Electromagnetic field generated by a modulated moving point source in a planarly layered waveguide

In the present work, we consider a modulated point source in an arbitrary motion in an isotropic planarly layered waveguide. The radiation field generated by this source is represented in the form of double oscillatory integrals in terms of the time and the frequency, depending on the large parameter λ. By means of the stationary phase method, we analyze, in the waveguide, the Doppler effect, the retarded time, and the Vavilov–Cherenkov radiation. Numerically, the problem of the moving source is approached by the method of spectral parameter power series.