Analysis of scattering from fractally rough surfaces by using the T-matrix method

In this paper, a time-varying band-limited fractal model is proposed for modeling dynamic evolution of sea surface. A new method for scattering from fractally rough perfectly conducting or dielectric surfaces is formulated with use of the T-matrix analysis and the extended boundary condition method. We expand the field through generalized Floquet modes and obtain the analytical formula of the expression of matrix elements in the term of the Bessel functions. We obtain analytical closed-form expression for the scattering amplitudes for both horizontal and vertical polarization of the incident electromagnetic waves. The validity of this method is checked through the energy-balance parameter and comparison with approximate method. Backscattering energy pattern versus incident angle, fractal dimension have also been discussed. We also calculate the scattering coefficient as function of time using this method. Finally, numerical scattering results from fractal surfaces are provided.