By I. Ya. Barit, V. A. Sergeev (auth.), Academician D. V. Skobel’tsyn (eds.)

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21) In calculations of the angular distribution of the radiation intensity of waves having one or the other polarization, the vectors of the spherical waves of the corresponding polarization must be inserted in these equations. These results are the basis for radiation calculation which will be performed under various assumptions regarding the motion of a charged particle in the presence of a boundary. E. PAFOMOV CHAPTER 2 Radiation in the Presence of a Separating Boundary § 5. Time and Path of Coherence The path transgressed by a particle during a time within which the phase of the wave changes by about unity at the point of the particle plays an important role in the theory of electromagnetic wave radiation.

Expansion in the exponent of the exponential function in the integral of Eq. 2) tends to zero. is greater than a right angle. This means that when the particle's path in Hence, the angle the medium has a finite length, the cylindrical wave of the Cerenkov radiation fills the region of the space which is behind the particle (Fig. 8). The cylindrical wave of the Cerenkov radiation is computed with Eq. 12), in which we have Im n > 0 (Im n « I Ren J) in the frequency range involving negative group velocities.

47) The range in which the results stated in Eqs. 48) while Eqs. 45) are correct for lk;IR:. ;>1. 49) When neither absorption nor total reflection occur in medium s, R 5 and Rj are real and equal to the distance (in the direction of the wave vector of the refracted wave) between dipole A (Fig. 3) and the boundary (R5 =AB) and to the distance between the boundary and point C of observation (Rj = BC). When absorption or total reflection of the wave occurs, Rs and Rj are complex and no longer have that simple ameaninginterms ofphysics.

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