)

J. H. Bruning, Y. T. Lo, “Multiple scattering of em waves by spheres. I. Multiple expansion and ray-optics solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971) II.“Multiple scattering of em waves by spheres. II. Numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[Crossref]

1970 (1)

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

1967 (1)

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

1965 (2)

1964 (2)

V. Twersky, “Rayleigh scattering,” Appl. Opt. 3, 1150–1162 (1964).
[Crossref]

K. Germey, “Die Beugung einer ebenen elektromagnetische Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,” Ann. Phys. 13, 237–251 (1964).
[Crossref]

1963 (1)

O. A. Germogenova, “The scattering of a plane electromagnetic wave by two spheres,” Izv. Akad. Nauk SSR Ser. Geofiz. XX, 648–653(1963).

1962 (1)

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

1961 (2)

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

N. R. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering I and II,” J. Math. Phys. 2, 394–406 (1961).
[Crossref]

1954 (1)

B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).

1952 (1)

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[Crossref]

1933 (1)

W. Trinks, “Zur Vielfachstreuung an kleinen Kugeln,” Ann. Phys. Dtsch. 22, 561–590 (1933).

1929 (1)

J. A. Gaunt, “The triplets of helium,” Philos. Trans. R. Soc. London Ser. A 228, 151–196 (1929).
[Crossref]

1863 (1)

R. F. A. Clebsch, “Ueber die Reflexion an einer Kugelfläche,” Crelle's J. 61, 195–251(1863).

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Shaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

Barakat, R.

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Shaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

Bennett, H. S.

Bertrand, J. C.

J. W. Young, J. C. Bertrand, “Multiple scattering by two cylinders,” J. Acoust. Soc. Am. 58, 1190–1195 (1975).
[Crossref]

Bohren, C. F.

Borghese, F.

Bruning, J. H.

J. H. Bruning, Y. T. Lo, “Multiple scattering of em waves by spheres. I. Multiple expansion and ray-optics solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971) II.“Multiple scattering of em waves by spheres. II. Numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[Crossref]

Chang, R. K.

Ciric, I. R.

M. F. R. Cooray, I. R. Ciric, “Electromagnetic wave scattering by a system of two spheroids of arbitrary orientation,” IEEE Trans. Antennas Propag. 37, 608–619 (1989).
[Crossref]

Clebsch, R. F. A.

R. F. A. Clebsch, “Ueber die Reflexion an einer Kugelfläche,” Crelle's J. 61, 195–251(1863).

Cooray, M. F. R.

M. F. R. Cooray, I. R. Ciric, “Electromagnetic wave scattering by a system of two spheroids of arbitrary orientation,” IEEE Trans. Antennas Propag. 37, 608–619 (1989).
[Crossref]

Cruzan, O. R.

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

Dean, C. E.

Denti, P.

Friedman, B.

B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).

Fukumitsu, O.

Fuller, K. A.

Gaunt, J. A.

J. A. Gaunt, “The triplets of helium,” Philos. Trans. R. Soc. London Ser. A 228, 151–196 (1929).
[Crossref]

Germey, K.

K. Germey, “Die Beugung einer ebenen elektromagnetische Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,” Ann. Phys. 13, 237–251 (1964).
[Crossref]

Germogenova, O. A.

O. A. Germogenova, “The scattering of a plane electromagnetic wave by two spheres,” Izv. Akad. Nauk SSR Ser. Geofiz. XX, 648–653(1963).

Greenberg, J. M.

Gresh, D. L.

D. L. Gresh, “Voyager radio occultation by the Uranian rings: structure, dynamics, and particle sizes,” Sci. Rep. D845-1990-1 (Center for Radar Astronomy, Stanford Electronics Laboratory, Standford University, Stanford, Calif. 94305-4055).

Heaviside, O.

O. Heaviside, Electromagnetic Theory (Dover, New York, 1950), Sec.182.

Humphreys, T. J.

G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Inoue, M.

SeeM. Inoue, K. Ohtaka, “Enhanced Raman scattering by a two-dimensional array of dielectric spheres,” Phys. Rev. B 26, 3487–3490 (1985) and references contained therein.
[Crossref]

Jarzembski, M. A.

