Evanescent Floquet Waves Research Articles

High-frequency Green's function for a semi-infinite array of electric dipoles on an infinite grounded stratified dielectric slab: part III $phase-matched wave interactions and numerical results

The particular effects of phase matching in interactions between different wave species and interaction mechanisms pertaining to the asymptotic Green's function for a semi-infinite phased array of parallel dipoles on an infinite grounded stratified dielectric slab are addressed. The two previous parts have lead to a grouping of certain asymptotic terms, which provides physically appealing interpretations of interacting wave processes that involve slab-modulated propagating (radiating) Floquet waves (FW), slab-guided leaky waves (LW), evanescent (nonradiating) FWs and surface waves (SW), together with their associated conical edge-coupled wave constituents. Special attention is now given to the role, in these wave interaction functions,of the difference between the propagating wave numbers (i.e., the degree of phase matching) that characterizes any pair of propagating FWs and LWs, and evanescent FWs and SWs. Cutoff transitions of FWs from the evanescent to the propagating regime are described also in terms of a second wave interaction function, structured similarly to the first. In connection with applications, the interaction between SWs and evanescent FWs, as well as FW transitions from evanescent to propagating, are discussed from the perspective of scan blindness in actual arrays. Various numerical studies highlight the role of phase matching in different problem scenarios.

Asymptotic high-frequency Green's function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions

This paper deals with the derivation and physical interpretation of a uniform high-frequency representation of the Green's function for a large planar rectangular phased array of dipoles with weakly varying excitation. Thereby, our earlier published results, valid for equiamplitude excitation, and those for tapered illumination in one dimension are extended to tapering along both dimensions, including dipole amplitudes tending to zero at the edges. As previously, the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high-frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields, which arise from FW scattering at the array edges and vertexes. To accommodate the weak amplitude tapering, new generalized periodicity-modulated edge and vertex slope transition functions are introduced, accompanied by a systematic procedure for their numerical evaluation. Special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm. The resulting array Green's function forms the basic building block for the full-wave analysis of planar weakly amplitude-tapered phased array antennas, and for the description of electromagnetic radiation and scattering from weakly amplitude-tapered rectangular periodic structures

Time-domain green's function for an infinite sequentially excited periodic planar array of dipoles

The present paper is a continuation of previous explorations by the authors, aimed at gaining a basic understanding of the time domain (TD) behavior of large periodic phased (i.e., sequentially turned-on) array antennas and related configurations. Our systematic investigation of the relevant canonical TD dipole-excited Green's functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays, parameterized in terms of radiating (propagating) and nonradiating (evanescent) conical TD Floquet waves (FW) and truncation-induced TD FW-modulated tip diffractions. The present contribution extends these investigations to an infinite periodic sequentially pulsed planar array, which generates pulsed plane propagating and evanescent FW. Starting from the familiar frequency domain (FD) transformation of the linearly phased element-by-element summation synthesis into summations of propagating and evanescent FWs, we access the time domain by Fourier inversion. The inversion integrals are manipulated in a unified fashion into exact closed forms, which are parameterized by the single nondimensional quantity /spl eta/=c/v/sup (p)//sub u1/, where v/sup (p)//sub u1/ and c are the excitation phase speed along a preferred phasing direction u/sub 1/ in the array plane and the ambient wave speed, respectively. The present study deals with the practically relevant rapidly phased propagating case /spl eta/<1, reserving the more intricate slowly phased /spl eta/>1 regime for a future manuscript. Numerical reference data generated via element-by-element summation over the fields radiated by the individual dipoles with ultrawide band-limited excitation are compared with results obtained much more efficiently by inclusion of a few TD-FWs. Physical interpretation of the formal TD-FW solutions is obtained by recourse to asymptotics, instantaneous frequencies and wavenumbers, and related constructs. Of special interest is the demonstration that the TD-FWs emerge along "equal-delay" ellipses from the array plane; this furnishes a novel and physically appealing interpretation of the planar array TD-FW phenomenology.

A uniform asymptotic evaluation of the field radiated from collinear array antennas

A uniform asymptotic representation of the electromagnetic field radiated from arbitrary collinear array antennas is presented. The asymptotic field is obtained applying the saddle-point technique to the radiation integrals after expressing the current excited along the array axis by means of a Fourier spectral representation. The resulting electromagnetic field is expressed in terms of propagating and evanescent truncated Floquet waves (FWs). The leading asymptotic term of the FWs exhibits an optical behavior and is responsible for the slow decay of the array near-field, which can be described as cylindrical in character. The transition toward the spherical wave propagation regime is due to the interference of the cylindrical field with the relevant scattered field from the array truncations, while the reactive energy storage is due to the evanescent FWs, as well as to the progressive inductive and progressive electrostatic FWs excited close the antenna axis. Using the asymptotic field representation, prediction formulas for the spatial locations where the array near-field exhibits peak deviation from the cylindrical decay, and where the transition from cylindrical to spherical wave propagation regime takes place, have been derived. The proposed analytical technique can be adopted to analyze the spatial field distributions and the radiation mechanisms of periodic and nonperiodic linear arrays.

