A spiral wave front source produces an acoustic field that has a phase that is proportional to the azimuthal angle about the source. The concept of a spiral wave front beacon is developed by combining this source with a reference source that has a phase that is constant with the angle. The phase difference between these sources contains information about the receiver's azimuthal angle relative to the beacon and can be used for underwater navigation. To produce the spiral wave front, two sources are considered: a "physical-spiral" source, which produces the appropriate phase by physically deforming the active element of the source into a spiral, and a "phased-spiral" source, which uses an array of active elements, each driven with the appropriate phase, to produce the spiral wave front. Using finite element techniques, the fields produced by these sources are examined in the context of the spiral wave front beacon, and the advantages of each source are discussed.

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Transducers for acoustic beacons which can produce outgoing signals with wave fronts whose horizontal cross sections are circular or spiral are studied experimentally. A remote hydrophone is used to determine its aspect relative to the transducers by comparing the phase of the circular signal to the phase of the spiral signal. The transducers for a "physical-spiral" beacon are made by forming a strip of 1-3 piezocomposite transducer material around either a circular or spiral backing. A "phased-spiral" beacon is made from an array of transducer elements which can be driven either in phase or staggered out of phase so as to produce signals with either a circular or spiral wave front. Measurements are made to study outgoing signals and their usefulness in determining aspect angle. Vertical beam width is also examined and phase corrections applied when the hydrophone is out of the horizontal plane of the beacon. While numerical simulations indicate that the discontinuity in the physical-spiral beacon introduces errors into the measured phase, damping observed at the ends of the piezocomposite material is a more significant source of error. This damping is also reflected in laser Doppler vibrometer measurements of the transducer's surface velocity.

Caustics can be formed in the water column when sound scatters off a curved-reflecting surface such as the ocean floor or surface. The simplest caustic is an Airy caustic formed by the merging of two rays. Small targets lying in or near Airy caustics have backscattered echoes that can be focused both to the target and upon return. For a point target, the doubly focused backscattering amplitude is proportional to the square of an Airy function whose argument depends on the target location through the changes in relative return times of contributing rays. For a finite sized target, the symmetry is broken and the amplitude unfolds into a hyperbolic umbilic catastrophe. The arguments for the hyperbolic umbilic function are calculated using the relative return times of transient echoes. These doubly focused echoes can lead to amplitudes larger than that of direct or singly focused echoes ͑echoes which focus once, either to the target or upon return͒. Experiments using a cylindrical half-pipe as a reflecting surface confirm these predictions.