Electromagnetic scattering by harmonically expanding surfaces and related complex resonances

A relativistically exact iterative method is developed for scattering of electromagnetic waves by expanding surfaces. In particular, the problems of the expanding cylinder and sphere are computed. It is shown that expanding scatterers respond to harmonic excitation by radiating nonharmonic waves. These waves involve complex frequencies computed here. The method given here involves secular terms in t, therefore its validity for harmonic excitation is limited to early times. However, in the case of impulse excitation and transient scattering this problem is automatically resolved by the fact that the signal is exponentially decaying and the secular terms have no large‐time effect.