Karp, S. N.

N. R. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering I and II,” J. Math. Phys. 2, 394–406 (1961).
[Crossref]

Kattawar, G. W.

Kiefer, W.

Köhler, S.

Lakhtakia, A.

Liang, C.

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

Lind, A. C.

Lo, Y. T.

J. H. Bruning, Y. T. Lo, “Multiple scattering of em waves by spheres. I. Multiple expansion and ray-optics solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971) II.“Multiple scattering of em waves by spheres. 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).

Logan, N. A.

N. A. Logan, “Survey of some early studies of the scattering of a plane wave by a sphere,” Proc. IEEE 53, 773–785 (1965).
[Crossref]

Ohtaka, K.

SeeM. Inoue, K. Ohtaka, “Enhanced Raman scattering by a two-dimensional array of dielectric spheres,” Phys. Rev. B 26, 3487–3490 (1985) and references contained therein.
[Crossref]

Olaofe, G. O.

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

Pendleton, J. D.

J. D. Pendleton, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, N.M. 88002 (personal communication, 1990).

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Peterson, B.

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

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Rao, T. C.

Rayleigh, Lord

Lord Rayleigh, Scientific Papers IV (Cambridge U. Press, London, 1903).

Rosasco, G. J.

Russek, J.

B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).

Saija, R.

Schlicht, B.

Schuerman, D. W.

R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental results of dependent light scattering by two spheres,” Opt. Lett. 6, 543–545 (1981).
[Crossref] [PubMed]

D. W. Schuerman, “The Microwave Analog Facility at SUNYA: Capabilities and current programs,” in Light Scattering by Irregularly Shaped Particles., D. W. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Shaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Shaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

Sindoni, O. I.

Singham, S. B.

Srivastava, V.

Stein, S.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Ström, S.

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

Takenaka, T.

Thurn, R.

Toscano, G.

Trinks, W.

W. Trinks, “Zur Vielfachstreuung an kleinen Kugeln,” Ann. Phys. Dtsch. 22, 561–590 (1933).

Tsang, L.

L. Tsang (Department of Electrical Engineering, University of Washington, Seattle, Wash. 98195),J. K. Chou, L. S. Yian, “Light scattering by irregular particles and cluster structures using the T matrix method,” (unpublished).

Twersky, V.

V. Twersky, “Rayleigh scattering,” Appl. Opt. 3, 1150–1162 (1964).
[Crossref]

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[Crossref]

van de Hulst, H. C.

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

Varadan, V. K.

Varadan, V. V.

Wall, K. F.

Wang, R. T.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, London, 1962).

Yokota, M.

Young, J. W.

J. W. Young, J. C. Bertrand, “Multiple scattering by two cylinders,” J. Acoust. Soc. Am. 58, 1190–1195 (1975).
[Crossref]

Yousif, H. A.

Zitron, N. R.

N. R. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering I and II,” J. Math. Phys. 2, 394–406 (1961).
[Crossref]

Ann. Phys. (1)

K. Germey, “Die Beugung einer ebenen elektromagnetische Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,” Ann. Phys. 13, 237–251 (1964).
[Crossref]

Ann. Phys. Dtsch. (1)

W. Trinks, “Zur Vielfachstreuung an kleinen Kugeln,” Ann. Phys. Dtsch. 22, 561–590 (1933).

Appl. Opt. (8)

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Crelle's J. (1)

R. F. A. Clebsch, “Ueber die Reflexion an einer Kugelfläche,” Crelle's J. 61, 195–251(1863).

IEEE Trans. Antennas Propag. (2)

J. H. Bruning, Y. T. Lo, “Multiple scattering of em waves by spheres. I. Multiple expansion and ray-optics solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971) II.“Multiple scattering of em waves by spheres. II. Numerical and experimental results,” IEEE Trans. Antennas Propag. AP-19, 391–400 (1971).
[Crossref]

M. F. R. Cooray, I. R. Ciric, “Electromagnetic wave scattering by a system of two spheroids of arbitrary orientation,” IEEE Trans. Antennas Propag. 37, 608–619 (1989).
[Crossref]

Izv. Akad. Nauk SSR Ser. Geofiz. (1)

O. A. Germogenova, “The scattering of a plane electromagnetic wave by two spheres,” Izv. Akad. Nauk SSR Ser. Geofiz. XX, 648–653(1963).

