High Frequency Diffraction Research Articles

Fifty years of high frequency diffraction

The study of high frequency diffraction phenomena mostly associated with geometrical theory of diffraction, uniform theory of diffraction, physical theory of diffraction, and their alternatives is reviewed. Several examples illustrate these theories and their applications in antennas and scattering problems. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.

High-Frequency Diffraction of a Plane Electromagnetic Wave by an Elongated Spheroid

An asymptotic formula for the problem of diffraction by a strongly elongated body of revolution is constructed. Its uniform nature with respect to the parameter that characterizes the rate of elongation is demonstrated. The results are in good agreement with numerical simulations.

High-frequency diffraction of a electromagnetic plane wave by an imperfectly conducting rectangular cylinder

We shall consider the problem of determining the scattered far-wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. On the basis of the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller’s method and multiple diffraction, a high-frequency far-field solution to the problem is given for two edge diffractions.

Simultaneous study of the diffraction by a 2D-convex obstacle through boundary layer method and microlocal analysis

In this paper we consider the high frequency diffraction of electromagnetic waves by a strictly convex obstacle. We restrict ourselves to the case of an obstacle in 2D and to the diffraction of a TE or TM wave. The aim of this paper is to present simultaneously with the same notations, unknowns and special functions the boundary layer analysis of this problem with stretched variables using the intuition of the solutions and the microlocal analysis way of construction of an adapted parametrix. We concentrate on the case of diffraction, i.e. studying the representation of a creeping wave on the boundary, which occurs in the case of the study of a glancing point. We use both methods to derive the exact solution near a diffractive point, obtaining results in terms of suitable Airy functions.

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.

Large-Size Local-Domain Basis Functions with Phase Detour and Fresnel Zone Threshold for Sparse Reaction Matrix in the Method of Moments

Locality in high frequency diffraction is embodied in the Method of Moments (MoM) in view of the method of stationary phase. Local-domain basis functions accompanied with the phase detour, which are not entire domain but are much larger than the segment length in the usual MoM, are newly introduced to enhance the cancellation of mutual coupling over the local-domain; the off-diagonal elements in resultant reaction matrix evanesce rapidly. The Fresnel zone threshold is proposed for simple and effective truncation of the matrix into the sparse band matrix. Numerical examples for the 2-D strip and the 2-D corner reflector demonstrate the feasibility as well as difficulties of the concept; the way mitigating computational load of the MoM in high frequency problems is suggested.

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

The aim of this work is to propose an accurate and efficient numerical approximation for high frequency diffraction of electromagnetic waves. In the context of the boundary integral equations presented in F. Collino and B. Després, to be published in J. Comput. Appl. Math., the strategy we propose combines the microlocal discretization (T. Abboud et al., in: Third International Conference on Mathematical Aspects of Wave Propagation Phenomena, SIAM, 1995, pp. 178–187) and the multilevel fast multipole method (J.M. Song, W.C. Chew, Microw. Opt. Tech. Lett. 10 (1) (1995) 14–19). This leads to a numerical method with a reduced complexity, of order O( N 4/3ln( N)+ N iter N 2/3), instead of the complexity O( N iter N 2) for a classical numerical iterative solution of integral equations. Computations on an academic geometry show that the new method improves the efficiency, for a solution with a good level of accuracy. To cite this article: A. Bachelot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).

High-frequency diffraction by a rectangular impedance cylinder on an impedance plane

The scattering of a line source field by a rectangular impedance cylinder on an infinite impedance plane is studied. The diffraction problem is formulated into a modified Wiener–Hopf equation of the third kind and then solved approximately. The solution contains two infinite sets of constants satisfying two infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the surface reactance, width and height of the rectangular cylinder, whereby the effects of these parameters on the diffraction phenomenon is studied. The results are compared with the corresponding physical optics solution and the agreement is very satisfactory.

Optical strain sensor using position-sensitive detector and diffraction grating: error analysis

A new optical strain sensor is developed to rival the traditional electrical strain gauge. It directly measures in-plane strains using a high frequency grating and two position-sensitive detectors (PSDs). The strain measurement is independent of the rigid body motion of the grating. A high frequency diffraction grating attached to the surface of a specimen is illuminated by a focused or collimated laser beam. The centroids of the two symmetric diffracted beam spots from the grating are determined by the PSD sensors connected to a personal computer. The shift of diffracted beam spots due to the specimen deformation is transformed to strain components. Several measures are taken to improve strain sensitivity including residual strain error due to the misalignment of laser and grating. The measured strain is directly displayed on the monitor in both digital and graphical forms in real time. Strain sensitivity of 1 x strain and a spatial resolution of 0.1 mm can be achieved.

Imaging interferometric lithography: A wavelength division multiplex approach to extending optical lithography

The critical dimension (CD) limits of conventional optical lithography follow directly from the low-pass filter characteristics of the imaging optical system (|k|≲2πNA/λ where λ is the optical wavelength and NA the numerical aperture). In contrast, the linear systems limits of optics extend to spatial frequencies of 4π/λ (interference between counterpropagating beams at grazing incidence). Imaging interferometric lithography is introduced as a technique to approach this linear systems limit while retaining the arbitrary pattern capability of an imaging optical system. Multiple, wavelength-division-multiplexed exposures are used, each exposure recording a different portion of frequency space. A conventional, coherent illumination exposure provides the low frequency information, within the lens passband. Offset exposures provide the high spatial frequency information. Off-axis illumination shifts a portion of the high spatial frequency diffraction from the mask into the lens passband and interference with a reference beam resets the frequencies once they are transmitted through the optical system. For a typical x-y geometry pattern, offset exposures in the x and y directions provide a sufficient coverage of frequency space. Model calculations illustrate that the imaging capabilities of imaging interferometric lithography (IIL) for dense features extend to ∼λ/3 (130 nm at I line; 65 nm at an ArF exposure wavelength). Initial experiments are reported at I line with a modest (NA=0.04) optical system. The results are in good agreement with the model calculations. A resolution enhancement of ∼3× from dense 6 μm CDs for a conventional, coherent illumination exposure to ∼dense 2 μm CDs for an IIL exposure sequence is demonstrated.

