Complex Source Beam Research Articles

An efficient FEM-BEM solution for electromagnetic analysis of inhomogeneous objects

An efficient finite element method-boundary element method (FEM-BEM) is proposed for electromagnetic analysis of inhomogeneous objects. The problem domain is discretized and evaluated with FEM, and the BEM introduces a truncated boundary on the surface of the domain utilizing boundary integral equations (BIEs) technique. To guarantee the precision, much dense discretization is usually required when modeling and simulating the inhomogeneous media, which will lead to a large and dense impedance matrix from the BEM part. Therefore, the nested complex source beam (NCSB) method is proposed in the FEM-BEM system to accelerate the evaluation of the BIEs, where the interaction between far-field groups is equivalent to that of the complex source beams located on the equivalent sphere of each group in an aggregation, translation and disaggregation process. Furthermore, the adaptive grouping technique for the NCSB is employed to improve the performance of the solution. Numerical results show the efficiency of the proposed method.

Diffraction of an Arbitrary Uniform Complex-Source Beam by a Perfectly Conducting Wedge

Diffraction of an Arbitrary Uniform Complex-Source Beam by a Perfectly Conducting Wedge

Vector-spherical-harmonics representation of vector complex source beams carrying vortices

Vectorial solutions of Maxwell's equations describing highly focused and variously polarized vector complex source vortex beams are investigated. An analytical representation of these beams in the vector-spherical basis of electromagnetic multipoles is presented. In particular, three different families of optical vector vortex beams are studied in detail. Whereas the vortical solutions derived within spherical symmetry can be represented only by electric (magnetic) multipoles, solutions derived within cylindrical and Cartesian symmetry also exhibit magnetic (electric) multipole components. We utilize the representation of the studied beams in vector-spherical harmonics to investigate their interaction with a cluster of nanoparticles.

Scattering and diffraction of a uniform complex-source beam by a slit in a perfectly conducting plane screen

Abstract. A new multipole solution in plane-polar coordinates for the scattering of an arbitrary TE- or TM-polarized incident field by an infinitely extended slit in a plane screen is derived. To this end a classical three-domain problem with a complete multipole expansion in each of the domains is formulated. The unknown multipole amplitudes are found from the continuity conditions of the tangential electric and magnetic field components. Finally an infinite system of linear equations is derived which can be approximated by a numerically tractable finite one leading to a solution with an arbitrary accuracy. The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle. Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave.

An adaptive nested complex source beam method for electromagnetic scattering of composite conducting-dielectric objects

A new nested complex source beam (NCSB) method based on the volume-surface integral equation (VSIE) is proposed for fast electromagnetic scattering analysis of composite conducting-dielectric objects. This scheme is based on the nested equivalent structure of the complex source beams to approximate the far-field interactions of both the RWG basis functions and SWG basis functions with an acceptable accuracy. An adaptive grouping technique is introduced in the traditional NCSB method to adaptively group the model based on the distribution of unknowns. Therefore, the new NCSB method is termed as adaptive nested complex source beam (ANCSB) method. The computational complexity and memory storage with a quasi-linear variation can be realized same as NCSB, and numerical results demonstrate the accuracy and higher efficiency than traditional NCSB for the electromagnetic scattering analysis of composite conducting-dielectric objects.

On Two Alternative Uniformly Asymptotic Procedures for Analyzing the High-Frequency Diffraction of a Complex Source Beam by a Straight Wedge

When spectral wave integrals, representing the radiation and diffraction of electromagnetic waves, are characterized by a first-order saddle point and poles in the integrand, they can usually be evaluated, in essentially closed form, at high frequencies by the leading terms of any of the two well-known alternative uniformly asymptotic procedures, namely, the Pauli–Clemmow method (PCM) and the Van der Waerden method (VWM), respectively. The PCM has the advantage that its leading terms directly yield a solution in the simple ray format of the uniform geometrical theory of diffraction (UTD). On the other hand, it is commonly noted that it is not the leading term of the PCM but that of the VWM which remains valid for the case of complex waves. Nevertheless, it is shown here that the PCM can surprisingly work even for some special complex wave cases, only if certain conditions are met. Indeed, it is demonstrated here that the PCM meets these conditions for the special case of the diffraction of a complex source beam (CSB) by a wedge. Also, the PCM directly yields a UTD like solution for this case. The latter result is significant as it provides a strong justification for obtaining a simple UTD type solution for the more general problem of the diffraction of a CSB incident from an arbitrary direction on a wedge with arbitrary curvature, directly via analytic continuation of the corresponding UTD result available for a curved wedge illuminated by a point source in real space. It is also shown that the VWM solution can be trivially cast in the UTD format, by expressing it as a sum of the PCM solution plus a UTD slopelike correction term; a similar result was obtained previously using a higher order term from a generalization of the PCM procedure given elsewhere.

