Complex Source Point Beam Research Articles

Excitation of Guided Waves on a Lossless Dielectric Slab by an E-Polarized Complex Source Point Beam

A lossless slab excited by an E-polarized two-dimensional (2-D) complex source point (CSP) beam is studied analytically. Such a source, unlike a Gaussian beam, satisfies exactly the Helmholtz equation and radiation condition, without paraxial approximation or formulation incompleteness. The guided-waves fields as well as the scattered fields in the regions above and below the slab are determined; in turn, the corresponding powers are directly calculated. Numerical results on the variations of these quantities with respect to the slab electrical thickness, the beam angle of incidence, the source aperture size and location are presented. Substantial power transfer from the finite directive source into each of the slab’s guided waves is recorded especially in the case of near-grazing beam illumination. Such a finding may inspire further theoretical and experimental efforts towards numerous research directions like non-invasive sensing, wireless optical tagging and energy teleportation.

Fast modeling of electromagnetic scattering from 2D electrically large PEC objects using the complex line source type Green's function

AbstractThis study introduces an alternative approach to the numerical solution of two-dimensional (2D) electromagnetic scattering problems by a numerical method of moments (MoM). The real source position vector is replaced by a complex quantity, then Green's function generates a complex source point beam, therefore the interactions between the far zone elements in the impedance matrix are neglected, except the basis functions near to the edges, strongly localizing the impedance matrix. The memory storage increases with the number of edges, but for a fixed number of the edges, it is linearly proportional with N, i.e. O(N). Consequently, the overall running time can be drastically reduced and the far zone scattering pattern and the near field can be found. The proposed procedure is first explained for the single perfectly electrically conducting (PEC) strip geometry, then extended to the scattering by 2D PEC objects with closed polygonal cross-sections. Numerical results are presented for a strip and a square cylinder in both polarizations. The relative errors are also compared with the standard MoM.

Scattering and absorption of a complex source point beam by a grounded lossy dielectric slab with a superstrate

Considered is the scattering and absorption of an E-polarized two-dimensional (2D) beam generated by a complex-source-point (CSP) feed in the presence of a lossy grounded dielectric slab with a lossless superstrate. The solution is found analytically in the Fourier-transform domain. Numerical results demonstrate the ways of obtaining enhanced absorption in the slab by a proper selection of the slab electrical thickness and the parameters of the superstrate. The effects of internal resonances in the slab are analyzed and discussed.

Modeling of transient dynamics in two-dimensional circular microresonators using the pulsed complex source point beam concept

An analytical method for transient dynamics description in microresonators is used to characterize and visualize the transient effects. In the frame of this method, the pulsed complex source point concept is used to simulate an incident transient beam. The excited fields in the microcavity are described by means of a rigorous mathematical approach that is based on the analytical solution in the Laplace transform domain and accurate evaluation of residues at singular points corresponding to the excited modes. The effects of transient mode beating and ultrashort pulse splitting inside the microresonator for short pulse excitation are discussed.

Exact Gaussian-Beam Theory for Outgoing and Standing Spherical Waves: Application to Transmitting and Receiving Antennas

Outgoing spherical vector-wave functions are expressed in terms of Gaussian beams (also called complex source-point beams) radiating in all directions. By use of a vector-wave expansion, the electromagnetic field of an arbitrary source of finite extent is thus expressed in terms of Gaussian beams with weights determined directly from the spherical expansion coefficients of the source. These outgoing-wave formulas allow the field of any transmitting antenna to be expressed in terms of Gaussian beams. Elementary Gaussian-beam receivers are introduced as the electromagnetic field at complex points in space. The outputs of elementary Gaussian-beam receivers pointing in all directions determine the spherical expansion coefficients in a standing-wave expansion. These standing-wave formulas allow the output of any receiving antenna to be expressed in terms of the outputs of elementary Gaussian-beam receivers. Combining the formulas for outgoing and standing waves produces a new antenna-antenna transmission formula based solely on Gaussian beams. The theory is exact and validated through numerical examples.

Analysis of an Arbitrary Conic Section Profile Cylindrical Reflector Antenna, H-Polarization Case

Two-dimensional scattering of waves by a perfectly electric conducting reflector having arbitrary smooth profile is studied in the H-polarization case. This is done by reducing the mixed-potential integral equation to the dual-series equations and carrying out analytical regularization. To simulate a realistic primary feed, directive incident field is taken as a complex source point beam. The proposed algorithm shows convergence and efficiency. The far field characteristics are presented for the reflectors shaped as quite large-size curved strips of elliptic, parabolic, and hyperbolic profiles.

Scattering of Antenna Beams By Local Cylinders

Two-dimensional scattering by conducting circular cylinders of small to moderate size in wavelengths in the presence of local directive sources is rigorously analyzed. The sources are both extended apertures, represented by arrays of complex source point (CSP) beams and by single CSP beams. From scattering patterns the latter are shown to accurately represent cosine squared aperture distributions as sources and with less accuracy other symmetrically tapered distributions. Scattering cross sections calculated show that for E-polarized local sources the cross section first decreases and then increases with increasing directivity whereas for H-polarized sources the reverse occurs. An explanation for this unexpected behavior is offered.

Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed cylindrically layered elastic structures

This paper extends the complex ray analysis developed for nonspecular reflection of quasi-Gaussian acoustic beams from fluid-loaded plane elastic structures [S. Zeroug and L. B. Felsen, ‘‘Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed plane layered elastic structures,’’ J. Acoust. Soc. Am. 95, 3075–3089 (1994)] to cylindrically layered configurations. Except for the adaptation to cylindrical geometry, the rigorous spectral and subsequent asymptotic techniques employed for the plane layered case remain intact. Thus the quasi-Gaussian beams with arbitrary collimation and arbitrary incidence angles are again modeled by the complex source point (CSP) method and the formal complex wave-number spectral integrals for the total scattered field are reduced asymptotically to yield numerically efficient algorithms parametrized in terms of self-consistently interacting specularly reflected and leaky wave fields, which model the proper wave physics. Results are obtained for reflection of two-dimensional (2-D) and three-dimensional (3-D) CSP beams from an aluminum solid cylinder in water, and for 2-D CSP beams from a fluid-loaded cylindrical shell whose modes are assumed, in the high-frequency regime, to be derivable approximately from those for the fluid-loaded plate. The data reveal a strong dependence on the cylindrical surface curvature which manifests itself in the resulting reflectivity pattern through multiple beam splitting for diverging as well as collimated incident beams. These observations pertain not only when the incident beam is phase matched to a leaky wave but also for incidence angles far from the phase-matched condition. Physical explanations are given for these phenomena which are compared with, and related to, those encountered for the planar configurations. As for the planar case, the outcome is a versatile algorithm for predicting interaction of arbitrarily collimated 2-D and rotationally symmetric 3-D acoustic beams with cylindrically curved elastic media, at arbitrary angles of incidence.