Parallel Plane Waveguide Research Articles

Electromagnetic modeling of a resonant commutator

Nonsymmetric inhomogeneous step expansion in a plane-parallel waveguide is studied. Its coupling with the regular channel is arranged through a closely spaced grating of metal strips on the substrate. Scattering characteristics are found from the solution of the electromagnetic problem by use of the double-side equivalent boundary conditions and the method of moments. The influence of the resonant cavity parameters on single-mode and multimode regimes of work is analyzed. © 1997 John Wiley & Sons, Inc.

Resonance Phenomena in Local Perturbations of Parallel-plane Waveguides

We study initial and boundary value problems for the wave equation ∂ t 2 u - Δu = fe -iωt with Dirichlet or Neumann boundary data in smooth domains Ω, which coincide with Ω o = R 2 x (0,1) outside a sufficiently large sphere. The concept of a standing wave, introduced in [7], seems to be of special relevance. A standing wave of frequency ω is defined as a non-trivial solution U of the equation ΔU + ω 2 U = 0 in Ω, which satisfies on ∂Ω the prescribed boundary condition U = 0 or ∂U/∂n = 0, respectively, and a suitable condition at infinity. For instance, U(x) = sin πkx 3 is a standing wave of frequency πk in the unperturbed domain Ω o with Dirichlet boundary data. As shown in a series of joint papers with K. Morgenrother, u(x,t) is bounded as t → ∞ if Ω does not admit standing waves of frequency ω. The main purpose of the present paper is the proof of the converse statement: If standing waves of frequency ω exist in Ω, then u(x,t) is unbounded as t → ∞ for suitably chosen f ∈ C 0 ∞(Ω). Thus the appearance of resonances is closely related to the presence of standing waves. The leading term of the asymptotic expansion of u(x, t) as t → ∞ will be specified. In particular, it turns out that the resonance rate is either t or In t. The rate t appears if and only if ω 2 is an eigenvalue of the spatial operator, while the rate In t can only occur if ω = πk. In the case of Neumann boundary data, U = 1 is a standing wave of frequency 0 for every local perturbation Ω of Ω 0 . The corresponding resonance has already been studied in [21].

On the coupling of energy in parallel plane waveguides

Many EM phenomena may be framed in the context of the excitation and propagation of waves between parallel conducting planes at frequencies below f/sub 0/ where only the TEM or "zero" mode propagates. For a localized source, propagation is in the radial TEM mode, described by Hankel functions, with E and H decreasing much slower in the far field (r/sup -1/2/) than free-space radiation (r/sup -1/). The excitation of these waves has frequently been underestimated. Source currents below the TEM cutoff frequency f/sub 0/ couple capacitively, with a coupling factor determined by a simple distance ratio. Higher frequency sources are more complex, but computer analysis shows that rapid transients launch wavelets whose frequency is somewhat below f/sub 0/ to satisfy quasistatic boundary conditions, with total energy comparable to that "radiated" at the source frequencies. The combination of strong coupling and slow decrease with distance may help explain "anomalously" large EM signals over a broad range of frequencies and geometric scales, from ELF energy between the Earth and ionosphere which may sustain for milliseconds the mesospheric optical emissions known as "red sprites" to VHF energy in portable electronic devices (PEDs) which may have sometimes interfered with avionic systems. The coupling of energy into the boundaries is thought to be due largely to excess charge momentarily released into the conductors by passing wavelets.

Ray mode coupling analysis of EM wave scattering by a partially filled trough

Electromagnetic plane wave scattering by a partially filled trough on the ground has been analyzed by high frequency asymptotic techniques based on Geometrical Theory of Diffraction. Field in the trough region has been formulated in terms of parallel plane waveguide modes, whose excitation (coupling) coefficients are obtained by ray-mode conversion techniques. Previous investigation for obtaining such excitation coefficients has now been extended to account for multiple edge interaction effects. Numerical calculation has been done extensively and thus obtained results are then compared with those by other methods. Good agreements have been observed except for grazing incidence case. It is found that first and secondary modal re-radiation fields from the indented trough region play an important role for scattering far field, and primary edge diffracted field contributes mainly to reflection boundary direction. It is also found that the formulation with these higher order interaction terms can be used even ...