J. Acoust. Soc. Am. (2)

V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” J. Acoust. Soc. Am. 24, 42–46 (1952).
[Crossref]

J. W. Young, J. C. Bertrand, “Multiple scattering by two cylinders,” J. Acoust. Soc. Am. 58, 1190–1195 (1975).
[Crossref]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, S. A. Shaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[Crossref]

J. Math. Phys. (1)

N. R. Zitron, S. N. Karp, “Higher-order approximations in multiple scattering I and II,” J. Math. Phys. 2, 394–406 (1961).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Opt. Lett. (4)

Philos. Trans. R. Soc. London Ser. A (1)

J. A. Gaunt, “The triplets of helium,” Philos. Trans. R. Soc. London Ser. A 228, 151–196 (1929).
[Crossref]

Phys. Rev. B (1)

SeeM. Inoue, K. Ohtaka, “Enhanced Raman scattering by a two-dimensional array of dielectric spheres,” Phys. Rev. B 26, 3487–3490 (1985) and references contained therein.
[Crossref]

Phys. Rev. D (1)

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

Proc. IEEE (1)

N. A. Logan, “Survey of some early studies of the scattering of a plane wave by a sphere,” Proc. IEEE 53, 773–785 (1965).
[Crossref]

Q. Appl. Math. (3)

B. Friedman, J. Russek, “Addition theorems for spherical waves,” Q. Appl. Math. 12, 13–23 (1954).

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

Radio Sci. (2)

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

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

Other (11)

O. Heaviside, Electromagnetic Theory (Dover, New York, 1950), Sec.182.

Lord Rayleigh, Scientific Papers IV (Cambridge U. Press, London, 1903).

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, London, 1962).

L. Tsang (Department of Electrical Engineering, University of Washington, Seattle, Wash. 98195),J. K. Chou, L. S. Yian, “Light scattering by irregular particles and cluster structures using the T matrix method,” (unpublished).

D. W. Schuerman, “The Microwave Analog Facility at SUNYA: Capabilities and current programs,” in Light Scattering by Irregularly Shaped Particles., D. W. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

R. T. Wang, “Extinction signatures of nonspherical/nonisotropic particles,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980).

K. A. Fuller, Ph.D. dissertation (Department of Physics, Texas A&M University, College Station, Tex., 1987).

G. W. Kattawar, T. J. Humphreys, “Electromagnetic scattering from two identical pseudospheres,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

D. L. Gresh, “Voyager radio occultation by the Uranian rings: structure, dynamics, and particle sizes,” Sci. Rep. D845-1990-1 (Center for Radar Astronomy, Stanford Electronics Laboratory, Standford University, Stanford, Calif. 94305-4055).

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

J. D. Pendleton, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, N.M. 88002 (personal communication, 1990).

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Figures (24)

Fig. 1
Fig. 1

Scattering-ladder representation of the OS process. A term of the form lk(j) is understood to be the wave vector of the jth-order multiply scattered field or the jth-order partial field emanating from the lth sphere, and lθ is the angle between the wave vectors lk(j) and the z axis.

Fig. 2
Fig. 2

Comparison of the resonance spectra of two cooperatively scattering spheres at different separations with that of a single sphere.

Fig. 3
Fig. 3

Comparison of the resonance spectrum of two identical spheres (taken from Fig. 1) with the spectra of bispheres with slightly dissimilar constituents. The two spheres are in contact in all cases.

Fig. 4
Fig. 4

Comparison of the resonance spectrum of two identical spheres with the spectrum of a system in which the size parameter of one of the spheres is 10% smaller than that of the other.

Fig. 5
Fig. 5

Effects of relatively small contaminants of various refractive indices on the resonance spectrum of the principal sphere.

