TM Incident Research Articles

Wavelet-based simulations of electromagnetic scattering from large-scale two-dimensional perfectly conducting random rough surfaces

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed.

Computer simulation for two-dimensional near-field optics with use of a metal-coated dielectric probe

In our previous paper [J. Opt. Soc. Am. A15, 101 (1998)], the integral equations that are suitable for simulations of near-field optics with use of an uncoated dielectric probe were proposed. We extend the integral equations to near-field optical circuits by using a metal-coated dielectric probe with an aperture. The derivation of the integral equations is described in detail for the incident TM mode, because it is impossible to derive them with the same procedures as those used in the case of the uncoated dielectric probe. Simulations of the illumination/collection mode of a two-dimensional scanning near-field optical microscope (2D-SNOM) are performed. All numerical results satisfy the energy conservation law within an accuracy of 1%. One-dimensional scanning images of a 2D-SNOM obtained by using the metal-coated dielectric probe with an aperture and those obtained by using the uncoated dielectric probe are compared, and advantages of the metal-coated dielectric probe are described.

Complementary frequency selective surfaces

A concept in frequency selective surface (FSS) technology that stems from Babinet's principle, whereby a hybrid of two closely coupled FSS, a layer of conducting elements and a layer of aperture elements are etched either side of a dielectric substrate, acronymed as complementary FSS (CFSS) is introduced. There are two narrow passbands separated by a distinct null. The CFSS creates electrically large elements from physically small ones to such an extent that a conventional λ/2 resonator in free space at the lower passband resonant frequency would be over three times longer than the dipole length employed in the CFSS. This passband is highly stable for normal and oblique TE and TM incidences, with less than 2% frequency shift. A full wave modal analysis is developed and two integral equations (IEs), an electric field IE and a magnetic field IE, are derived. These IEs are coupled and this renders them suitable for the solution of the CFSS problem. The interlayer dielectric region is critical to the location of the passbands as well as the in-band loss. Results are presented for dipole and ring CFSS and compared with measured data up to 40 GHz.

Radiation and Receiving Characteristics of Parallel Plate-Fed Slot Antennas Loaded By a Dielectric Cylinder: Tm-Case

An exact analysis is presented for investigating parallel plate-fed slot antennas loaded by a dielectric cylinder. The primary excitation is taken to be either a TM incident mode of the parallel-plate waveguide or an incident H-polarized plane wave. The analysis combines singular integral equations with separation of variables techniques. The resulting integral equations are discretized using quasi-analytical methods, which lead to computationally efficient expressions for all matrix elements. This, in conjunction with the small matrix sizes required, leads to very accurate results with low computational cost. The numerical results presented reveal the effect of the load on the characteristics of the antennas.

Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses

Various integral diffraction methods are systematically unified into a single framework, clearly illustrating the interconnections among the numerous scalar and rigorous formulations. This hierarchical depiction of the integral methods makes clear the specific approximations inherent in each integral method. The scalar methods are compared in detail with a rigorous open-region formulation of the boundary element method (BEM). The rigorous BEM provides a reference method for accurately determining the diffracted fields for both TE and TM incidence. The rigorous BEM and the various scalar methods are then applied to the case of focusing of normally incident plane waves by diffractive cylindrical lenses with f-numbers ranging from f/2 to f/0.5. From the diffracted-field calculations, a number of performance metrics are determined including focal spot size, diffraction efficiency, reflected and transmitted powers, and focal-plane sidelobe power. The quantitative evaluation of the performance of the scalar methods with these metrics allows the establishment, for the first time, of the region of validity of the various scalar methods for this application. As expected, the accuracy of the scalar methods decreases as the f-number of the diffractive lenses is reduced. Additionally, some metrics, particularly the focal-plane sidelobe power, appear to be particularly sensitive to the approximations in the scalar methods, and as a result their accuracy is significantly degraded.

