Micro-Doppler Frequency Comb Generation by Axially Rotating Scatterers

Abstract

Electromagnetic scattering in accelerating reference frames inspires a variety of phenomena, requiring employment of general relativity for their description. While the quasi-stationary field analysis could be applied to slowly-accelerating bodies as a first-order approximation, the scattering problem remains fundamentally nonlinear in boundary conditions, giving rise to multiple frequency generation (micro-Doppler shifts). Here a frequency comb, generated by an axially rotating subwavelength (cm-range) wire and split ring resonator (SRR), is analyzed theoretically and observed experimentally by illuminating the system with a 2GHz carrier wave. Highly accurate lock in detection scheme enables factorization of the carrier and observation of more than ten peaks in a comb. The Hallen integral equation is employed for deriving the currents induced on the scatterer at rest and a set of coordinate transformations, connecting laboratory and rotating frames, is applied in order to predict the spectral positions and amplitudes of the frequency comb peaks. Unique spectral signature of micro-Doppler shifts could enable resolving an internal structure of the scatterers and mapping their accelerations in space, which is valuable for a variety of applications spanning from targets identification to stellar radiometry.