Lips caustics in light backscattered from an acoustically levitated spheroidal water drop
Harry J. Simpson, Philip L. Marston · The Journal of the Acoustical Society of America · 1989
Cusp diffraction catastrophes that open up roughly transverse to the propagation direction are known to exist for both light and sound [P. L. Marston, J. Acoust. Soc. Am. 81, 226–232 (1987)]. They may be produced by reflecting high-frequency sound from curved surfaces. In the present research, a closely related caustic in which the cusp curves join to form a pair of lips is studied. This caustic was predicted to exist [J. F. Nye, Nature 312, 531–532 (1984)] in light backscattered from horizontally illuminated oblate drops of water, provided the axis ratio q = D/H was within certain ranges. The associated rays are diffracted at the drop's surface and have only one internal reflection. As q is increased above the critical value q4≈1.31 associated with a hyperbolic umbilic focal section, the cusp points at the ends of the lips caustic were predicted to merge in the backward direction at a “lips event” when q = qL1 ≈ 1.42. For qL1 < q < qL2 ≈ 1.58, no caustics for this class of ray are expected while a second lips event occurs at qL2. Observations of farfield scattering from levitated drops support Nye's analysis and illustrate a mechanism for producing lips caustics. The observed backscattering is weak for q between qL1 and qL2. [Work supported by ONR.]