Generalised iterative method for solving 2D multiscattering problems using spectral techniques

An iterative method for two-dimensional problems with multiple scatterers is presented. Spectral techniques are used to characterise a scatterer by its transfer function. To obtain this transfer function physical optics and the method of moments have been used. An iterative method analysing the existence of a new object at each new iteration is outlined. The method produces combined transfer functions that give the response of the multiple scattering problem to several incident fields. A useful alternative iteration for clumped groups of scatterers is also presented. Results for a parabolic reflector, a Cassegrain structure and a horn for TM incidence are analysed and comparison with theoretical data is discussed. Finally, the extension of the method for the TE case and for 3D problems is outlined.

Numerical calculation of diffraction coefficients of generic conducting and dielectric wedges using FDTD

Classical theories such as the uniform geometrical theory of diffraction (UTD) utilize analytical expressions for diffraction coefficient for canonical problems such as the infinite perfectly conducting wedge. We present a numerical approach to this problem using the finite-difference time-domain (FDTD) method. We present results for the diffraction coefficient of the two-dimensional (2-D) infinite perfect electrical conductor (PEC) wedge, the 2-D infinite lossless dielectric wedge, and the 2-D infinite lossy dielectric wedge for incident TM and TE polarization and a 90/spl deg/ wedge angle. We compare our FDTD results in the far-field region for the infinite PEC wedge to the well-known analytical solutions obtained using the UTD. There is very good agreement between the FDTD and UTD results. The power of this approach using FDTD goes well beyond the simple problems dealt with in this paper. It can, in principle, be extended to calculate the diffraction coefficients for a variety of shape and material discontinuities, even in three dimensions.

Multimode equivalent network representation for the scattering from multistrip gratings

A multimode equivalent network representation (MEN) is proposed for the scattering from a multistrip grating. Previously, rigorous analytical results were developed involving gratings with one or two strips in a period. In the present paper, the MEN representation is extended to planar gratings with an arbitrary number of strips or apertures per unit cell. Both TE and TM incidence are described. The extension is obtained combining the MEN formulation with the method of moments solution (MoM) of the relevant integral equation. The code thus obtained retains the key feature of the MEN representation, namely the frequency independence of the characterization, and is much more flexible than the analytical solutions previously derived. The MoM solution procedure is described in detail and several application examples are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An analysis technique for buried inhomogeneous dielectric objects in the presence of an air-Earth interface

Complex geological structures are modelled in the presence of an air-Earth interface. A cross-borehole configuration of target, source, and receiver is assumed, with the target itself not restricted as to geometrical cross section or complex permittivity value. Two-dimensional method-of-moment formulations are employed, utilizing cylindrical pulse basis functions and point matching. Scattering from buried dielectric objects is computed near the air-Earth interface for both TE and TM incident fields. A Sommerfeld-Green function is used to represent the effect of the air-Earth interface on the incident fields and the impedance matrix. The TE case is examined for scattering of both the copolarized and cross-polarized electric fields, and several examples are given for a cylindrical target at depths that vary from one to twenty four wavelengths, after which the presence of the air-Earth interface can be neglected. Some experimental results utilizing a 1/40th laboratory scale model and a tunnel-like target are also included for comparison. The technique enables the user to investigate electromagnetic scattering from a variety of complex buried objects whose dimensions are typically in or below the resonance region. The simultaneous relaxation of restrictions on cross section, material properties, and burial depth, together with experimental validation, is not found in the literature to date.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of multilayer wave absorber for oblique incidence using the point frequency matching method

AbstractThe desirable characteristics of the wave absorber are such that it has good absorbing characteristics not only for the normal incidence but also the oblique incidence and that it has an effective absorbing capability for any polarization.In this paper, a program is developed for design of a multilayer wave absorber for the oblique incidence by means of the point frequency matching method and subsequently a design is carried out. It was successful in designing a broadband wave absorber for which the reflection coefficient is less than a certain value at frequencies above a certain design frequency once an incident angle and a polarization are specified for an obliquely incident TE or TM wave.To study both the frequency characteristics and the incident angle dependence of the designed wave absorber, contour maps were developed. By means of the contour maps, the absorbing characteristics of the wave absorber were studied. It was confirmed that good results can be obtained for oblique incidence.