Hybrid Wavefront-Resonance Representation for Transient Scattering by an Open Cavity Part II: Numerical Results and Interpretation

In this second part in a three part sequence, the hybrid wavefront-resonance scheme developed in Part I is applied and explored numerically for the transient field scattered by a plane parallel waveguide cavity configuration. Emphasis is on validating the effectiveness of this representation and on explaining the observed features in the scattered signal at early, intermediate, and at late observation times. Utilizing results reported earlier for the complex resonances [3], it is shown that the late-time observables carry the signature of a cluster of high-Q internal resonances that occurs near modal cutoff frequency, in the form of a slowly decaying typical waveform which is independent of the incident angle or the excitation pulse but is related to the cavity dimensions. The early-time field is expressed as a rapidly decaying series of external wavefront interactions, while at intermediate times the internal resonances synthesize the dispersive guided mode return. The convergence of the resonance series...

Hybrid Wavefront-Resonance Representation for Transient Scattering by an Open Cavity Part III: Analytical Models for the Late Time Oscillations

The numerical results of the second portion of this three part sequence dealing with transient scattering by an open ended plane-parallel waveguide cavity, clearly reveal the existence of a distinct late-time observable in the form of a slowly decaying, aspect-independent typical waveform that carries the signature of a cluster of high-Q resonances that occur near the cavity's mode cutoff frequencies. In this paper, we derive analytic approximations for the resonance frequencies, for the late-time waveform, and for the low-frequency beats that appear in this late-time waveform. These observables are related to the cavity dimensions. It is shown that the late-time waveform is essentially independent of the incidence angle and of the excitation pulse.

Coupling between free propagating and guided modes in a hybrid resonator for a waveguide free electron laser

The modes of a hybrid resonator in which the guiding structure is a plane parallel waveguide are calculated. The calculations take into account the diffraction of the free space (gaussian) mode from the edge of the guide and are carried on in the hypothesis of maintaining the best coupling between the guided and the gaussian modes.

Hollow microstructural waveguides for propagation of infrared radiation

Theoretical results are presented on the propagation of infrared radiation in micron-sized parallel plane waveguides whose walls are gold-coated and separated by empty space. Propagation characteristics of the TE/sub 10/, TM/sub 10/, and TEM modes are described. The most loss-free propagation occurs for the TE/sub 10/ mode, due to the high reflectance for s polarization at the gold-coated surface. The results, when extrapolated to propagation in hollow micron-sized waveguides of rectangular cross section, suggest that propagation is possible over a significant number of wavelengths in spite of the large circumference of such guides in relation to their cross-sectional area. Theoretical indications are that the most loss-free structures would have losses on the order of 0.3 dB/cm. >

Spontaneous emission and gain in a waveguide free-electron laser

A free-electron laser (FEL) enclosed in a waveguide of narrowly spaced parallel plates has been proposed as a compact, coherent source of far-infrared radiation. The spontaneous emission and small-signal gain of such a device are analyzed. Maxwell's equations are solved for the fields of a relativistic electron beam passing through a linearly polarized undulator in the presence of a parallel-plane waveguide. The radiation intensity is resolved into its component waveguide modes for the fundamental frequency and for all harmonics. The intensity profile in a given harmonic mode is altered significantly when a parameter involving the undulator period, beam energy, and transverse dimension of the guide is such that the radiation group velocity is close to the electrons' axial velocity. The small-signal gain in the waveguide FEL is calculated and related to the spontaneous emission. Near zero slip, the gain curve is significantly different from that of a free-space FEL with the same parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reducing slip in a far-infrared free-electron laser using a parallel-plane waveguide

There are several interesting applications for a picosecond, far-infrared (100–1000 μ) free-electron laser. One obstacle to its development is the slip that occurs between the electron beam and the radiation. This can be reduced by operating the laser in a parallel-plane waveguide, and choosing the laser parameters and transverse guide dimension such that the group velocity of the wave nearly matches the axial velocity of the electrons. The laser wavelength depends on both the electron energy and the waveguide dimension, and the laser can be tuned by varying either. Both the tuning characteristics and the slip as a function of wavelength are different from those of a conventional free-electron laser.

