Establishing a precise electromagnetic scattering model of surfaces is of great significance for comprehending the underlying mechanics of synthetic aperture radar (SAR) imaging. To describe surface electromagnetic scattering more comprehensively, this paper established a nonlinear integral equation model with the Creamer model and bispectrum (IEM-C). Based on the IEM-C model, the effect of parameters, such as radar wave incidence angle, wind speed and direction of sea surfaces, and different polarization modes on the backscattering coefficients of C-band radar waves, was systematically evaluated. The results show that the IEM-C model can characterize both the vertical nonlinear features due to wave interactions and the horizontal nonlinear features due to the wind direction. The sensitivity of the sea surface backscattering coefficient in the IEM-C model to nonlinear effects varies with different incident angles. At the incident angle of 30°, the IEM-C model exhibits the most significant nonlinear effects. The nonlinear effects of the IEM-C model vary under different wind speeds. By comparing with the measured data, it is proved that the IEM-C model is closer to the real sea surface scattering situation than the IEM model.

Electromagnetic scattering from the sea surface is of great significance in radar detection, target recognition, ocean remote sensing, etc. By introducing the action spectrum, the modified spatio-temporal variation wave spectrum is used to establish a nonlinear sea surface with currents in this paper. Traditional capillary wave modification facet scattering model (CWMFSM) can only calculate the backscattering from the wind-driven sea surface. By using the new spatio-temporal variation wave spectrum to modify the scattering amplitude of every facet, the new CWMFSM can be used to calculate the nonlinear sea surface scattering with surface currents. Therefore, the model simultaneously considers the modulation of sea surface wind and currents to the radar back echo. The dependence of backscattering coefficient from nonlinear sea surface on the incident angle and the polarization are discussed. The results verify that the nonlinear model is more consistent with the measurement data. This paper also investigates the Doppler spectrum characteristics of the sea with currents. It is found that the effect of wave–current interaction on Doppler spectra is weaker than that of wave–wave interaction. The SAR images of nonlinear sea surfaces are also simulated and different bands, polarizations, and baseline length effects on sea current detection performance of along-track interference SAR are analyzed.

This study introduces an alternative approach to the numerical solution of two-dimensional (2D) electromagnetic scattering problems by a numerical method of moments (MoM). The real source position vector is replaced by a complex quantity, then Green's function generates a complex source point beam, therefore the interactions between the far zone elements in the impedance matrix are neglected, except the basis functions near to the edges, strongly localizing the impedance matrix. The memory storage increases with the number of edges, but for a fixed number of the edges, it is linearly proportional with N, i.e. O(N). Consequently, the overall running time can be drastically reduced and the far zone scattering pattern and the near field can be found. The proposed procedure is first explained for the single perfectly electrically conducting (PEC) strip geometry, then extended to the scattering by 2D PEC objects with closed polygonal cross-sections. Numerical results are presented for a strip and a square cylinder in both polarizations. The relative errors are also compared with the standard MoM.

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields.This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous three-dimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain.The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers.Our analysis extends results originally obtained in [Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Model. Numer. Anal. 37 (2003) 159–173] for steady state voltage potentials to time-harmonic Maxwell's equations.

The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.

We show that the support of a (possibly) coated anisotropic medium is uniquely determined by the electric far-field patterns corresponding to incident time-harmonic electromagnetic plane waves with arbitrary polarization and direction. Our proof avoids the use of a fundamental solution to Maxwell’s equations in an anisotropic medium and instead relies on the well-posedness and regularity properties of solutions to an interior transmission problem for Maxwell’s equations.

AMS 2000 Mathematics subject classification: Primary 35R30; 35Q60. Secondary 35P25; 78A45