Low-frequency diffraction by a planar junction of a metallic and a wire-mesh halfplane

The canonical problem of an electromagnetic field incident on a metallic halfplane joined to a wire-mesh halfplane is considered. It is assumed that the wire radius is small in comparison with the spacing between the wires, and that this spacing is small with respect to the free-space wavelength. Under this hypothesis, it is shown that the problem can be solved in closed form by using a Wiener-Hopf technique for any nonuniform electromagnetic incident field. The field transmitted through the structure is computed, considering as uniform sources both TE and TM incident planewaves.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Monte Carlo simulations and backscattering enhancement of random metallic rough surfaces at optical frequencies

The finite element method of Monte Carlo simulations of random rough surface scattering is extended to plane and tapered wave scattering from random metallic surfaces at optical frequencies. The backscattering enhancement associated with these rough surfaces is studied for both TE and TM incident waves. Numerical results of the finite element method are presented and compared with those of the tapered wave integral equation method. In all the cases considered, both the TE and TM incident waves show backscattering enhancement. The lossy surfaces scatter more power for TE incident waves than those of TM due to the TM surface waves. No TE surface wave is supported by rough surfaces simulated in this paper.

Optical characterization of liquid crystals by means of half-leaky guided modes

Optical excitation of half-leaky guided modes has been used, for the first time to our knowledge, to characterize in detail the optical tensor profile in a liquid-crystal layer. The thin liquid-crystal layer is sandwiched between a high-index pyramid, with an index greater than the maximum index of the liquid crystal, and a glass substrate with an index lower than the minimum index of the liquid crystal. Analysis of this geometry shows that over a small angle range encompassed by a pseudocritical angle and a critical angle associated with the pyramid–liquid crystal and the pyramid–glass-substrate boundaries, respectively, there may exist sharp resonant features in the angle-dependent optical reflectivity. More particularly, if the director is tilted and twisted out of the plane of incidence there is strong TE-to-TM optical conversion over this small angular window, which is sensitive to details of the director profile. A 90° twisted, homogeneously aligned nematic liquid-crystal layer has been studied with this technique at two different wavelengths, 632.8 and 514.5 nm. Greater than 60% conversion from TM incident radiation to TE output has been recorded from sharp resonances in the half-leaky guided-wave angle window. If one fits these resonances with predictions from multilayer optics theory, one obtains extraordinary detail of the director profile in the cell. Since no metallic coatings are used, and all that is required are two glass plates of high and low index, respectively, the technique offers the potential of extremely useful applications in the examination of detailed director profiles in commercially fabricated cells.

A finite element approach to the electromagnetic interaction with rotating penetrable cylinders of arbitrary cross section

A method for evaluating the fields excited by an obliquely incident plane wave inside and outside a rotating cylinder is presented. A differential formulation of the problem is developed with respect to the comoving reference frame of the scatterer on a closed circular domain including the scatterer cross section; the boundary conditions account for the far-field conditions through a series expansion of the total field on the domain contour. The results at oblique incidence are then particularized for normal incidence and a hybrid finite element numerical solution is presented and discussed for TM incidence. The present FEM approach and the related computer code are directly applicable to the study of rotating piecewise-homogeneous cylinders at normal incidence, as well as metallic cylinders coated by layers of penetrable materials. Through a comparison, for normal incidence, between the quasi-stationary and the Galileian relativistic approach, a method for approximately reconstructing the Doppler frequency shift in the quasi-stationary method is derived. Far-field and near-field numerical results for circular and arbitrarily shaped (metallic or dielectric) cylinders are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

TM scattering by conducting strips right on the planar interface of a three-layered medium

