Abstract

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.

© 2012 Optical Society of America

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References

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  1. P. L. Marston, J. Opt. Soc. Am. A 69, 1205 (1979).
    [CrossRef]
  2. P. L. Marston and D. L. Kingsbury, J. Opt. Soc. Am. A 71, 358 (1981).
    [CrossRef]
  3. D. S. Langley and P. L. Marston, Appl. Opt. 23, 1044(1984).
    [CrossRef]
  4. C. E. Dean and P. L. Marston, Appl. Opt. 30, 4764(1991).
    [CrossRef]
  5. G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).
  6. N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
    [CrossRef]
  7. J. A. Lock, J. Opt. Soc. Am. A 20, 499 (2003).
    [CrossRef]
  8. H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).
  9. F. Onofri, M. Krzysiek, and J. Mroczka, Opt. Lett. 32, 2070 (2007).
    [CrossRef]
  10. F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
    [CrossRef]
  11. F. R. A. Onofri, M. A. Krzysiek, S. Barbosa, V. Messager, K.-F. Ren, and J. Mroczka, Appl. Opt. 50, 5759 (2011).
    [CrossRef]
  12. W. P. Arnott and P. L. Marston, Appl. Opt. 30, 3429 (1991).
    [CrossRef]
  13. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  14. S. Asano and G. Yamamoto, Appl. Opt. 14, 29 (1975).
    [CrossRef]
  15. M. I. Mishchenko and L. D. Travis, Opt. Commun. 109, 16 (1994).
    [CrossRef]
  16. F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
    [CrossRef]
  17. G. E. Davis, J. Opt. Soc. Am. A 45, 572 (1955).
    [CrossRef]
  18. L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
    [CrossRef]
  19. K.-F. Ren, F. R. A. Onofri, C. Rozé, and T. Girasole, Opt. Lett. 36, 370 (2011).
    [CrossRef]

2011

2010

F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
[CrossRef]

2009

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
[CrossRef]

2007

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

F. Onofri, M. Krzysiek, and J. Mroczka, Opt. Lett. 32, 2070 (2007).
[CrossRef]

2003

1994

M. I. Mishchenko and L. D. Travis, Opt. Commun. 109, 16 (1994).
[CrossRef]

1991

1984

1981

P. L. Marston and D. L. Kingsbury, J. Opt. Soc. Am. A 71, 358 (1981).
[CrossRef]

1979

P. L. Marston, J. Opt. Soc. Am. A 69, 1205 (1979).
[CrossRef]

1975

1955

G. E. Davis, J. Opt. Soc. Am. A 45, 572 (1955).
[CrossRef]

1838

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Airy, G. B.

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Arnott, W. P.

Asano, S.

Barbosa, S.

Bohren, C. F.

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

Bonnet, J.-P.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
[CrossRef]

Davis, G. E.

G. E. Davis, J. Opt. Soc. Am. A 45, 572 (1955).
[CrossRef]

Dean, C. E.

Fiedler-Ferrari, N.

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef]

Girasole, T.

Gouesbet, G.

F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
[CrossRef]

Huffman, D. R.

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

Kingsbury, D. L.

P. L. Marston and D. L. Kingsbury, J. Opt. Soc. Am. A 71, 358 (1981).
[CrossRef]

Krzysiek, M.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
[CrossRef]

F. Onofri, M. Krzysiek, and J. Mroczka, Opt. Lett. 32, 2070 (2007).
[CrossRef]

Krzysiek, M. A.

Langley, D. S.

Li, G.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Li, X.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Lock, J. A.

F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
[CrossRef]

J. A. Lock, J. Opt. Soc. Am. A 20, 499 (2003).
[CrossRef]

Marston, P. L.

Messager, V.

Mishchenko, M. I.

M. I. Mishchenko and L. D. Travis, Opt. Commun. 109, 16 (1994).
[CrossRef]

Mroczka, J.

Nussenzweig, H. M.

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef]

Onofri, F.

Onofri, F. R. A.

Radev, S.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
[CrossRef]

Ren, K.-F.

Rozé, C.

Travis, L. D.

M. I. Mishchenko and L. D. Travis, Opt. Commun. 109, 16 (1994).
[CrossRef]

van de Hulst, H. C.

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

Wiscombe, W. J.

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef]

Wu, L.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Xu, F.

F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
[CrossRef]

Yamamoto, G.

Yang, B.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Yang, H.

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Appl. Opt.

Exp. Fluids

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, Exp. Fluids 47, 721 (2009).
[CrossRef]

J. Opt. Soc. Am. A

G. E. Davis, J. Opt. Soc. Am. A 45, 572 (1955).
[CrossRef]

P. L. Marston, J. Opt. Soc. Am. A 69, 1205 (1979).
[CrossRef]

P. L. Marston and D. L. Kingsbury, J. Opt. Soc. Am. A 71, 358 (1981).
[CrossRef]

J. A. Lock, J. Opt. Soc. Am. A 20, 499 (2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

L. Wu, H. Yang, X. Li, B. Yang, and G. Li, J. Quant. Spectrosc. Radiat. Transfer 108, 54 (2007).
[CrossRef]

Opt. Commun.

M. I. Mishchenko and L. D. Travis, Opt. Commun. 109, 16 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. A

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef]

F. Xu, J. A. Lock, and G. Gouesbet, Phys. Rev. A 81, 43824 (2010).
[CrossRef]

Trans. Cambridge Philos. Soc.

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Other

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

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

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of the scattering problem.

Fig. 2.
Fig. 2.

Virtual wavefronts of rays p=0 for air bubbles in water with circular and elliptical cross sections.

Fig. 3.
Fig. 3.

Comparison with LMT predictions: (a) near-critical-angle scattering diagrams for a=ac, and (b) angular positions of the first two bows.

Equations (16)

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

cos2ϕ=2x2/(ax4N2)1,sin2ϕ=2xy/(N2ax2ay2).
xc=ax4/(ax2+ay2tan2ϕc),yc=ay4/(ay2+ax2tan2ϕc).
(uv)=(sin2ϕccos2ϕccos2ϕcsin2ϕc)(xfyf).
v0+(dv/du)u+(d2v/du2)u2/2!+O(u)3.
pc=cos2ϕcxf+sin2ϕcyf,qc=sin2ϕcxf+cos2ϕcyf.
xf=2xc2/(ax4Nc2),yf=ay2xcax2ycNc2[1ay2xc2ax2(1ax2+1ay2)].
p=cos2ϕcxf+sin2ϕcyf.
xf=8xc/(ax4ay2Nc4),yf=4ax2ay2[2xc2ycax2Nc4(1ay21ax2)+ay2ycNc2(yc2ay2xc2ax2)]ay4ax2yc3.
v=αeu2withαe=p/(2qc2).
fj(η)=rj(u)eik(αu2ηu)du,
u0+(xfxc)u=qc(ϕϕc)ϕ.
fj(η)=±0ei[k(αu2+ηu)+βju1/2]du.
fj(η)=±eikη2/(4α)×0ei(kα[u+η/(2α)]2+βju1/2)du.
fj(η)=±eikη2/(4α)Awei(kαA2z2+βjA1/2[z+w]1/2)dz.
g(w)ei[kη24αψj(w,0)]wei(πz22)dz.
I(θ,φ)=I0(ac,ac,R2)g(θ)g¯(θ)8,

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