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Integral equation formulations for electromagnetic scattering from two-dimensional inhomogeneities in conductive earth
Integral equation formulations for electromagnetic scattering from two-dimensional inhomogeneities in conductive earth - appendices, figures, bibliography, and computer programs
In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.
Differential reflectivity concept use in determining scattered electromagnetic radiation from lunar surface
It is known from the Apollo magnetometer experiments that significant electromagnetic induction takes place in the lunar interior. This induction is excited by fluctuations of the interplanetary magnetic field and is detected by the induced fields on the surface of the moon. These results are reviewed briefly and the formal properties of the theory are discussed. It is shown that the mathematical treatment parallels that for classical electromagnetic scattering. Further the wavelength spectrum of the fluctuations of the interplanetary magnetic field include scales consistent with the radius of the moon. The consequence is that the moon is excited in several modes. Quadrupole and possibly octupole magnetic multipoles are found in the data. The electric type radiation corresponding to transverse magnetic excitation appears suppressed and far below the detection threshold of the magnetometers.
The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.
Quasi-specular radar data used to determine apparent surface roughness of geologic surfaces displays a variable wavelength dependence. The strongest changes with wavelength are observed in lunar maria, while scatter from lunar highlands is nearly wavelength independent. Commonly used, gently undulating surface models for electromagnetic scatter predict no wavelength dependence. Wavelength dependence occurs whenever a significant fraction of the surface has local radii of curvature comparable to the observing wavelength. This condition can be determined by comparison of the value of the integrated surface curvature spectrum with the radar wave number, multiplied by a constant that depends on the geometry. Variations in curvature statistics calculated from photogrammetric reduction of lunar images are consistent with the observed variations in quasi-specular scatter between wavelengths of 13 and 116 cm at the same locations. Variations in the strength of the wavelength dependence are correlated with the sizes of lunar craters that lie near the upper size limit for the local steady-state distribution. This correlation is also consistent with variations in the curvature spectrum calculated from crater size-frequency distributions.
We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.
This paper uses Mie theory to treat electromagnetic scattering and to evaluate field enhancement in the forward direction of a small droplet irradiated by a high-energy beam and compares the results of calculations with the field-enhancement evaluation obtained via geometrical optics treatment. Results of this comparison suggest that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support laser-induced Raman scattering. The results are supported by experimental observations of the interaction of a 120-micron-diam water droplet with a high-energy Nd:YAG laser beam.
An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.
An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.
The theory of scattering by charged particle fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of: (1) a three wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion acoustic), and (2) a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves in large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of those cases to determine the lower order corrections to the usual high frequency scattering formulas.
A modification of the classical Rayleigh technique utilizing the fast Fourier transform, developed into the so-called Rayleigh-FFT method for electromagnetic scattering, is shown to obtain valid scattering results from arbitrary irregular periodic structures composed of a rough layer over a rough half-space. The considerable usefulness of the Rayleigh approach is thus established, and Beckmann's (1968) contention (that the convergence of the method is reasonably rapid only if the roughness is very slight) is refuted.
The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.
The single-scattering properties (SSPs) of hydrometeors are the fundamental quantities for physics-based precipitation retrievals. Thus, efficient computation of their electromagnetic scattering is of great value. Whereas the semi-analytical T-Matrix methods are likely the most efficient for nonspherical hydrometeors with axial symmetry, they are not suitable for arbitrarily shaped hydrometeors absent of any significant symmetry, for which volume integral methods such as those based on Discrete Dipole Approximation (DDA) are required. Currently the two leading T-matrix methods are the Extended Boundary Condition Method (EBCM) and the Invariant Imbedding T-matrix Method incorporating Lorentz-Mie Separation of Variables (IITM+SOV). EBCM is known to outperform IITM+SOV for hydrometeors with modest aspect ratios. However, in cases when aspect ratios become extreme, such as needle-like particles with large height to diameter values, EBCM fails to converge. Such hydrometeors with extreme aspect ratios are known to be present in solid precipitation and their SSPs are required to model the radiative responses accurately. In these cases, IITM+SOV is shown to converge. An efficient, parallelized C++ implementation for both EBCM and IITM+SOV has been developed to conduct a performance comparison between EBCM, IITM+SOV, and DDSCAT (a popular implementation of DDA). We present the comparison results and discuss details. Our intent is to release the combined ECBM IITM+SOV software to the community under an open source license.
A parametric analysis of the coherent electromagnetic losses due to scattering from volume weak inhomogeneities is reported. It is shown that even in the case of very weak inhomogeneities, the loss could be appreciable in a resonance region and thus play a more dominant role than conductivity losses.
We examine the behavior of the scattered electromagnetic field from random Gaussian power-law surfaces for near grazing incidence.
A description is given of the physics of electromagnetic scattering from the sea and a guideline is presented to relate an observable (such as the radar cross section) to the hydrodynamics or physical properties of the sea. As specific examples of the interdisciplinary science of electromagnetics and geophysical oceanography, the physics is discussed in connection with data provided by three instruments: namely, the scatterometer, the altimeter, and the imaging radar. The data provided by each instrument are discussed in context with specular point and Bragg scattering theories. Finally, the degrading effect of extraneous sources of noise is discussed as a limiting mechanism of the accuracy of the ocean surface measurement.