Combining the Fourier transform with powerful singular integral equation methods, the authors investigate the scattering properties of a variety of two-dimensional, three-layered planar structures loaded by a strip or a couple of coplanar strips right on an interface. The primary excitation is the lowest-order incident TM (to strip axis) surface wave mode or an incident E-polarized plane wave. In the practical case where the entire space is magnetically homogeneous, the kernel of the integral equations is most conveniently decomposed into a singular closed-form term added to an exponentially convergent inverse Fourier integral. An efficient, accurate, and stable numerical code is obtained and used to determine the strip-induced current densities as well as any quantity of practical interest. Plotted results reveal that by a proper choice of certain geometrical parameters the structures may become very efficient radiators, which can be designed to exhibit either very wideband and high directivity or considerable frequency scanning.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of a banded matrix iterative approach to monte carlo simulations of scattering of waves by a random rough surface: TM case

AbstractA banded matrix iterative approach is applied to study scattering of a TM incident wave from a perfectly conducting one‐dimensional random rough surface. It is much faster than the full matrix inversion approach. When compared to the Kirchoff iterative approach, it is of comparable CPU time, is more accurate, and works for cases when the Kirchoff iteration fails. © 1993 John Wiley &amp; sons, Inc.

Wideband filters employing multilayer gratings

Multilayer surfaces, consisting of stacked inductive and capacitive strips or grids, have been used to design wideband filters in the 5–40 GHz range, with rapid transitions between reflection and transmission. For singly polarised applications, transmission bandwidths of 70–100% and edge transition ratios of 1.1–1.3 are realisable at 45° TM incidence using 4–8 layers of capacitive and inductive strips. Factors which constrain the passbands are highlighted. In dual polarised designs using doubly periodic grids, the widths are restricted to 35–40% by TE incidence grating responses at the upper passband edge. In TM they are even more restricted by a TE11 mode resonance. Wider passbands require high inductances to reduce the low frequency edge, implying very fine conductors.

Design of lightweight, broad-band microwave absorbers using genetic algorithms

A procedure for synthesizing multilayered radar absorbing coatings is presented. Given a predefined set of N/sub m/ available materials with frequency-dependent permittivities in /sub i/(f) and permeabilities mu /sub i/(f) (i=1,. . ., N/sub m/), the technique determines simultaneously the optimal material choice for each layer and its thickness. This optimal choice results in a screen which maximally absorbs TM and TE incident plane waves for a prescribed range of frequencies (f/sub 1/,f/sub 2/,. . ., f/sub N/f) and incident angles ( theta /sub 1/, theta /sub 2/,. . ., theta /sub N theta /). The synthesis technique is based on a genetic algorithm. The technique automatically places an upper bound on the total thickness of the coating, as well as the number of layers contained in it, which greatly simplifies manufacturing. In addition, the thickness or surface mass of the coating can be minimized simultaneously with the reflection coefficient. The algorithm was successfully applied to the synthesis of wideband absorbing coatings in the frequency ranges of 0.2-2 GHz and 2-8 GHz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Banded matrix iterative approach to Monte-Carlo simulations of scattering of waves by large-scale random rough surface problems: TM case

A banded matrix iterative approach is applied to study the scattering of a TM incident wave from a perfectly conducting one-dimensional random rough surface. It is accurate and is much faster than the full matrix inversion approach or the conjugate gradient method. Applications of this method to large-scale rough surface problems are illustrated.

Accurate computation of wide-band response of electromagnetic systems utilizing narrow-band information

Cauchy's technique for interpolating a rational function from samples of frequency responses and/or their derivatives is investigated. This technique can be used to speed up the numerical computations of parameters, including input impedance and RCS of any linear time-invariant electromagnetic system. This technique is utilized to find the far field of a slit conducting cylinder (TM incidence) over a bandwidth utilizing the information about the current and its derivatives at a few sample points. The numerical results are presented are in good agreement with exact computational data. This technique is a true interpolation/extrapolation technique as it provides the same defective result as the original electric field integral equation at a frequency which corresponds to the internal resonance of the closed structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>