Fig. 6
Fig. 6

Effects on the resonance spectrum of the principal sphere induced by a relatively small contaminant at various distances from its surface.

Fig. 7
Fig. 7

Spectrum of a resonating sphere in contact with a relatively small, highly absorbing particle. In contrast to previous figures the radiation impinges at broadside incidence. The case marked NIS is an approximation where dependent scattering is ignored. In the case of forward scattering this quantity is independent of the incident angle.

Fig. 8
Fig. 8

Illustration of the effect of orientation of the bisphere with respect to the incident wave vector: α is defined in Fig. 1. The incident field is polarized parallel to the plane of incidence. The bisphere consists of identical constituents with N = 2.

Fig. 9
Fig. 9

Same as in Fig. 8 but for incident polarization that is perpendicular to the plane of incidence. Also shown is the intensity calculated from the average of the fields scattered by the bisphere, which is rotated in steps of 5° from α = 0−90°, and for both polarizations.

Fig. 10
Fig. 10

Same as in Fig. 8 but for a bisphere made up of a small, highly absorbing contaminant that is attached to a principal sphere with N = 2.

Fig. 11
Fig. 11

Same as Fig. 9 except that the bisphere is like that in Fig. 10.

Fig. 12
Fig. 12

Illustration of the off-axis prominence in the source function that can arise in conditions of optical resonance. The source function is taken in the equatorial plane containing the incident field, and the resonance is TM 53 ( 1 ). The size parameter and the refractive index of the sphere are 40.7969233685 and 1.47, respectively. The plane wave propagates in the positive z direction and is incident on the sphere at z/a = −1. The source function is determined in this plane in all subsequent figures.

Fig. 13
Fig. 13

Source function of a nonresonant sphere with a refractive index of 2.0 and a size parameter of 10.614, which is taken in the same configuration as that in Fig. 12.

Fig. 14
Fig. 14

Source function for the case shown in Fig. 13 but with the sphere tuned to the TM 16 ( 1 ) resonance at ka = 10.5945365. Note that, as in the case depicted in Fig. 12, S is dominated by maxima, that are located just off the z axis.

Fig. 15
Fig. 15

Source function produced when two of the monomers of Fig. 14 are brought in contact. This bisphere is illuminated at endfire incidence with the extreme shadow surface tangent to z/a = 3. Note that the structure of, S which is characteristic of an optical resonance as seen in Fig. 14, has been replaced by a structure similar to that arising in the nonresonant monomer of Fig. 13.

Fig. 16
Fig. 16

Source function that arises when the bisphere of Fig. 15 is tuned to the resonance shown in Fig. 9 for the case of α = 0. This MDR is centered at ka = 10.614. As seen in Fig. 13 the source function of a single sphere of this size does not exhibit any resonance character. While S is greatly enhanced in the resonating bisphere it remains an order of magnitude below its largest values in the isolated sphere. Note also that the off-axis prominences seen in Fig. 14 are present in the bisphere as well.

Fig. 17
Fig. 17

Near-field source function of a sphere of ka = 50 and. N = 1.2 This figure is set up to illustrate the lensing properties of such a scatterer. Such a sphere is used as a lens for the investigation presented in Figs. 1824.

Fig. 18
Fig. 18

Source function of an isolated sphere of ka = 10.593 and N = 2.0, i.e., slightly off the TM 16 ( 1 ) resonance of Fig. 14.

Fig. 19
Fig. 19

Same as Fig. 18 but with sphere centered in the focal volume of the lens of Fig. 17.

Fig. 20
Fig. 20

Same as Fig. 19, but now the target sphere has been tuned to its TM 16 ( 1 ) MDR. The size parameter of this resonance differs slightly in scale from that of the monomer.

Fig. 21
Fig. 21

Same as Fig. 20 but with the target sphere located tangent to the optic axis of the lensing sphere.

Fig. 22
Fig. 22

Source function arising inside a resonating sphere located so that the optic axis of the lensing sphere coincides with the ray predicted by the localization principle to excite the TM 16 ( 1 ) resonance of the target sphere. The closest approach of the optic axis to the target surface is about one half of the target radius.

