Guided Waves Propagating Along the Magnetostatic Field at a Plane Boundary of a Semi-Infinite Magnetoionic Medium

The characteristics of the surface waves supported by a plane boundary of a semi-infiite region of gyrotropic plasma are investigated for the case in which the direction of the magnetostatic field is parallel to both the interface and the propagation direction. Two cases are considered, one for which the plasma is terminated by a perfectly conducting screen, and the other for which it is terminated by a semi-infinite region of free space. Surface waves are found to be propagated for all frequencies below both the plasma and the gyromagnetic frequency in the first case, and below both the plasma and 1/ /spl radic/2 times the upper hybrid resonant frequency in the second case. The characteristics of the surface waves are discussed, and numerical results of the phase velocity and the propagation coefficient of the surface waves along the interface, as well as their attenuation rates normal to the interface, are given.     

Surface waves at a plane interface between vacuum and plasma with the magnetostatic field normal to the interface

The characteristics of the surface waves sustained by a plane interface which separates semi-infinite regions of vacuum and magnetoionic medium are investigated for the case in which the magnetostatic field is normal to the interface. It is found that plane surface waves exist if the gyromagnetic frequency is less than the plasma frequency and in the range of frequencies lying between the gyromagnetic frequency and1/sqrt{2}times the upper hybrid resonant frequency. The phase velocity of the surface waves is always less than the velocity of electromagnetic waves in free space, and it decreases monotonically with the increase in the frequency and goes to zero at1/sqrt{2}times the upper hybrid resonant frequency.     

Asymptotic theory of mode coupling in a space-time periodic medium—Part II: Unstable interactions

A singular perturbation analysis of the coupling of plane electromagnetic waves in an unbounded medium having its permittivity modulated by a progressive sinusoidal wave is carried out for the waves progressing parallel to the modulation direction. The phase velocity of the wave modulation is greater than that of the electromagnetic waves in the unmodulated medium. The interactions of the fundamental wave progressing in the direction of the modulating wave with the first four harmonics progressing in the reverse direction are investigated. The periodic inhomogeneity gives rise to self and mutual interactions. The self effect, in general, produces a phase shift and causes the mutual effect to occur for smaller wavenumbers and higher frequencies than those predicted by the Bragg conditions. The mutual interaction introduces a complex change in the frequencies resulting in absolute instability of the interacting waves. Analytical expressions for the shifts of the wavenumber and the frequency as well as the other characteristics of the waves and instabilities in the interaction region are deduced. The asymptotic results are compared with the numerical results evaluated from the mode theory.     

Asymptotic theory of mode coupling in a space-time periodic medium—Part I: Stable interactions

A singular perturbation analysis of the coupling of plane electromagnetic waves in an unbounded medium having its permitivity modulated by a progressive sinusoidal wave is carried out for the waves progressing parallel to the modulational direction. The phase velocity of the wave modulation is less than that of the electromagnetic waves in the unmodulated medium. The interactions of the fundamental wave progressing in the direction of the modulating wave with the first four harmonics progressing in the reverse direction are investigated. The periodic inhomogeneity introduces self-effect and mutual effect. The self effect, in general, produces a phase shift and causes the mutual effect to occur for different frequencies and wavenumbers from those predicted by the Bragg conditions. The mutual effect introduces a complex change in the wavenumber resulting in the evanescence of the interacting waves. Analytical expressions for the shifts in the frequency and the wavenumber as well as the other characteristics of the waves in the interaction region are deduced. The asymptotic results are compared with the numerical results evaluated from the mode theory.     

Radiation from an electromagnetic source in a half-space of compressible plasma-surface waves

The radiation characteristics of a line source of magnetic current are studied for the case in which the source is situated in a half-space of isotropic, compressible plasma which is bounded on one side by a perfectly conducting, rigid plane screen. In addition to the electromagnetic and plasma space waves, the line source excites a boundary wave. This boundary wave is a coupled wave. It has associated with it both a magnetic field component and the pressure term. This is in contrast to the space waves which can be decomposed into an electromagnetic (EM) mode with no pressure term and a plasma (P) mode with no magnetic field associated with it. The characteristics of this boundary wave are evaluated. The boundary wave propagates for all frequencies and the power carried by the boundary wave becomes smaller as the frequency is increased.     

Surface waves on a grounded anisotropic plasma slab

The dispersion relations of the plane surface waves supported by a grounded magnetoplasma slab immersed in free space are discussed for the case in which the magnetostatic field is parallel to both the direction of propagation and the vacuum-plasma interface. The dependence of the surface-wave characteristics on the thickness of the plasma slab and the strength of the magnetostatic field is also examined.     

