### Abstract

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_{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.

Original language | English (US) |
---|---|

Pages (from-to) | 19-31 |

Number of pages | 13 |

Journal | IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1992 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Acoustics and Ultrasonics

### Cite this

**Nondiffracting X waves--Exact solutions to free-space scalar wave equation and their finite aperture realizations.** / Lu, Jian yu; Greenleaf, James F.

Research output: Contribution to journal › Article

}

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

PY - 1992/1

Y1 - 1992/1

N2 - 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 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 - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=0026678389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026678389&partnerID=8YFLogxK

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 -