EM Scattering From a Simple Water Surface Composed of Two Time-Varying Sinusoidal Waves

Some novel phenomena, which cannot be well explained by the traditional Bragg scattering theory, have been observed through the electromagnetic (EM) scattering from a water surface composed of two sinusoidal waves. According to the traditional Bragg scattering theory, the scattering intensity from water surface is only proportional to the spectral density of the Bragg resonant waves. However, the scattering field numerically simulated by the method of moment (MoM) method reveals that the resonant scattering field would also be affected by the amplitude of the non-resonant wave. In some special cases, despite the existence of the Bragg resonant waves, the Bragg resonant scattering field disappears when the amplitude of the non-resonant water wave is equal to some specific values. From the numerical results, another noticeable phenomenon is found that the Doppler spectrum of the scattering field is distorted seriously due to the frequency leakage. When the water surface with finite length is illuminated by a plane EM wave, not only the resonance spectral peaks corresponding to the phase velocity of the water wave but also other harmonic peaks appear on the spectrum curve. However, if a Gaussian beam is used instead of the plane EM wave, the harmonic peaks can be effectively suppressed. To better understand the phenomena, the theoretical model of the scattering field from the simple water surface is derived in the framework of the first-order small slope approximation method. And the empirical formulas for selecting the Gaussian beam width and water surface length are also proposed.