Electromagnetic fields in dispersive chiral media generated by modulated nonuniformly moving sources

A representation for the fields generated by moving sources in chiral media in the form of double time-frequency oscillating integrals is obtained by using quaternionic analysis methods. Some additional assumptions concerning the source allow us to introduce a large dimensionless parameter λ > 0 which characterizes simultaneously the slowness of variations of the amplitude and of the velocity of the source. Application of the two-dimensional stationary phase method to the integral representation of the field leads to asymptotic formulas for the electromagnetic field for large λ > 0, and efficient formulas for the frequency and the time Doppler effects in dispersive chiral media. As an application of the proposed method, we consider the Vavilov-Cherenkov radiation in chiral dispersive media.