Solutions to range-dependent benchmark problems by the finite-difference method

An explicit second-order finite-difference scheme has been used to solve the elastic-wave equation in the time domain. Solutions are presented for the perfect wedge, the lossless penetrable wedge, and the plane parallel waveguide that have been proposed as benchmarks by the Acoustical Society of America. Good agreement with reference solutions is obtained if the media is discretized at 20 gridpoints per wavelength. There is a major discrepancy (up to 20 dB) in reference-source level because the reference solutions are normalized to the source strength at 1 m in the model, but the finite-difference solutions are normalized to the source strength at 1 m in a homogeneous medium. The finite-difference method requires computational times between 10 and 20 h on a super minicomputer without an array processor. The method has the advantage of providing phase information and, when run for a pulse source, of providing insight into the evolution of the wave field and energy partitioning. More complex models, including velocity gradients and strong lateral heterogeneities, can be solved with no additional computational effort. The method has also been formulated to include shear wave effects.

Numerical solutions of range-dependent benchmark problems in ocean acoustics

Accurate numerical solutions are presented for benchmark problems associated with propagation in a wedge with different bottom boundary conditions as well as in a plane-parallel waveguide with changing profile with range. The benchmark problems are solved with three different general-purpose numerical codes: (1) a coupled-mode code providing a full-spectrum two-way (backscatter included) solution of the wave equation, (2) a finite-difference PE code providing a wide-angle solution of the one-way parabolic approximation of the wave equation, and (3) a split-step PE code providing a more narrow-angle solution of the one-way parabolic approximation of the wave equation. Only the two-way coupled-mode results can be considered accurate solutions of the benchmark problems.

Wide-angle parabolic equation solutions to two range-dependent benchmark problems

Numerical solutions are presented to two benchmark problems involving acoustic propagation in range-dependent media. The two problems deal with: (1) upslope propagation in a wedge-shaped channel with a penetrable bottom, and (2) propagation in a plane-parallel waveguide with a range-varying sound-speed profile. The solutions are based on a pair of wide-angle, variable-density, parabolic equations, one of which is solved using a finite-difference algorithm while the other is solved using a split-step algorithm.

The finite difference method for time domain solutions to range‐dependent bottom‐interaction problems

An explicit second‐order finite difference scheme has been used to solve the elastic wave equation in the time domain. Solutions are presented for the perfect wedge, the lossless penetrable wedge, and the plane parallel waveguide, which have been proposed as benchmarks by the Acoustical Society of America. Good agreement with reference solutions is obtained if the media is discretized at 20 grid points per wavelength. The principle disadvantage of the technique is long computational times that are between 10 and 20 h on a minicomputer without an array processor. The method has the advantage of providing phase information and, when run for a pulse source, of providing insight into the evolution of the wave field and energy partitioning. Arbitrarily more complex models including velocity gradients, strong lateral heterogeneities, and random media can be solved with no additional computational effort. The method has also been formulated to include shear wave effects. [Work supported by ONR.]

Dispersion in a plane-parallel semiconductor waveguide with arbitrary contacts

Dispersion in a plane-parallel semiconductor waveguide with arbitrary contacts

Rays and modes for plane wave coupling into a large open-ended circular waveguide

