TY - JOUR

T1 - Nondiffracting X Waves-Exact Solutions to Free-Space Scalar Wave Equation and Their Finite Aperture Realizations

AU - Lu, Jian Yu

AU - Greenleaf, James F.

N1 - Funding Information:
Manuscript received April 10, 1991; revised and accepted June 17, 1991. This work was supported in part by grant CA 43920 from the National Institutes of Health. The authors are with the Biodynamics Research Unit, Department of Physiology and Biophysics, Mayo Clinic and Foundation, Rochester, MN 55905 IEEE Log Number 9103584.

PY - 1992/1

Y1 - 1992/1

N2 - Novel families of generalized nondiffracting waves have been discovered. They are exact nondiffracting solutions of the isotropic/homogenous scalar wave equation and are a generalization of some of the previously known nondiffracting waves such as the plane wave, Durnin's beams, and the nondiffracting portion of the Axicon beam equation in addition to an infinity of new beams. One subset of the new nondiffracting waves have X-like shapes that are termed “X waves.” These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broad band 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. The phase of the X waves changes smoothly with time across the aperture of the radiator, therefore, X waves can be realized with physical devices. A zeroth-order bandlimited X wave was produced and measured in water by our 10 element, 50 mm diameter, 2.5 MHz PZT ceramic/polymer composite J0 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.

AB - Novel families of generalized nondiffracting waves have been discovered. They are exact nondiffracting solutions of the isotropic/homogenous scalar wave equation and are a generalization of some of the previously known nondiffracting waves such as the plane wave, Durnin's beams, and the nondiffracting portion of the Axicon beam equation in addition to an infinity of new beams. One subset of the new nondiffracting waves have X-like shapes that are termed “X waves.” These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broad band 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. The phase of the X waves changes smoothly with time across the aperture of the radiator, therefore, X waves can be realized with physical devices. A zeroth-order bandlimited X wave was produced and measured in water by our 10 element, 50 mm diameter, 2.5 MHz PZT ceramic/polymer composite J0 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.

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U2 - 10.1109/58.166806

DO - 10.1109/58.166806

M3 - Article

AN - SCOPUS:0026678389

VL - 39

SP - 19

EP - 31

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

SN - 0885-3010

IS - 1

ER -