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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 71, Iss. 2 — Feb. 1, 1981
  • pp: 192–196

Scattering by a bubble in water near the critical angle: interference effects

Philip L. Marston and Dwight L. Kingsbury  »View Author Affiliations

JOSA, Vol. 71, Issue 2, pp. 192-196 (1981)

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A physical-optics approximation is derived for light scattering by dielectric spheres with refractive indices less than their surroundings, and it is applied to air bubbles in water. The approximation gives the coarse structure in the scattering when the scattering angle Ø is near the critical scattering angle Øc, where Øc ࣃ 83° for bubbles in water. Diffraction has been observed to be important in the critical region because of an abrupt change in the amplitude of the reflected wave [P. L. Marston, J. Opt. Soc. Am. 69, 1205–1211 (1980)]. Interference that is due to a refracted wave produces oscillations in the intensity with an angular quasi-period of magnitude (λ/a)½ rad near Øc, where λ is the wavelength and a is the radius. Unlike diffraction-related oscillations, the interference oscillations increase in magnitude as forward scattering is approached. Optical tunneling through bubbles is also discussed.

© 1981 Optical Society of America

Philip L. Marston and Dwight L. Kingsbury, "Scattering by a bubble in water near the critical angle: interference effects," J. Opt. Soc. Am. 71, 192-196 (1981)

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. H. M. Nussenzveig, "Complex angular momentum theory of the rainbow and the glory," J. Opt. Soc. Am. 69, 1068–1079 (1979).
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  6. Unlike in Ref. 4, h0,2 and r2 are written here without minus signs in front of their right-hand sides because this convention gives a description of the interference that is convenient for comparison with Mie theory.
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  17. The absolute phases of S1, and S2 are not calculated here because the coordinate system used in Sec. 1 was not centered on the bubble and because wave-front curvature orthogonal to the scattering plane introduces an undetermined phase factor independent of the polarization. Equation (25) is to be used in the evaluation of Eq. (28).
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