Fig. 23
Fig. 23

Same as Fig. 22. The scale of the z axis has been adjusted to display the structure of the source function better.

Fig. 24
Fig. 24

Same as Fig. 20 but with the surface of the target sphere located at ∼1 radius from the optic axis of the lensing sphere. Note that the scale of the z axis has been returned to that of Fig. 20.

Equations (14)

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E s = n = 1 m = n n l = 1 L ( A l E l m n N m n ( 3 ) + A l H mn 1 M m n ( 3 ) ) ,
M j m n ( 3 ) = ν = 1 μ = ν ν [ M l μ ν ( 1 ) A μ ν m n + N l μ ν ( 1 ) B μ ν m n ] , N j m n ( 3 ) = ν = 1 μ = ν ν [ N l μ ν ( 1 ) A μ ν m n + M l μ ν ( 1 ) B μ ν m n ] .
A μ ν m n = ( 1 ) μ i ν n 2 ν + 1 2 ν ( ν + 1 ) p = | n ν | n + ν ( i ) p [ n ( n + 1 ) + ν ( ν + 1 ) p ( p + 1 ) ] × a ( m , n , μ , ν , p ) ξ p ( k d j , l ) × P n m μ ( cos θ j , l ) exp [ i ( m μ ) ϕ j , l ] ,
B μ ν m n = ( 1 ) μ i ν n 2 ν + 1 2 ν ( ν + 1 ) p = | n ν | n + ν ( i ) p b ( m , n , μ , ν , p , p 1 ) × ξ p ( k d j , l ) P n m μ ( cos θ j , l ) exp [ i ( m μ ) ϕ j , l ] ,
b ( m , n , μ , ν , p , p 1 ) = 2 p + 1 2 p 1 [ ( ν μ ) ( ν + μ + 1 ) × a ( m , n , μ 1 , ν , p 1 ) ( p m + μ ) ( p m + μ + 1 ) × a ( m , n , μ + 1 , ν , p 1 ) + 2 μ ( p m + μ ) × a ( m , n , μ , ν , p 1 ) ] ,
P n m ( cos θ ) P ν μ ( cos θ ) = p | n ν | n + ν a ( m , n , μ , ν , p ) P p m + μ ( cos θ )
a ( m , n , μ , ν , p ) = 2 p + 1 2 ( p m μ ) ! ( p + m + μ ) ! 1 1 P n m ( x ) P ν μ ( x ) P p m + μ ( x ) d x .
A l E m n = υ l n [ p l m n + j l ν μ ( A j E μ ν A m n μ ν + A j H μ ν B m n μ ν ) ] , A l H m n = u l n [ q l m n + j l ν μ ( A j H μ ν A m n μ ν + A j E μ ν B m n μ ν ) ] ,
j = 0 l = 1 L E l s ( j ) ,
E l s ( j ) = n , m [ a l m n ( j ) N l m n ( 3 ) + b l m n ( j ) M l m n ( 3 ) ] .
a 1 m n ( j ) = υ 1 n ν μ [ a 2 μ ν ( j 1 ) A m n μ ν + b 2 μ ν ( j 1 ) B m n μ ν ] , b 1 m n ( j ) = u 1 n ν μ [ b 2 μ ν ( j 1 ) A m n m ν + a 2 μ ν ( j 1 ) B m n μ ν ] , a 2 m n ( j ) = υ 2 n ν μ [ a 1 μ ν ( j 1 ) A m n μ ν + b 1 μ ν ( j 1 ) B m n μ ν ] , b 2 m n ( j ) = u 2 n ν μ [ b 1 μ ν ( j 1 ) A m n μ ν + a 1 μ ν ( j 1 ) B m n μ ν ] .
A l E m n = j = 0 a l m n ( j ) , A l H m n = j = 0 b l m n ( j ) .
p l 1 , 39 ν ( A j E 1 ν A 1 , 39 1 ν + A j H 1 ν B 1 , 39 1 ν ) .
S ( r ) = | E t ( r ) | 2 | E 0 ( r ) | 2 ,

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