Diffraction by a perfectly conducting semi-infinite screen in an anisotropic plasma

The scattering of a plane electromagnetic wave by a perfectly conducting semi-infinite screen embedded in a homogeneous plasma is investigated. A uniform magnetic field is assumed to be impressed externally in a direction parallel to the edge of the half plane. The plasma is idealized to be a dielectric characterized by a tensor dielectric constant. The direction of the incident wave is assumed to be in a plane perpendicular to that of the screen. This vector problem is separable into two equivalent scalar problems for which either the electric or the magnetic vector is parallel to the edge of the half plane. It is found that for the case of theEmode, the magnetic vector parallel to the edge of the half plane satisfies a simple wave equation and a new type of impedance boundary condition on the screen. This problem is formulated in terms of an integral equation which specifies the current induced on the screen. The integral equation is of the Wiener-Hopf type and is solved by the usual function-theoretic methods. For a given orientation of the external magnetic field, a surface wave is found to exist along the screen but on one side only. The characteristics of this surface wave are determined.     

Analytical study of a radiating nonlinear electromagnetic crystal under mixing conditions

A nonlinear radiating electromagnetic crystal excited by the plane wave of free space at the signal frequency and the wave of the electromagnetic crystal at the heterodyne frequency is considered. Transformation of the electromagnetic energy of the plane wave into the crystal wave at the intermediate frequency is analyzed. An approximate model of the structure in the form of a system of differential equations is constructed. An analytical solution of this system is obtained. This solution is used to show that the highest efficiency of energy transformation is attained under the conditions of the spatial synchronism of waves at frequencies of the signal and heterodyne and the intermediate frequency.     

Surface waves on a uniaxial plasma slab--Their group velocity and power flow

The relation between group velocity and the velocity of energy transport for surface waves in plane-stratified, anisotropic, dispersive media, which was derived in [1], is verified by direct calculation for the case of surface waves on a uniaxial, cold plasma slab located in free space. A superimposed dc magnetic field of infinite strength and parallel to the interfaces generates the uniaxial anisotropy in the slab. Surface waves having an arbitrary direction of propagation with respect to the dc magnetic field are considered. A useful graphical presentation of the dispersion relation is given, from which the direction of propagation of "surface wave rays" is directly obtained.     

Group velocity and power flow relations for surface waves in plane-stratified anisotropic media

Two aspects of power flow associated with electromagnetic waves in plane-stratified, dispersive, anisotropic media that are also lossless and linear are considered. One aspect is the relation between group velocity and the velocity of energy transport of surface waves in such media. It is shown that the group velocity of surface waves is equal to the ratio of the real part of the complex Poynting vector, integrated over the coordinate of stratification, to the corresponding integral of the stored energy density. The second aspect is the relation between the dyadic surface impedance representing either a slab of plane-stratified medium above a perfectly conducting plane or a semi-infinite region, the latter for the case of evanescent fields, and the power flow in the respective structures. The significance of the surface impedance and power relations for surface waves is discussed.     

Isofrequency surfaces and dependences of electromagnetic waves in infinite ferromagnetic space

Isofrequency surfaces and dependences of various (spin, nonresonant, and postresonant) electromagnetic waves that propagate in infinite ferromagnetic space under saturated magnetization are calculated. In a frequency interval of ω_H < ω < ω_⊥, the propagation of spin waves is characterized by open isofrequency dependences and the cutoff angles that depend on the frequency and material parameters. When the conditions are not satisfied, closed dependences are obtained. The properties of the isofrequency dependences that determine specific features of the reflection and diffraction divergence of waves are analyzed. The spin wave that propagates perpendicularly to the uniform magnetic field may exhibit zero angular width of the beam in the plane that is parallel to the magnetic field vector. In the same plane, the nonresonant wave with linear dispersion may have the diffraction divergence that is significantly less than that of the wave in isotropic media. In the presence of a plane interface, the reflection of the wave to the ferromagnetic material may give rise to two reflected beams.     

A Semi-Infinite Array of Parallel Metallic Plates of Finite Thickness for Microwave Systems

An array of parallel metallic plates of finite thickness are useful in microwave lenses. The effect of finite thickness in the idealized situation of a semi-infinite array of perfect conductivity, is treated theoretically and experimentally for normal incidence of a uniform plane wave on the plane interface separating the medium from free space. The theoretical discussion involves the approximate variational method and a procedure is given for estimating the order of magnitude of the error in the final result. It is shown that it can be advantageous to use plates of finite thickness since the reflection from the interface can be reduced from that existing for infinitely thin plates.     

Surface Wave Radiation from a Thick, Semi-Infinite Plane with a Reactive Surface

The idealized surface wave radiator considered here is a thick, semi-infinite plane with a reactive surface. The scattered field is found when symmetrical and unsymmetrical surface waves are radiated at the termination of the plane. Since there are semi-infinite boundary conditions, the Wiener-Hopf technique is used for finding equations describing the scattered field. These equations contain a series of unknown constants which require numerical solution. Field patterns are plotted for different plane thicknesses and surface reactances with even excitation. The scattering of a plane wave by a thick, reactive plane is also discussed briefly.     