Geometrical optics-based ray field tracing method for complex source beam applications**Project supported by the National Natural Science Foundation of China (Grant Nos. 61301056 and 61231001), the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2014J012), the Fok Ying Tung Education Foundation, China (Grant No. 141062), the Aero-Science Fund, China (Grant No. 20142580012), and the “111” Project (Grant No.

Due to the fact that traditional ray field tracking approaches require a large number of geometrical optical (GO) ray tubes, they are very inefficient in many practical applications. An improved ray model scheme for a complex source beam (CSB) tracking technique is proposed in this paper. The source field can be expressed by a superposition of CSBs, then every CSB basis function has a Gaussian-type amplitude distribution and is suitable for replacing a GO ray tube in the ray tracing approach. The complex phase matching technique is adopted to find the reflected beam in the reflection point where local approximation is used to represent the curved surface in its neighborhood. A new solution to multiple reflections using the conventional right-handed reflected system is used to track the field easily. Numerical results show the accuracy of the proposed method.

Electromagnetic reflection\u2013transmission problems in a Wilson basis: fiber-optic mode-matching to homogeneous media

The Wilson basis features strong localization in both the spatial and the spectral domain. This enables us to efficiently describe high-frequency wavefields through a parsimonious set of coefficients. By choosing a single universal basis to expand fields, one effectively detaches scattering problems from the specific design of optical waveguides and components that form an optical interface. Equipped with a sparse, diagonally-dominant translation operator, the Wilson basis functions are convenient building blocks to address scattering problems in a more general setting. The physical interface may be reconfigured, while preserving the computational effort of the initial expansion. In this paper, we demonstrate optical reflection–transmission problems for interfaces between optical fibers and homogeneous media. In particular, we treat the construction of one-way propagating electromagnetic fields in the Wilson basis that are generated by Wilson-basis discretized equivalent dipole-source distributions. The Green’s function spectral integrals benefit from the strong localization to achieve good convergence. The decomposition of a wavefield in one-way forward and backward propagating wavefields is the result of careful construction of equivalent sources, and is effectively a Wilson-basis discretized Poincaré–Steklov operator. The decomposition of each and every guided fiber mode to one-way forward and backward propagating fields in homogeneous space can be accomplished in such a way that the boundary conditions are satisfied. These one-way propagating fields subsequently serve as building blocks for the decomposition of arbitrary incident fields, so that the scattering problems are properly solved. The reflection due to a guided mode as excitation is the same as the reflection due to the specific excitation of the same but backward propagating mode up to the accuracy of the numerical quadratures. Upon illuminating the fiber through a complex-source beam wavefield for a number of lateral steps, the Wilson basis formulation immediately produces the corresponding change in the modal power distribution.

Wilson basis expansions of electromagnetic wavefields: a suitable framework for fiber optics

To detach large vectorial full-wave electromagnetic scattering problems from the specific, dissimilar bases that are typically associated with the optical waveguiding structures comprising an optical interface, we propose and demonstrate the expansion of wavefields in a single universal Wilson basis. We construct a Wilson basis by following the derivation in the paper by Daubechies, Jaffard and Journé. This basis features exponentially decaying basis functions in both the spatial and spectral domain. The strong localization in phase-space, with basis functions that strongly resemble wavefields, allow for efficient expansions of high-frequency electromagnetic fields. In a Wilson basis, the interface scattering problem is effectively separated from the physical configuration. For the evaluation of multiple, laterally displaced interface configurations, one may reuse electromagnetic fields in the Wilson basis, because the translation operator is sparse and diagonally dominant. We consider actual reflection-transmission problems comprising optical fibers and homogeneous media in the Wilson basis framework in a companion paper. There, the localization in the spectral domain aids the conversion of the numerical scheme to generate electromagnetic fields in homogeneous media due to Wilson-basis discretized electromagnetic sources. In this paper, we review the Wilson basis construction, demonstrate the expansion of modal electromagnetic fields in an optical fiber, and complex-source beams that are tilted with respect to the optical axis. Even for largely tilted beams (up to 60°), despite being highly oscillatory in the cross-sectional plane, the fields are well represented by a finite number of higher-order Wilson basis functions.

