Propagation of limited-diffraction X-waves in dissipative media

Author

Sushilov, Nikolai V. ; Tavakkoli, Jahangir ; Cobbold, Richard S C

Author_Institution

Inst. of Biomaterials & Biomed. Eng., Toronto Univ., Ont., Canada

Volume

49

Issue

6

fYear

2002

fDate

6/1/2002 12:00:00 AM

Firstpage

675

Lastpage

682

Abstract

Diffractionless solutions of the wave equation in the form of X-waves have previously been obtained based on the inviscid form of the wave equation. A new general solution to the cylindrically symmetric wave equation for a medium with classical viscous losses is obtained. Particular solutions called dissipative Arcsin X-waves have been derived from this general solution. The properties of these waves are discussed for both infinite and finite size transducers and for different viscous liquids. To calculate the field produced by a finite transducer diameter, we have derived a dissipative form of the Rayleigh integral.

Keywords

Fourier transforms; absorbing media; ultrasonic absorption; ultrasonic propagation; ultrasonic transducers; wave equations; 3-D representations; Rayleigh integral; X-waves propagation; absorption losses; classical viscous losses; cylindrically symmetric equation; diffractionless beams; dissipative Arcsin X-waves; dissipative media; finite size transducers; infinite size transducers; inviscid form; lateral velocity potential profiles; limited-diffraction X-waves; space-time Fourier transform; wave equation; Absorption; Apertures; Associate members; Diffraction; Integral equations; Life members; Liquids; Partial differential equations; Propagation losses; Transducers;

fLanguage

English

Journal_Title

Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on

Publisher

ieee

ISSN

0885-3010

Type

jour

DOI

10.1109/TUFFC.2002.1009326

Filename

1009326