Scattering by thin dielectric strips

A plane wave incident on a thin dielectric strip with infinite length is considered, letting the incident electric field vector be parallel with the edges of the strip. The field is expanded in the dielectric region as the sum of three plane waves (the forced wave and two surface waves). Thex-axis andy-axis propagation constants are known for each wave, and Galerkin's method is employed to determine the amplitudes of these waves. Finally, the far-zone scattered field is determined by considering the polarization currents radiating in free space. Numerical data are presented to illustrate the scattering properties of lossless and lossy dielectric strips as a function of the angle of incidence and the width of the strip. The calculations show excellent agreement with an earlier moment method using pulse bases and point matching.     

Harmonic generation by an electromagnetic wave in an inhomogeneous isotropic plasma

The generation of harmonic waves by a plane electromagnetic wave normally incident on a collision-free plasma with a linear density profile is considered. The solution for the primary wave in the plasma region is first obtained, and nonlinear polarization currents for the higher harmonics are expressed in terms of the lower harmonic fields by a perturbation method. The analysis shows that the plasma excites a longitudinally oscillating second harmonic electric field which is totally confined inside the plasma and has a singularity. The third harmonic wave excited in the plasma, however, radiates back into free space, although the effect is negligibly small in a quasi-homogeneous limit. The amplitude of this radiated field oscillates as a function ofomega^{3}, and the electron density gradient has little effect on it.     

Surface Electromagnetic Modes of a Ferrite Slab

The dispersion relationship describing the propagation of electromagnetic (EM) surface modes supported by a ferrite slab of finite thickness magnetized parallel to the planes of its air-ferrite-air or air-ferrite-metal interfaces is investigated. Surface wave propagation at frequencies greater than the ferrite-metal mode resonance is predicted for thick grounded ferrite slabs thereby clarifying prior results based upon semi-infinite and magnetostatic analyses. The relative energy densities of the electromagnetic surface modes is examined at the air-ferrite interfaces of an ungrounded slab.     

Analysis of Perfectly Matched Double Negative Layers Via Complex Coordinate Transformations

Complex coordinate transformations are introduced for the analysis of time-harmonic electromagnetic wave propagation in perfectly matched double negative layers. The layer is perfectly matched to free space in the sense that any incident plane wave is transmitted through the free space-material interface without reflection, irrespective of the frequency and angle of incidence of the plane wave. The material constitutive parameters are obtained by mapping spatial coordinates into a manifold in complex space. The layer turns out to be anisotropic in general, and the special case where the medium is isotropic can be deduced from the coordinate transformations. The left-handedness, as well as the reversal in phase velocity appear naturally as a result of the mapping of the spatial coordinates into complex space. The consequences of this analysis are demonstrated by some examples     

Bound Waves in Compressible Plasma Gaps†

It is shown that a planar gap in a plasma medium is an appropriate idealized model for studying electromagnetic and plasma waves in a variety of situations, including plasma sheaths and ionospheric layers. A uniform, isotropic, lossless, warm plasma gap is investigated and is found to support both surface and interface waves which consist of an electromagnetic mode coupled to a plasma pressure mode. The surface waves are fast and they occur primarily at frequencies below the plasma frequency, whereas the interface waves are slow and are present at all frequencies ; in both cases, the waves may be either of the forward- or backward-travelling variety. In addition, the presence of leaky waves of the spectral type is demonstrated at frequencies above the plasma frequency. Dispersion curves are calculated for o large range of the parameters involved and the results are compared to those for surface waves along a dielectric slab which, in certain respects, represents a configuration analogous to the plasma gap if pressure effects are neglected.     

Scattering of Electromagnetic Waves by a Cylinder Moving Along its Axis

The scattering of a time-harmonic, linearly polarized plane electromagnetic wave by a cylinder uniformly moving along its axis is discussed. The formalism is relativistically exact, and explicit forms are provided for first-order velocity effects. Consideration is given to both a cylinder moving in free space, using the procedure suggested by Einstein, and two refractive media; it is veritied that the first case is a special case of the second one. Thin scatterers are considered and it is shown that no first-order velocity effects are present. For a moving medium, having in its rest frame the same constitutive parameters as the surrounding medium, it is shown that the velocity-independent part vanishes, but scattered fields of the first order in the velocity are still present. Moreover, these waves appear with the opposite polarization (compared to the incident wave).     

Waveguides Containing Moving Dispersive Media

Perturbation formulas are derived for the changes in the dispersion curves and phase velocity for the modes in an arbitrary composite waveguide structure containing dispersive media in relative motion. The formulas are also valid when the media are fluids with arbitrary velocity distributions. It is shown that the relativistic transformation laws for the frequency and wave vector of uniform plane waves are also valid for waveguide modes provided that all moving media that make up the guide move with the same velocity. There are also difficulties when the moving media are dispersive. In general, one most therefore obtain the dispersion relation directly from the field equations or from the perturbation formulas. An example involving a simple surface wave along the interface of a moving plasma and a dielectric is worked out by both methods. As an interesting side result, it is found that plane waves in an unbounded isotropic plasma have phase velocities independent of the motion of the plasma.