By Thomas Hagstrom (auth.), Bjorn Engquist, Gregory A. Kriegsmann (eds.)
This IMA quantity in arithmetic and its purposes COMPUTATIONAL WAVE PROPAGATION relies at the workshop with an identical name and used to be a vital part of the 1994-1995 IMA application on "Waves and Scattering." we want to thank Bjorn Engquist and Gregory A. Kriegsmann for his or her labor in organizing this assembly and in enhancing the complaints. We additionally take this chance to thank the nationwide technological know-how origin, the military study place of work, and the workplace of Naval examine, whose monetary help made this workshop attainable. A vner Friedman Robert Gulliver v PREFACE even supposing the sphere of wave propagation and scattering has its classical roots within the final century, it has loved a wealthy and colourful lifestyles over the last 50 abnormal years. Scientists, engineers, and mathematicians have devel oped subtle asymptotic and numerical instruments to unravel difficulties of ever expanding complexity. Their paintings has been spurred on via rising and maturing applied sciences, basically curious about the propagation and reception of knowledge, and the effective transmission of power. The power of this medical box isn't waning. elevated calls for to exactly quantify, degree, and keep an eye on the propagation and scattering of waves in more and more advanced settings pose demanding clinical and mathematical difficulties. those push the envelope of study and comput ing, simply as their forerunners did 50 years in the past. those sleek technological difficulties variety from utilizing underwater sound to watch and expect worldwide warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure lengthy diversity electronic communication.
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E probe coordinate system (x, y, z) is fixed with respect to the probe such that the axis of the probe is parallel to the z axis as shown in Figure SPHERICAL NEAR-FIELD SCANNING IN THE TIME DOMAIN 57 Probe x y z FIG. 3. The probe coordinate system. 3. We denote the location of some reference point of the probe by r. 1]' . The propagation vector of this incident plane wave is k = kxx + kyY + IZ with I = '"V I hlp - k'f, - k~1 for k~ + k~ < k 2 and = il·yx /p + pY - PI for k 2 + k Y2 > k 2 • X To derive the linear differential operator formula one begins by noting that the receiving characteristic RE (k x , ky) is an analytic function of the variables (k x , ky) and may be expanded in a series of spherical harmonics , , and .
Taflove, and K. R. Umashakar, "A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach", IEEE Trans. , vol. AP-35, no. 2, pp. 153-161, 1987. FORMULATION OF SPHERICAL NEAR-FIELD SCANNING IN THE TIME DOMAIN THORKILD B. HANSEN' Abstract. Spherical near-field scanning techniques are formulated for acoustic and electromagnetic fields in the time domain so that a single set of time-domain nearfield measurements yields the far field in the time domain or over a wide range of frequencies.
Spherical near-field scanning, which is the topic of the present paper, was first formulated in 1970 in the thesis of Jensen . Jensen derived a probe-corrected spherical near-field formula that expresses the field of an antenna (called the test antenna), located inside the scan sphere, in terms of the receiving characteristic of the probe and the probe output on the scan sphere. Wacker  then showed how a special symmetric probe could be used to deconvolve Jensen's formulas to give a practical set of spherical near-field formulas.