Three-dimensional Green’s function for planar rectangular phased dipole arrays

This paper deals with the construction, physical interpretation and application of a uniform high-frequency representation of array Green’s functions (AGFs) for planar rectangular phased arrays of dipoles. An AGF is the basic constituent for the full-wave description of electromagnetic radiation from large periodic structures. For efficient treatment of high-frequency phenomena, the AGF obtained by direct summation over the contributions from the individual radiators is globally restructured via the Poisson sum formula into a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted waves, which arise from FW scattering at the array edges and vertexes. These results are obtained by high-frequency uniform asymptotics applied to the wave integrals generated by Poisson summation in the spatial or spectral domains. The final algorithm is physically appealing, numerically accurate, and efficient, owing to the rapid convergence of both the FW series and the series of corresponding FW-modulated diffracted fields away from the array plane. The use of the asymptotic AGF in the full-wave analysis of large slot arrays is discussed, with the inclusion of numerical results.

Asymptotic high‐frequency Green's function for a planar phased sectoral array of dipoles

This paper deals with the derivation and physical interpretation of a uniform high‐frequency Green's function for a planar right‐angle sectoral phased array of dipoles. This high‐frequency Green's function represents the basic constituent for the full‐wave description of electromagnetic radiation from rectangular periodic arrays and scattering from rectangular periodic structures. The field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high‐frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW‐modulated diffracted fields, which arise from FW scattering at the array edges and vertex. Emphasis is given to the analysis and physical interpretation of the vertex diffracted rays. The locally uniform asymptotics governing this phenomenology is physically appealing, numerically accurate, and efficient, owing to the rapid convergence of both the FW series and the series of corresponding FW‐modulated diffracted fields away from the array plane. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm.

Frequency-domain Green's function for a planar periodic semi-infinite phased array .I. Truncated floquet wave formulation

This two-part sequence deals with the derivation and physical interpretation of a uniform high-frequency solution for the field radiated at finite distance by a planar semi-infinite phased array of parallel elementary electric dipoles. The field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent Floquet waves (FWs) together with corresponding diffracted rays, which arise from scattering of the FW at the edge of the array. The formal aspects of the solution are treated in the present paper. They involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent. Different species of spectral poles define the various species of propagating and evanescent FW. Their interception by the steepest descent path (SDP) determines the variety of shadow boundaries for the edge truncated FW. The uniform asymptotic reduction of the SDP integrals, performed by the Van der Waerden (1951) procedure and yielding a variety of edge-diffracted fields, completes the formal treatment.

High-frequency analysis of an array of line sources on a truncated ground plane

A uniform high-frequency solution is presented for the field radiated at finite distance by a semi-infinite beam-scanning array of magnetic line sources located on a perfectly conducting half-plane. The field is represented in terms of Floquet waves plus their relevant singly and doubly diffracted rays, which arise from both the end of the array and the edge of the half-plane. This representation is uniformly valid also when transition conditions from propagating to evanescent Floquet waves occur. Furthermore, it provides a simple and attractive physical interpretation and is found numerically very effective, due to the fast convergence of the Floquet wave expansion for the field.

Wave scattering and guidance by dielectric waveguides with periodic surfaces

Stratified media with periodic surfaces have been used in waveguide-input and waveguide-output couplers and distributed-feedback lasers. We apply the extended-boundary-condition approach to treat the problem of scattering and guidance by stratified media with period surfaces for both the TE and TM polarizations in a unified manner with the use of a transition matrix. Theoretical results are shown to compare well with the experimental data for metallic gratings with surface-plasmon excitations. The anomalous behavior of the diffraction efficiencies is explained with the evanescent Floquet waves, which are excited with incidence angles corresponding to the locations of the dips in the total reflected efficiency plots. Diffraction efficiencies are plotted for wave scattering from corrugated thin-film waveguides with an angle of incidence near that for the waveguide-mode excitation. The guiding constants are also calculated and compared with the results obtained by other numerical methods. The origins of the imaginary parts in the guiding constants are discussed in light of the nonevanscent waves excited in the substrate.