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

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 ϕ is near the critical scattering angle ϕc, where ϕc ≃ 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)1/2 rad near ϕc, 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.