Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control ferroelectrics, and frequency control, 1992-01, Vol.39 (1), p.19-31
• Main Authors: Lu, J.-Y., Greenleaf, J.F.
• Format: Article
• Language: English
• Subjects: Acoustic beams; Acoustic imaging; Acoustic transducers; Acoustics; Apertures; Ceramics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); H infinity control; Laplace equations; Partial differential equations; Physics; Polymers; Ultrasonic transducers; Ultrasonics, quantum acoustics, and physical effects of sound
• ISSN: 0885-3010; 1525-8955
• DOI: 10.1109/58.166806

The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J/sub 0/ Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed.< >