Experimental verification of nondiffracting X waves

Jian yu Lu, James F Greenleaf

Research output: Contribution to journalArticle

210 Citations (Scopus)

Abstract

The propagation of acoustic waves in isotropic/homogeneous media and electromagnetic waves in free space is governed by the isotropic/homogeneous (or free space) scalar wave equation. The first nondiffracting beam that was an exact solution of the free-space scalar wave equation was discovered by J. Durnin (1987). It is now known that families of generalized non-diffracting solutions of the free-space scalar wave equation exist. The first experimental production of acoustic forms of a subset of these solutions that the authors term, X waves is reported. The waves are named so because they have X-like shapes in a plane along their wave axis. A zeroth-order acoustic X wave (axially symmetric) was experimentally produced with an acoustic annular array transducer. The generalized expression includes a term for the frequency response of the system and parameters for varying depth of field versus beam width of the resulting family of beams. Excellent agreement between theoretical predictions and experiment was obtained. An X wave of finite aperture driven with realizable (causal, finite energy) pulses is found to travel with a large depth of field (nondiffracting length).

Original languageEnglish (US)
Pages (from-to)441-446
Number of pages6
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
StatePublished - May 1992

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Wave equations
Acoustics
wave equations
acoustics
scalars
Electromagnetic waves
Frequency response
Transducers
Acoustic waves
frequency response
travel
set theory
electromagnetic radiation
transducers
apertures
propagation
Experiments
predictions
pulses
energy

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics

Cite this

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title = "Experimental verification of nondiffracting X waves",
abstract = "The propagation of acoustic waves in isotropic/homogeneous media and electromagnetic waves in free space is governed by the isotropic/homogeneous (or free space) scalar wave equation. The first nondiffracting beam that was an exact solution of the free-space scalar wave equation was discovered by J. Durnin (1987). It is now known that families of generalized non-diffracting solutions of the free-space scalar wave equation exist. The first experimental production of acoustic forms of a subset of these solutions that the authors term, X waves is reported. The waves are named so because they have X-like shapes in a plane along their wave axis. A zeroth-order acoustic X wave (axially symmetric) was experimentally produced with an acoustic annular array transducer. The generalized expression includes a term for the frequency response of the system and parameters for varying depth of field versus beam width of the resulting family of beams. Excellent agreement between theoretical predictions and experiment was obtained. An X wave of finite aperture driven with realizable (causal, finite energy) pulses is found to travel with a large depth of field (nondiffracting length).",
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