Angular-spectrum representation of nondiffracting X waves

Abstract
We derive the nondiffracting X waves, first discussed within acoustics by Lu and Greenleaf [IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19 (1992)], using the general mathematical formalism based on an angular spectrum of plane waves. This serves to provide a unified treatment of not only the fundamental zeroth-order X waves of Lu and Greenleaf, but also of the lesser-known higher-order derivative X waves, first discussed here in terms of a single, universal, angular spectrum. The characteristic crossed (letter-X-like) shape and the special properties of the X waves, as well as of their angular-spectrum representation, are discussed and illustrated in detail. Asymptotically, for increasing order, the appearance of the X waves is found to transform into a triangular wedgelike waveform. © 1996 The American Physical Society.

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