TY - GEN

T1 - Complexified Spherical Waves and Their Sources in the Physical Space

AU - Tagirdzhanov, A.M.

AU - Kiselev, A.P.

PY - 2013

Y1 - 2013

N2 - Abstract| We address spherical waves complexi¯ed by a complex shift in a coordinate of the point source. These waves have been studied since the early 1970s in both time-harmonic and non-time-harmonic cases as exact localized solutions of the wave equation. We deal with the fundamental mode described by u = f(µ¤) R¤ , where R¤ = p x2 + y2 + (z ¡ ia)2, a > 0 is a free positive constant, µ¤ = R¤¡ct is a complex phase and f(µ¤) is an arbitrary function describing the waveform. Such a function satis¯es the inhomogeneous wave equation uxx+uyy+uzz¡c¡2utt = F with a certain source function F = F(x; y; z; t), which is a generalized function supported by a 2D surface in the real 3D physical space. Here, c > 0 is the constant wave speed. The function F is dependent on the waveform f as well as on the de¯nition of the branch of the square root in the \complex distance" R¤. Unlike several earlier studies, in which sources in the complex space were discussed, we focus on explicitely ¯nding the source function F in the rea

AB - Abstract| We address spherical waves complexi¯ed by a complex shift in a coordinate of the point source. These waves have been studied since the early 1970s in both time-harmonic and non-time-harmonic cases as exact localized solutions of the wave equation. We deal with the fundamental mode described by u = f(µ¤) R¤ , where R¤ = p x2 + y2 + (z ¡ ia)2, a > 0 is a free positive constant, µ¤ = R¤¡ct is a complex phase and f(µ¤) is an arbitrary function describing the waveform. Such a function satis¯es the inhomogeneous wave equation uxx+uyy+uzz¡c¡2utt = F with a certain source function F = F(x; y; z; t), which is a generalized function supported by a 2D surface in the real 3D physical space. Here, c > 0 is the constant wave speed. The function F is dependent on the waveform f as well as on the de¯nition of the branch of the square root in the \complex distance" R¤. Unlike several earlier studies, in which sources in the complex space were discussed, we focus on explicitely ¯nding the source function F in the rea

KW - Complex source

KW - spherical waves

KW - localized wave propagation

M3 - Conference contribution

SN - 978-1-62993-458-7

SN - 9781934142264

SP - 270

EP - 273

BT - Progress In Electromagnetics Research Symposium PIERS 2013 in Stockholm, Sweden, 12-15 August, 2013

PB - Curran Associates, Inc.

ER -