J. A. Kong

Theoretical Models For Polarimetric Radar Clutter

The Mueller matrix and polarization covariance matrix are described for polarimetric radar systems. The clutter is modelled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields.

Vector Hankel transform analysis of annular-ring microstrip antenna

A rigorous analysis of the resonant frequency characteristics of an annular-ring conductor printed on a dielectric substrate backed by a ground plane is presented. The problem is cast into a set of vector dual integral equations by using vector Hankel transform (VHT). Galerkins method is then applied to compute the resonant frequencies of both transverse magnetic modes (TM 11 and TM 12 ) of the microstrip antenna. The real part of the resonant frequency shift of the TM 11 mode increases with increasing dielectric thickness in contrast to the TM 12 mode. While the TM 11 mode has a high Q , it is a poor radiating mode; the TM 12 mode is more suitable for antenna applications. For a probe excitation the input impedance is obtained using single mode approximation for both the TM 11 and TM 12 modes. It is shown that the TM 12 mode of the annular ring has a greater bandwidth than the TM 11 mode.

Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism

An experimental observed fact in scattering of electromagnetic waves by dense distribution of discrete scatterers is that the assumption of independent scattering leads to overestimation of scattering effects. To account for this phenomenon in the present paper, the method of coherent potential is applied to the study of multiple scattering of electromagnetic waves by random distribution of discrete scatterers. Comparisons are made with results obtained by using the effective field approximation and the quasicrystalline approximation. Numerical results of the effective dielectric constant and the scattering attenuation rates, as a function of the fractional volume occupied by the scatterers, are illustrated using parameters frequently encountered in the microwave remote sensing of snow and soil moisture. It is shown that the coherent potential method as applied to quasicrystalline approximation is superior to the other approximations in accounting for the overestimation factor.

Polarimetric passive remote sensing of ocean wind vectors

This paper investigates the theory of polarimetric passive remote sensing of wind-generated sea surfaces and the potential application of polarimetric radiometry to ocean wind remote sensing. Theoretical polarimetric emission coefficients of small-scale sea surfaces are evaluated using the small perturbation method (SPM). The SPM is derived to second order and applied to the Stokes vectors of thermal emission from random rough dielectric surfaces described by anisotropic directional spectra. To verify the accuracy of the SPM, a Monte Carlo simulation is performed to calculate the Stokes vectors of the emission from the simulated one-dimensional random rough surfaces with a power law spectrum for various observation angles and surface parameters. The theoretical results of the SPM for all four Stokes parameters are in excellent agreement with the numerical results obtained from the Monte Carlo simulation. Moreover, the second-order coherent fields are indispensable in the theoretical evaluation of the third and fourth Stokes parameters. Otherwise, the reflectivities of random rough surfaces would be significantly overestimated, and the signs of the third and fourth Stokes parameters would be incorrect. The SPM is then applied to small-scale sea surfaces described by an empirical sea surface spectrum. It is found that the azimuthal signatures of Stokes parameters agree qualitatively well with aircraft Ku-band radiometer data. Theoretical model functions of the Stokes parameters are illustrated. Advantages of wind direction retrieval using polarimetric Q and U measurements are discussed, and it is expected that a spaceborne polarimetric radiometer has a potential of providing wind vector measurements with uniform accuracy across all parts of swath.

Multiple scattering of acoustic waves by random distribution of discrete spherical scatterers with the quasicrystalline and Percus–Yevick approximation

In studying the multiple scattering of acoustic waves by random distributions of scatterers with appreciable concentration, the approach of quasicrystalline approximation together with hole correction (QCA–HC) has been a common method. We show that such an approach will give rise to negative attenuation rate indicating a growth of the coherent wave in space which is a nonphysical solution. To derive better results, we employ the solution of the Percus–Yevick equation together with quasicrystalline approximation (QCA–PY) to study multiple scattering of acoustic waves by discrete spherical scatterers. Waterman’s T matrix formalism is used in formulating the multiple scattering problem. Closed form solutions are obtained for the effective propagation constants in the low‐frequency limit. Effective propagation constants at higher frequencies are calculated by numerical methods. The result of QCA–HC for the two‐dimensional case is also discussed.

Effective propagation constants for coherent electromagnetic wave propagation in media embedded with dielectric scatters

In studying the multiple scattering of electromagnetic waves by random distributions of scatterers with appreciable fractional volume, the approach of quasicrystalline approximation together with the hole correction approximation has been a common method. In this paper, it is shown that such an approach will give rise to negative attenuation rate indicating a growth of the coherent wave in space which is a nonphysical solution. The result of the Percus–Yevick equation is a better representation of the pair distribution function for appreciable concentration. We use it together with the quasicrystalline approximation to study multiple scattering of electromagnetic waves by discrete spherical scatters. Waterman’s T matrix formalism is used in formulating the multiple scattering problem. Closed from solutions are obtained for the effective propagation constants in the low frequency limit and agree with Twersky’s results. Effective propagation constants at higher frequencies are calculated by numerical methods.

Resonance of nonaxial symmetric modes in circular microstrip disk antenna

Resonant frequencies of the nonaxial symmetric modes in a microstrip disk are computed using two approaches: Galerkin’s method and a perturbative approach. The perturbative approach is good when the substrate of the microstrip disk is thin compared to its radius and when the dielectric constant of the substrate is high. Galerkin’s method can be used to compute the resonant frequency to high accuracy but the perturbative approach is more efficient for thin substrate and large dielectric constant. In applying Galerkin’s method, the problem is first cast into a vector dual integral equation using vector Hankel transform (VHT). Using VHT, it is also shown that the magnetic‐wall model is only good when the substrate is of zero thickness. Using zero‐order current distribution on the disk, we also derive the radiation field and radiation pattern. Also, by taking into account the radiation loss, the resonant frequencies are complex. We find discrepancies when we compare our results for the resonant frequency shif...

Enhancement of Smith–Purcell radiation from a grating with surface-plasmon excitation

The Smith–Purcell radiation from a charge moving across a penetrable grating is studied. We account for the finite permittivity and the absorption effect of the grating and find that enhancement of the radiation will occur near particular angles of observation at which the phase-matching condition for the excitation of the surface-plasmon mode is satisfied.

Tapered wave with dominant polarization state for all angles of incidence

Typical applications of the method of moments (MoM) to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such a wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out.

Resonance of the axial‐symmetric modes in microstrip disk resonators

Three methods have been used to calculate the resonant frequencies for the axial‐symmetric modes in the microstrip disk resonators which also have the application as radiating antennas. The variational Galerkin’s method provides the most accurate result for the estimation of both the real and imaginary parts of the resonant frequency shifts with judicious choices of basis functions. The iterative approach gives good results for the imaginary part of the frequency shift and very crude approximations for the real part. The perturbation formula is the most efficient in computational time and is useful for sufficiently large permittivity for the substrate material and small ratio of substrate thickness to disk radius. To illustrate the application of the circular microstrip disk as a radiating antenna, the radiation pattern for the axial‐symmetric mode is also plotted.