Generalizing an earlier study of high-frequency plane wave coupling into a wide semi-infinite parallel-plane waveguide, this investigation is concerned with coupling into a large semi-infinite circular waveguide. Emphasis is placed on the interplay between ray fields and mode fields, on the excitation mechanism of each, and on their properties when the field incidence angle is strongly oblique, thereby introducing marked azimuthal asymmetries. The tools of analysis are the geometrical theory of diffraction (GTD), physical optics (PO) and hybrid ray-mode theory. The results reveal that coupling from edge-diffracted rays into a waveguide mode occurs when such rays emanating from the flash points on the edge line up with rays in the modal congruence. However, the diffracted ray caustics between initial reflections do not coincide with the cylindrical caustic of the mode, and only after many reflections is there synchronism between the edge-diffracted and modal rays. Complete synchronism throughout obtains for each angular harmonic constituent of the field, for which the incident wave is conical. Under these conditions, one may also distinguish a multiple reflected truncated conical geometric optical beam, the analog of the geometric optical sheet beam in plane parallel geometry. A variety of other ray and modal characteristics are elucidated as well from different perspectives, thereby granting insight into the ray-mode phenomenology in the circular wave-guide environment. Such insight is expected to be useful when one attempts to deal with nonideal but strongly guiding configurations.

Rays, modes and beams for plane wave coupling into a wide open-ended parallel-plane waveguide

A plane wave incident obliquely onto the open end of a wide parallel-plane waveguide generates an interior field that resembles a geometric optical sheet beam whose initially well-defined shape gets diffused after undergoing multiple reflection. This behavior can be confirmed, but not physically well explained, from numerical results obtained by summing over the aperture-excited guided modes. A phenomenologically incisive representation is obtained by subjecting the guided mode sum to partial Poisson summation that yields an exact hybrid field comprising the multiple reflected geometric optical beam, some multiple reflected edge-diffracted rays, some guided modes, plus remainder terms. Asymptotic approximations reduce these exact forms to the wave constituents of the nonuniform and, when required, uniformized geometrical theory of diffraction. Numerical results presented for various parameter regimes delineate the ranges of applicability of the asymptotic forms and also the relative importance of the individual wave contributions. In the parameter range where geometrical features of the field can still be resolved, the hybrid form is not only physically appealing but also numerically more efficient than alternatives involving only rays or only modes.

Ray acoustic analysis of plane‐wave coupling into large open waveguides: Plane parallel geometry

When a plane sound wave impinges on a wide open‐ended baffled or unbaffled plane parallel waveguide, the behavior of the sound field coupled into the interior differs from that when the waveguide is tubular [H. Shiral and L. B. Felsen, this meeting]. The difference is due to the fact that plane waves retain their integrity between wall reflections. By application of ray theoretic, modal, and hybrid ray‐mode methods, one may establish the connection between the geometrically sharply delineated multiple reflected sheet beam, the edge diffracted‐multiple reflected ray fields, and the guided modes. For very strongly overmoded conditions, the significantly contributing modes are those whose plane‐wave congruences have directions near that of the incident plane wave. Invoking ray‐mode equivalences, a hybrid form is found to describe the propagation phenomena in a physically incisive and numerically efficient manner, especially the diffusion of the initially well‐collimated sheet beam after undergoing multiple reflection. [Work supported by ONR.]

Technical memorandum: Analysis of electromagnetic systems by means of fourier transform techniques

We have developed a method for calculating eigenfrequencies and field distributions for the modes of waveguides and resonant cavities The core of the method is the application of Fourier transforms to a time-domain solution of Maxwell's equations. For quasi-one-dimensional systems we find a convergence criterion relating the spatial and time mesh widths which makes it extremely convenient. Finally, we have applied the method to two simple cases the homogeneous and the partially homogeneous parallel plane waveguides.

Theoretical and Experimental Study of a Novel H-Guide Transverse Slot Antenna (Short Papers)

Transverse slots in the upper plate of a dielectric-loaded parallel plane waveguide (H-guide) operating in the dominant mode (zero cutoff frequency) are proposed as slot antennas. A new theoretical approach to the analysis of a single-slot antenna is presented, leading to explicit expressions for the antenna input impedance and radiation efficiency. The computed values of the VSWR and radiation efficiency are in good agreement with laboratory measurements. The radiation efficiency of a single slot exceeds 10 percent in the 8-11-GHz frequency band, reaching a 50-percent theoretically predicted maximum at the slot resonance frequency, when the guide is terminated by a matched load. Experimental checks prove that the leakage, or parasitic, radiation power level is less than -40 dB relative to the measured radiated power.