Doppler characteristics of EM scattering from sinusoidal or weakly nonlinear choppy waves

The spectra of electromagnetic (EM) scattering fields from sinusoidal or weakly nonlinear choppy waves are presented. In general, we always consider that the Doppler shift of EM scattering from a Bragg resonant wave is determined by the phase velocity of the water wave. However, the recent wave tank experiments and the numerical simulations demonstrate that not only the spectral peak corresponding to the phase velocity of water wave but also other equally spaced harmonic peaks can be found when a EM wave is illuminated on a sinusoidal or a simple weakly nonlinear choppy wave. The intensities of the harmonic peaks are affected by the amplitude, the frequency, and the hydrodynamic model of the water wave. To better explain these phenomena, a theoretical model for the spectra from the simple water waves are derived by the first-order small slope approximation theory (SSA-I). The comparisons with the numerical simulations illustrated that all the interesting phenomena could be successfully explained the theoretical spectral model.