Abstract

A vectorial complex ray model is introduced to describe the scattering of a smooth surface object of arbitrary shape. In this model, all waves are considered as vectorial complex rays of four parameters: amplitude, phase, direction of propagation, and polarization. The ray direction and the wave divergence/convergence after each interaction of the wave with a dioptric surface as well as the phase shifts of each ray are determined by the vector Snell law and the wavefront equation according to the curvatures of the surfaces. The total scattered field is the superposition of the complex amplitude of all orders of the rays emergent from the object. Thanks to the simple representation of the wave, this model is very suitable for the description of the interaction of an arbitrary wave with an object of smooth surface and complex shape. The application of the model to two-dimensional scattering of a plane wave by a spheroid particle is presented as a demonstration.

© 2011 Optical Society of America

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References

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2009 (1)

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

2008 (1)

2006 (2)

1996 (3)

1995 (1)

1992 (1)

1979 (1)

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

1972 (1)

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).
[CrossRef]

Bonnet, J. -P.

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

Brunel, M.

Cai, X.

Carlson, B. E.

Coetmellec, S.

Deschamps, G. A.

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).
[CrossRef]

Hovenac, E. A.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

Krzysiek, M.

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

Lebrun, D.

Liou, K. N.

Lock, J. A.

Macke, A.

Marston, P. L.

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

Mishchenko, M. I.

A. Macke, M. I. Mishchenko, K. Muinonen, and B. E. Carlson, Opt. Lett. 20, 1934 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

Mroczka, J.

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

Muinonen, K.

Onofri, F.

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

Radev, St.

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

Ren, K. F.

Shen, J.

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

van de Hulst, H. C.

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

Verrier, N.

Xu, F.

Yang, P.

Appl. Opt. (6)

Exp. Fluids (1)

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

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Proc. IEEE (1)

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).
[CrossRef]

Other (2)

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

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

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Figures (3)

Fig. 1
Fig. 1

Ray tracing of the first four orders for a spheroid, a = 2 c , of water ( m = 1.33 ) illuminated by a plane wave at 40 ° . For clarity only a portion of the rays is presented.

Fig. 2
Fig. 2

Comparison of scattering diagrams computed by VCRM and LMT for an air bubble in water ( m = 0.75 ) of radius a = 50 μm illuminated by a plane wave of wavelength λ = 0.6328 μm . The result of LMT has been offset by a factor of 10 2 for clarity.

Fig. 3
Fig. 3

Scattering diagram of a spheroid ( a = 2 c = 20 μm ) of water, m = 1.333 , illuminated by a plane wave of wavelength λ = 0.6328 μm at 40 ° .

Equations (12)

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S q μ = A q μ e i Φ q k ^ q ,
( k q k q ) × n ^ = 0 ,
A q μ = D q | ϵ q μ | .
D q = R 11 R 21 R 12 R 22 · R 12 R 22 R 13 R 23 R 1 q R 2 q ( r + R 1 q ) ( r + R 2 q ) ,
( k k ) · n ^ C = k Θ T Q Θ k Θ T Q Θ ,
Φ = Φ inc + Φ path + Φ focal + ( Φ λ / 2 ) .
ρ 1 = c 2 [ 1 + ( a 2 / c 2 1 ) z 2 / c 2 ] 3 / 2 a ,
ρ 2 = a [ 1 + ( a 2 / c 2 1 ) z 2 / c 2 ] 1 / 2 .
k cos 2 β R 1 = k cos 2 α R 1 + k cos β k cos α ρ 1 ,
k R 2 = k R 2 + k cos β k cos α ρ 2 ,
A d = k 2 A b J 1 ( k A θ ) k A θ ,
A μ = p = 0 A p μ e i Φ p e m i k L p + A d ,

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