Jung-Woong Ra

Diffraction by an arbitrary-angled dielectric wedge. I. Physical optics approximation

A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45 degrees , relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150 degrees are plotted in figures, revealing abrupt discontinuities at dielectric interfaces. >

Diffraction by an arbitrary-angled dielectric wedge. II. Correction to physical optics solution

For pt.I see ibid., vol.39, no.9, p.1272-81 (1991). The error of the physical optics solution for the E-polarized plane wave incidence in connection with diffraction by an arbitrary-angled dielectric wedge is corrected by calculating the nonuniform current distributed along the dielectric interfaces. Two kinds of series expansions to the nonuniform current are employed. One is an asymptotic expansion as the multipole line source located at the edge of the dielectric wedge, since the correction field seems to be a cylindrical wave emanating from the edge in the far-field region. The other is arbitrary electric and magnetic surface currents expanded by infinite series of the Bessel functions, i.e. the Neumann expansion, of which fractional order is chosen to satisfy the edge condition near the edge of the dielectric wedge in the static limit. Both of the two different expansion coefficients for a wedge angle of 45 degrees , relative dielectric constants 2, 10, and 100, and the E-polarized incident angle of 150 degrees are evaluated by solving the dual series equation numerically after finite truncation.<<ETX>>

Moment method and iterative reconstruction of two-dimensional complex permittivity by using effective modes with multiple sources in the presence of noise

An iterative hybrid algorithm combining the steepest descent algorithm of Levenberg-Marquardt and the simulated annealing algorithm is used for reconstructing the complex permittivity of a two-dimensional, high-contrast, large object. The scattered fields calculated in a cost function are expanded in angular spectral modes. The “illposedness” in the inversion due to the noise in the scattered fields is regularized by keeping only the effective modes and filtering out the higher angular spectral modes. The object is discretized into N square cells of unknown permittivities and N or larger number of effective modes (P) are needed for this spectral domain iterative method to reconstruct the shape and the permittivity distribution of the object. When N > P, multiple view (K) and effective modes of each view (P) make the reconstruction possible if N ≤ PK.

Inverse scattering scheme based on the moment method in the spectral domain, part I: Theory

Recently, electromagnetic and ultrasonic imaging of inhomogeneous objects by applying the moment-method procedures of forward scattering problems in the reverse sequence have been developed. In this paper, the inverse scattering formulation has been modified to be applicable in the spectral domain. Compared to previous schemes, the suggested formulation illustrates clearly the actual mechanism of the inverse scattering process by explicit separation of the contributions from several variables, such as the measurement location, basis function, and geometry of objects. The ill-posedness inherent in inverse scattering problems was also explained easily in this spectral scheme by the exponentially-decaying behavior of high-frequency spectral components of the scattered field. It implies that enlargement of the discretized cell size is a key factor in regularizing the ill-posedness. In particular, since the singular kernel to be integrated on each cell became regular in the modified scheme, various types of basis functions instead of pulse function were adopted without additional difficulties. This advantage is expected to play an important role in regularizing the noise effect by selecting polynomial basis function on the enlarged cells of discretization in the spectral inverse scattering scheme.

Reconstruction of a high-contrast penetrable object in pulsed time domain by using the genetic algorithm

A three dimensional dielectric object having high relative dielectric constant of 7.0 and large size of wavelength cube is reconstructed from the scattered fields in the space-time domain when plane waves of gaussian pulse shine the object. This reconstruction is obtained from the iterative inversion method that minimizes the cost function by using the Levenberg-Marquardt algorithm and the genetic algorithm to find its global minimum, where the cost function is defined as the squared magnitude of the difference between the measured fields and the calculated fields from the assumed profile of the object. The scattered fields are calculated by the method of FDTD and measured fields used for reconstruction are assumed to have the measurement error.

Frequency dependence of GaAs FET equivalent circuit elements extracted from the measured two-port S parameters

An eight-element equivalent circuit for GaAs FETs is used to calculate their element values from the eight measured data values of the two-port S parameters exactly at each frequency. Three element values vary with frequency and two additional small inductances are needed to account for the frequency dependence. A ten-element equivalent circuit including these correction inductances closely predicts the wafer measured S parameters up to 18 GHz. >

Adaptive mesh refinement for boundary element method and its application to stripline analysis

Adaptive mesh refinements are incorporated in the boundary element method (BEM) for accurate calculation of electromagnetic fields. Refinements are based on local error estimates of the calculated potential and its normal derivative on the boundaries. Differences between two adjacent node values are used for simple local error estimates. Also, error at the middle of each element is calculated from an integral equation. To demonstrate its applicability, this adaptive scheme is applied to striplines with edge singularity. >

Inverse scattering scheme based on the moment method in the spectral domain, part II: Numerical simulation

A spectral inverse scattering scheme, applying the moment-method procedures with a polynomial basis function for the induced field in each enlarged cell, is implemented numerically and simulated for a simple test geometry. The method provides good results comparable to the discretization of object fine enough to adopt the pulse basis function. The effects of several variables on the reconstructed profile are simulated one by one. Simulation results for the scattered field contaminated by Gaussian random noise show large fluctuations in the reconstructed profiles. The validity of the inversion scheme to regularization of the noise effects is conformed by showing that averaging the reconstructed profile over each cell with a suitable weighting function reduces the reconstruction error to a nearly negligible value.

Diffraction pattern by a trapezoidal cylindrical cavity

Asymmetric diffraction patterns for a trapezoidal cylindrical cavity are calculated for the case in which the cavity size is comparable with the wavelength of the incident field. It is shown that asymmetric double dips and null patterns in the near-field region are also present. Amplitude and phase variations of the scattered field are calculated to show how they generate these double dips and null patterns as a function of frequency. The asymmetry of the cross section yields two different null frequencies, corresponding to the upper and the lower boundaries, respectively.<<ETX>>

Scattering by a composite wedge of metal and dielectric

Summary form only given. In an analysis of the diffraction by an arbitrary-angled dielectric wedge Kim, Ra, and Shin (1991) formulated two sets of dual integral equations in the spectral domain, one inside the dielectric and the other outside the dielectric. The physical optics (PO) solution is obtained by using the two-dimensional Greens theorem for the geometrical optical (GO) contributions along the dielectric interfaces. The PO solution gives the reflected and the refracted GO fields, and the edge diffracted fields. The edge diffracted fields of the PO solution are asymptotically two cylindrical waves emanating from the edge, one valid inside the wedge v/sub 2/ and the other valid outside the wedge v/sub 1/. Substituting the physical optics solution plus unknown correction field, which makes the exact field solution, into the dual integral equation, one obtains the relation between the correction field and two edge diffracted fields of PO. It turns out that if one finds the nonuniform currents along tile dielectric interfaces that produce a field v/sub 1/ inside and -v/sub 2/ outside the region of the wedge with a background medium of free space and a dielectric, respectively, they give the correction fields. One may apply this method of dual integral equations to the scattering of electromagnetic waves by a composite wedge of metal and dielectric.