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By Arioli G., Szulkin A.

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Jj . 97) to calculate Ap and Bp. For the case of TM waves, we use the Ez component. 99) Inside the disk, we have For the region above the disk, we have for z > t/1, Then Matching boundary conditions for the continuity of tangential electric and magnetic fields, we have at z = —t/1. 115) to calculate Cp and Dp. 104) the internal electric field is where fcjj_ = xk sin 0i cos <& + yk sin 9i sin

We note that as ka increases, Qext, Qsca, & begin to saturate. At resonance Qext and Qsca assume peak values. For this case, at resonance, Qext and Qsca assume values close to 4 and 3, respectively. The cross sections are, respectively, 4 and 3 times the geometric cross section. The albedo is also larger than that in the long wavelength case, meaning that scattering is comparable to absorption. In Figs. 5, we plot the bistatic scattering as a function of scattering angle 0. We compare the results between Mie scattering and Born approximation.

65), it follows that where (9P, p) are the angular variables that indicate the direction p. 66) with the incident electric field. 3 Spherical Waves 29 cosOiZ, and iii = 6^ hi = fa. 66) and take a dot product with the polarization vector, ei. We note that unless m = ±1. 66) The far-field solutions of the outgoing vector spherical waves are In Mie scattering, the results are often expressed in functions denoted by 7rn(cos0) and rn(cos0) [van de Hulst, 1957]. They are related to the associated Legendre functions by 30 1 ELECTROMAGNETIC SCATTERING BY SINGLE PARTICLE The special values when cos# = ±1 are 4* Then we can express the vector spherical harmonics for m + 1 as and for m = — 1 as For 0 — 0, we can set <^> = 0 without loss of generality to obtain 5 Acoustic Scattering Many of the techniques in this book are also applicable to acoustic wave scattering [Temkin, 1981; Morse and Ingard, 1987; Pierce, 1989].

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