Relationship Between High-Frequency Diffraction and Low-Frequency Scattering From a Sharp Wedge

ABSTRACT This article describes a new relationship between the two-dimensional high-frequency and low-frequency waves scattered by an obstacle with a sharp wedge. It is shown that these two extremal waves have a unique correspondence in the underlying description of electromagnetic fields. The low-frequency field, which is given as a quasi-static field, is represented in terms of a function of complex variable z = x + iy. The high-frequency field can also be represented in terms of this complex function. The time-harmonic electromagnetic scattered or diffracted fields varying with exp(jωt) are thus bicomplex, which contains two imaginary units i and j. Basic concepts for this bicomplex calculations were discussed in the early paper. To illustrate the new solution in comparison with the exact one, the result is extended here to a half-plane diffraction known as a canonical problem. The same idea is tested to obtain a uniform solution that has no geometric-optical singularity in the far zone.

Physical Optics Equivalent Edge Currents for a Half Sheet and Mechanism Extraction of High Frequency Diffraction Analysis

Physical Optics Equivalent Edge Currents for a Half Sheet and Mechanism Extraction of High Frequency Diffraction Analysis

Strain Measurement Using High-Frequency Diffraction Grating.

A new method was proposed for measuring normal strain using a high-frequency diffraction grating. A laser beam illuminated the grating attached on the surface of a specimen. The frequency of the grating was 900 lines/mm. The shift of diffracted beam spots from the grating was measured with two PCD linear image sensors connected to a personal computer in order to determine the normal strain caused by an applied load. The measured light intensity profile was approximated by a Gaussian function and the location of the intensity profile was determined as the main axis of the function. This method was applied to the measurement of elastic normal strain of a cantilever steel beam. The strain measured using this method agreed well with the strains measured using a strain gage and calculated from the elasticity theory.

Strain Measurement Using High-Frequency Diffraction Grating

A laser beam illuminated the grating attached on the surface of specimen. The frequency of the grating was 900 lines/mm. The shift of diffracted beam spots from the grating was measured with two PCD linear image sensors connected to a personal computer in order to determine the normal strain and out-of-plane rotation angle caused by an applied load. The measured light intensity profile was approximated by a Gaussian function and the location of the intensity profile was determined as the main axis of the function.

The High-Frequency Diffraction of Electromagnetic Waves by Cones of Arbitrary Cross Sections

The problem of diffraction of a plane polarized wave by perfectly conducting cones of arbitrary cross sections is considered. Using the Debye scalar potentials and the Sommerfeld transformation, th...

Wiener-Hopf法によるストリツプ回折問題の解析

Wiener-Hopf法によるストリツプ回折問題の解析

Plane Wave Diffraction by a Strip:Exact and Asymptotic Solutions*

High-frequency diffraction by a strip was previously analyzed approximately by the Geometrical Theory of Diffraction (GTD), but the GTD solution has an essential difficulty that it is valid only in the limited range of incidence and observation angles. To overcome this difficulty, in this paper, plane wave diffraction by a strip is reconsidered using the Wiener-Hopf technique and the complete high-frequency asymptotic solution is obtained, which is uniformly valid everywhere in space and has no restrictions on incidence and observation angles. Further asymptotic expansion is also carried out to derive the non-uniform asymptotic solution, which is compared with the previous GTD solution. As a result, some discrepancies are recognized.

Diffraction by a partially coated perfect electric conducting half plane

The high frequency diffraction (transverse electric case) by a partially dielectric‐coated, perfect electric conducting (PEC) half plane is considered. The coating is of finite length and is the same on both sides of the half plane. The length of the two dielectric strips can be different; however, to simplify the analysis and without loss of generality, it is assumed to be the same. This problem requires the solution of two canonical problems which are solved via the Wiener‐Hopf method. The coating is assumed to be thin, and it is modeled by a generalized impedance boundary condition of O(t), where t is the thickness of the coating on each face of the PEC half plane. The interactions between the edges of the coating, i.e., surface wave diffraction, doubly and triply diffracted fields, are also considered. These multiply diffracted fields, including two new terms, are obtained via an extended spectral ray method which is related to the spectral theory of diffraction. The backscattered and bistatic echo widths are computed with the solutions developed here and compared with an independent moment method solution. The agreement between the two solutions is very good.

Diffractive model of the high-frequency impedance.

High-frequency diffraction can be described by iterations based on an approximate formulation of the boundary conditions. The method formulated is analogous to the Born series of scattering theory. It is used to study the interaction of short bunches with the beam environment in terms of the impedances. The impedances of typical elements of an accelerator structure are obtained. The crosstalk between elements, the impedance of a periodic array, and the effect of a taper are discussed. The method can be applied to a cavity of an arbitrary shape.

High-frequency diffraction of a plane wave by a two-part impedance strip

This paper deals with the secondary and tertiary diffraction of plane waves by a two-part impedance strip. The method is based on taking the Fourier integral representation of the primary diffracted field by one edge as incident field for the second edge and performing the analysis with the Wiener-Hopf technique for the secondary diffraction. The tertiary diffraction is treated in a manner analogous to the secondary diffraction. In order to cast the results in a form appropriate for interpretation in the context of the geometrical theory of diffraction, new non-uniform diffraction coefficients are defined.