A simulation tool based on the finite-difference time-domain (FDTD) technique is developed to model the electromagnetic interaction of a focused optical Gaussian beam in two dimensions incident on a simple model of a corrugated dielectric surface plated with a thin film of realistic metal The technique is a hybrid approach that combines an intensive numerical method near the surface of the grating, which takes into account the optical properties of metals, with a free-space transform to obtain the radiated fields A description of this technique is presented along with numerical examples comparing gratings made with realistic and perfect conductors In particular, a demonstration is given of an obliquely incident beam focused on a uniform grating and a normally incident beam focused on a nonuniform grating The gratings in these two cases are coated with a negative-permittivity thin film, and the scattered radiation patterns for these structures are studied Both TE and TM polarizations are investigated Using this hybrid FDTD technique results in a complete and accurate simulation of the total electromagnetic field in the near field as well as in the far field of the grating It is shown that there are significant differences in the performances of the realistic metal and the perfect metal gratings

Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings

An improved accurate closed-form wave function analytic solution of two-dimensional scattering and diffraction of antiplane SH waves by a semicircular cylindrical hill on an elastic half space is presented. In the previous solution, stress and displacement residual auxiliary functions were defined at the circular interface above and below the circular hill. The method of weighted residues (moment method) was used to solve for the unknown scattered and transmitted waves by requiring each term of Fourier series expansion of these auxiliary residual functions to vanish. It was found that the stress residual amplitudes on both (left and right) rims of the hill (ideally should be zero) are not numerically insignificant, irrespective of how many terms used. It was pointed out that the shear stress at the rim is infinite, and that the stress auxiliary function is discontinuous at both rims of the hill, exhibiting a problem for the numerical solution that is more complicated than Gibbs' phenomenon. The problem with the overshoot of the stress residual amplitudes at the rim was most likely numerical. In this paper, all displacement and stress waves were expressed as cosine functions, and the solution of the circular hill problem was reformulated in this paper, and, for the solution to be correct, the computed stress and displacement residual amplitudes were shown to be numerically negligible everywhere, including those at both rims of the hill. Displacements at higher frequencies are also computed.

Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution

A modal theory is presented for solving the problem of electromagnetic scattering from a surface consisting of a finite number of one-dimensional rectangular grooves in a metallic plane. The incident plane wave can be polarized with either its electric or its magnetic field along the grooves. The formalism is applicable to perfectly conducting materials and to real metals with high (but finite) conductivity. Particular attention is paid to the changes appearing in the scattering pattern when the conductivity of the structure is changed from an infinite value (perfect conductor) to a finite value (highly conducting metal). The excitation of surface waves when the incident wave is p polarized is illustrated in some numerical examples that demonstrate the differences between the spectral amplitudes corresponding to s and p polarizations.

Scattering from metallic surfaces having a finite number of rectangular grooves

The problem of transverse electric plane wave scattering from a rectangular channel which is engraved in a perfect conducting plane is investigated. A Fourier transform technique is employed to express the scattered field in the spectral domain in terms of parallel-plate waveguide modes. The boundary conditions are enforced on the conducting surface and the channel aperture to obtain simultaneous equations for the transmitted field inside the channel. The simultaneous equations are solved to represent the transmitted field in a series form. By using the stationary phase approximation, the exact expression for the far-zone scattered field is obtained and the echo width behavior is numerically studied in terms of the scattering angle, frequency, and channel size. It is found that the behavior of the echo width versus the channel depth exibits resonance irrespective of the size of the channel width. An approximate series expression (Kirchhoff solution) for the echo width is valid for high-frequency scattering regimes (a > 2 λ). We also present an approximate closed form solution for nadir backscattering which is valid when a > 0.2λ.

An analysis of transverse electric scattering from a rectangular channel in a conducting plane

Acoustic scattering from a rectangular aperture in a thick hard screen is examined. The Fourier transform is used to represent the scattered wave in the spectral domain and the boundary conditions are enforced to represent a solution in closed form. Numerical computations are performed to illustrate the behavior of the scattered wave from a thick rectangular aperture. The solution is represented in series which are numerically efficient.

Acoustic scattering from a rectangular aperture in a thick hard screen

TM-wave scattering from rectangular grooves in a perfectly conducting plane is investigated. A Fourier-transform technique is employed to express the scattered field in the spectral domain as a superposition of the parallel-plate waveguide modes. The boundary conditions are enforced on the conducting surface and the groove apertures to obtain simultaneous equations for the transmitted field inside the grooves. The simultaneous equations are solved to obtain the transmitted field in a series representation that reduces to a closed form in a high-frequency scattering regime. With the use of the stationary phase approximation, the far-zone scattered field is obtained, and its scattering behavior is studied in terms of the scattering angle. The diffraction efficiency for the finite grating as the number of grooves increases is presented.

Analysis of TM scattering from finite rectangular grooves in a conducting plane

The problem of transverse‐magnetic plane‐wave scattering from a rectangular channel in a perfect conducting plane is investigated. A Fourier‐transform technique is employed to express the scattered field in the spectral domain in terms of parallel‐plate waveguide modes. An approximate series solution for scattering is presented in a closed form that is valid for a high‐frequency scattering regime. The presented formulation is computationally much more efficient than other existing numerical solutions.

Tah J. Park

Papers

An analysis of transverse electric scattering from a rectangular channel in a conducting plane

Analysis of TM scattering from finite rectangular grooves in a conducting plane

An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane

TM Scattering from a Dielectric-Loaded Semi-Circular Trough in a Conducting Plane

A Series Solution for Acoustic Radiation from a Flanged Circular Pipe