Flexible design method for freeform lenses with an arbitrary lens contour.

A method is presented that allows the design of freeform lenses with an arbitrary contour in a flexible and robust manner. The method is based on the generation of two equi-flux grids representing the source and target beams, with two separate curl-free mappings from an equi-spatial rectangular grid. Because the source and target grids are generated independently from one another, one can map arbitrary complex source beams with certain contours onto arbitrary complex target beams within other contours with high convergence probability. The method is illustrated by calculating a triangular freeform lens that reshapes a triangular beam from a Lambertian source into a uniform pentagonal irradiance distribution on a target plane.

A Novel Far-Field Transformation via Complex Source Beams for Antenna Near-Field Measurements on Arbitrary Surfaces

This paper presents a general technique for an efficient and accurate near-field (NF) to far-field (FF) transformation based on the complex source beam (CSB) method. This CSB-based NF–FF transformation is applicable to all three conventional NF measurement techniques, namely, to the planar, cylindrical, and spherical as well as to an arbitrary measurement surface. In this technique, a set of CSBs launched radially out from the antenna under test (AUT) is used to represent its NF. The weights of these CSB radiation basis functions are found by matching them to the measured AUT NF on the measurement surface. Once the CSB weights are found, the same CSBs remain continuously valid everywhere from NF to FF. It is noted that due to the occurrence of a natural Gaussian-like field taper away from each beam axis, only a relatively few CSBs are typically needed to represent the AUT fields at any point in its far zone in comparison to the conventional plane wave or vector wave function expansions for a given size of AUT. The remaining CSBs can be discarded with negligible error. This property among a few others leads to some advantages over conventional NF–FF methods.

Noninvasive Characterization of Solid Particle Streams Enclosed in a Dielectric Pipeline by a Bistatic Doppler Radar

This paper compares two radar configurations operating in the W-band with different antenna systems for measuring particle streams in the near-field range. A complex source beam is employed to describe the field characteristics. This new approach is used to derive the associated antenna gain and power patterns and applied in the radar equation for particle streams. We demonstrate how indoor measurements benefit from a bistatic radar configuration and provide measurement results for streams with particles in the micrometer size range. Owing to the bistatic configuration of the radar, the particle stream flowing through a plastic pipe has been detected showing the low interference caused by pipe walls, which enables nondestructive monitoring of particle streams through the dielectric pipe section.

Delaminating Quadrature Method for Physical Optics Integrals over High-Order Triangular Mesh for Complex Source Beam Applications

ABSTRACTA novel method for calculating physical optics (PO) integrals over an electrically large target illuminated by a complex source beam is presented. A high-order triangular element is used to mesh the surface of this target. The PO integrals over these elements are calculated with a delaminating quadrature method. This method is very stable, accurate, and efficient, and its computation cost remains constant as the frequency increased. The influence of critical points is taken into account by subdividing the integral intervals. Numerical results are shown in this article to demonstrate the efficiency of this approach.

Improved quasi‐analytic method for transient analysis of electrically large conducting targets illuminated by a complex source beam

Improved quasi‐analytic method for transient analysis of electrically large conducting targets illuminated by a complex source beam

An Efficient Method for Calculation the Physical Optics Integral by Using Complex Source Beam for Electrically Large Reflector Antenna Applications

ABSTRACTThe physical optics method is a widely used radiation and scattering estimation for electrically large-scaled objects, and it is finally reduced to the calculation of highly oscillatory integrals. In this article, the physical optics integrals over the reflecting surface for an incident complex source point is evaluated here in closed form. A complex source point can generate a beam field, which is employed to expand an arbitrary source via a complex extension of the surface equivalence principle. Then the complex source beam expansion method is applied to analyze the field of large reflector antennas via physical optics method. Numerical examples are presented to illustrate the accuracy and efficiency of this complex source beam-physical optics hybrid method for analyzing general parabolic reflectors.

