On the Singular Nature of the Second-Order Peaks in HF Radar Sea Echo

Electromagnetic (EM) scattering from the sea surface concerned with second-order Doppler spectra for finite-length pulses is theoretically analyzed in the scattering regime typical of, but not confined to, high-frequency (HF) radars. The Doppler spectra of the second-order cross section consist of three different parts: continuum and two pairs of peaks-the second harmonic and corner reflection peaks. This paper is the first investigation of fundamental properties of these peaks from the perspective of their use in measurements of surface currents. It is shown that these peaks are of singular nature in the following sense: The main (singular) contribution is due to particular pairs of waves, despite the fact that waves of many different wavelengths and directions contribute to these peaks. This fact opens a possibility to employ these peaks in remote sensing of vertical profiles of surface currents. Using the number of waves in the pulse ("the pulse length") LGt1 as a large parameter, an asymptotic description of these peaks is developed. Height, width, and position of the peaks are explicitly found in terms of L. The peak positions, to the leading order, do not depend on the pulse length, although a small explicitly found O(L^-1) shift has to be taken into account for the corner reflection peaks. The heights are ~lnL and ~L^1/2 for the second harmonic and corner reflection peaks, respectively. The results open the way for wider use of the second-order peaks for probing surface currents