A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method

This work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregation operations in NCSB. In our implementation, the aggregation/disaggregation matrices are solved by the truncated far-field matching, which is based on the directional far-field radiation property of the complex source beams (CSBs). Furthermore, the translation matrices are obtained according to the beam width of CSBs. Due to the high directivity of the radiation patterns of CSBs, all the far-field related interaction matrices are low-ranked. Therefore, TSVD can be employed and a new set of equivalent sources can be constructed by a linear combination of the original CSBs. It is proved that the radiation power of the new sources is proportional to the square of the corresponding singular values. This provides a theoretical guideline to drop the insignificant singular vectors in the calculation. In doing so, the efficiency of the original NCSB method can be much improved while a reasonably good accuracy is maintained. Several numerical tests are conducted to validate the proposed method.

Acceleration of Augmented EFIE Using Multilevel Complex Source Beam Method

The computation of the augmented electric field integral equation (A-EFIE) is accelerated by using the multilevel complex source beam (MLCSB) method. As an effective solution of the low-frequency problem, A-EFIE includes both current and charge as unknowns to avoid the imbalance between the vector potentials and the scalar potentials in the conventional EFIE. However, dense impedance submatrices are involved in the A-EFIE system, and the computational cost becomes extremely high for problems with a large number of unknowns. As an exact solution to Maxwell’s equations, the complex source beam (CSB) method can be well tailored for A-EFIE to accelerate the matrix-vector products in an iterative solver. Different from the commonly used multilevel fast multipole algorithm (MLFMA), the CSB method is free from the problem of low-frequency breakdown. In our implementation, the expansion operators of CSB are first derived for the vector potentials and the scalar potentials. Consequently, the aggregation and disaggregation operators are introduced to form a multilevel algorithm to reduce the computational complexity. The accuracy and efficiency of the proposed method are discussed in detail through a variety of numerical examples. It is observed that the numerical error of the MLCSB-AEFIE keeps constant for a broad frequency range, indicating the good stability and scalability of the proposed method.

Combined complex-source beam and spherical-multipole analysis for the electromagnetic probing of conical structures

The paper addresses the combination of the spherical-multipole analysis in sphero-conal coordinates with a uniform complex-source beam (CSB) in order to analyze the scattering of a localized electromagnetic plane wave by any desired part of a perfectly conducting elliptic cone. The concept of uniform CSB is introduced and rigorously applied to the diffraction by a semi-infinite elliptic cone. The analysis takes into account the fact that the incident CSB does not satisfy the radiation condition. A new modal form of the Green's function for the elliptic cone is derived based on the principle that there is no energy loss to infinity. The numerical evaluation includes the scattered far fields of a CSB incident on the corner of a plane angular sector with different opening angles. Cet article présente la combinaison de l'analyse de multipôles sphériques en coordonnées sphéro-coniques avec une faisceau de source complexe ( Complex Source Beam , CSB) dans le but d'analyser la diffusion localisée par un cône elliptique parfaitement conducteur d'une onde plane électromagnétique. Le concept de CSB est introduit au travers de la diffraction par un cône elliptique semi-infini. L'analyse prend en compte le fait que l'onde CSB incidente ne satisfait pas les conditions de radiation. Un nouveau modèle de la fonction de Green pour un cône elliptique est développé en faisant l'hypothèse qu'il n'y a pas de pertes d'énergie à l'infini. Le modèle numérique inclut la diffusion en champ lointain d'une source CSB sur le coin d'un secteur angulaire avec différents angles d'ouverture.

An Effective MoM Solution With Nested Complex Source Beam Method for Electromagnetic Scattering Problems

A nested complex source beam (NCSB) method based on octree structure is proposed to accelerate the method-of-moments (MoM) solution for three-dimensional (3-D) electromagnetic scattering analysis. At the finest level, the far-field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed on the equivalent sphere surface for every group. Furthermore, the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level. Similarly, the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level group. An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method, and only the CSBs at the finest level have the direct association with the basis functions in their group. The NCSB method is shown to be O(NlogN) computational complexity for both matrix–vector product (MVP) time and memory storage by numerical examples with appropriate parameters, and numerical results demonstrate the better efficiency of the proposed method than the current multilevel CSB method.

Complex Source Beam Method for Electromagnetic Scattering Problems of Dielectric Objects

A complex source beam (CSB) method, which was previously proposed to solve the electric field integral equation, is extended to solve the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation for the analysis of homogeneous dielectric objects. The PMCHWT equation is accelerated by approximating interactions between basis functions in separated groups with CSBs. The translation invariance of the dyadic Green's functions is exploited to further enhance the computational efficiency of the CSB method. The accuracy and efficiency of the proposed approach are demonstrated by numerical examples.