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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:50:47 +0000Electromagnetic Scattering Properties of a Resonant Plasma
https://resolver.caltech.edu/CaltechETD:etd-08062004-143419
Authors: Shapiro, Haskell
Year: 1957
DOI: 10.7907/60W8-N371
<p>A column of ionized mercury vapor is placed in a parallel plate transmission line and the resulting reflection coefficient observed. From the measurement of reflection coefficient as a function of discharge current, plasma resonance is demonstrated. In accordance with the theory applied, but in contrast to the results of other investigators, resonance is found at only one value of discharge current. The discharge current required to produce resonance is measured as a function of frequency. The functional dependence observed is as predicted by theory, but the current is higher than the theoretical value. The discharge current required to produce resonance is measured as a function of gas pressure. The dependence that is found follows that predicted theoretically at higher gas pressures, but deviates sharply from the theoretical form at lower gas pressures.</p>
https://thesis.library.caltech.edu/id/eprint/3022Asymmetrically Excited Electromagnetic Radiation from Circular Cylinders of Finite Length and Prolate Spheroids
https://resolver.caltech.edu/CaltechETD:etd-02172006-084352
Authors: Kuehl, Hans Henry
Year: 1959
DOI: 10.7907/KDNQ-NR51
<p>The far zone radiation from two types of asymmetrically excited systems is considered. The first is a finite cylinder excited by an electric dipole in the radial direction near the cylinder. The second is a prolate spheroid excited by a narrow belt of electric field around the surface of the spheroid. In both cases the body considered is perfectly conducting and the excitation is not necessarily centered at the midplane of the body. In the case of the finite cylinder excited by a radial dipole, an approximate method is used in which the current on the finite cylinder is taken to be identical with the current which would exist on an infinite cylinder under the same excitation. This approximation is shown to be valid analytically and experimentally if the cylinder is not short. The analytic and experimental results are compared for two cylinder lengths. The turnstile antenna mounted on a finite cylinder is considered analytically and the modification of the radiation by the cylinder is exhibited. In the case of the prolate spheroid excited by a narrow belt of electric field, experimental results are compared to analytic expressions. The differences between the experimental and analytic results are considered. The considerations in obtaining accurate experimental results in both asymmetrically excited systems are discussed.</p>
https://thesis.library.caltech.edu/id/eprint/652Spatial Distribution of Thermal Radiation at Microwave Frequencies
https://resolver.caltech.edu/CaltechETD:etd-02022006-142926
Authors: George, Nicholas A.
Year: 1959
DOI: 10.7907/CERS-Y395
<p>Theoretical and experimental radiation patterns are given in spectral form for the thermal radiation from thin slots or heated wires having dimensions of the order of the comparison wavelength. Maxwell's equations and noise theory form the basis of the analyses in which three independent methods are used to predict a spatial distribution which exhibits interference minima and maxima. In the first, the wave equation is solved for a noise-excited transmission line which is suddenly short- and open-circuited at alternate ends. By a study of the trapped noise currents, it is found that the radiation pattern has an interference structure which is smoothed as the loss is increased. Secondly, a formula is derived for the radiation pattern of a heated wire by a computation of its absorption in an isothermal enclosure and by an application of the principle of detailed balancing. Finally, the pattern of a long thin slot is computed directly using the Lpontovich-Rytov distributed source generalization of Nyquist's noise formula.</p>
<p>Fraunhofer pattern measurements are taken for a thin slot excited by a gaseous discharge at 10,100 ± 200°K. The pattern measuring apparatus is a Dicke radiometer having the following characteristics: frequency 9200 mc/s, bandwidth to the detector 16 mc/s, modulation frequency 1000 c/s, and residual noise level 0.3 rms°K.</p>
<p>The theory and the experiment demonstrate an interference phenomenon even though the source excitation is spatially extended and uncorrelated in time and space. The patterns are not even approximately Lambertian, e.g., a thin slot of 9.5 pi radians length exhibits a pattern having nine relative maxima in 180° with the maximum emission at 63° from the normal.</p>https://thesis.library.caltech.edu/id/eprint/460A Theoretical Study of the Scattering of Electromagnetic Impulses by Finite Obstacles
https://resolver.caltech.edu/CaltechTHESIS:07262011-163527834
Authors: Brown, Wilbur Parker
Year: 1962
DOI: 10.7907/4892-CE13
A general approach to the solution of pulse scattering by
finite obstacles is formulated. The essential feature of this approach is the identification and separate treatment of the individual terms in a wavefront expansion of the transforms of the field vectors. It is demonstrated that the dispersive effect of a finite conductivity in the scattering obstacle can be neglected for all metals but that it may be significant for poorly conducting
materials such as dry earth. The wavefront technique is
employed to solve the problems of the transmission of a delta pulse through a conducting dielectric slab and the reflection and diffraction of a delta pulse from a perfectly conducting sphere. The transmission problem results provide a convenient example of the usefulness of the wavefront approach. The results for the sphere problem indicate that the nature of the waves observed at a
given spatial point change in time, It is shown that the penumbra and the caustic region in the vicinity of the focal line θ = π are initially of zero extent. The rates of expansion of these regions with increasing time are obtained by a consideration of the error terms in the asymptotic expansions of the fields. The temporal behavior of the near and far field zones is obtained in a similar manner.https://thesis.library.caltech.edu/id/eprint/6548Electromagnetic surface-wave propagation along a dielectric cylinder of elliptical cross section
https://resolver.caltech.edu/CaltechTHESIS:08182011-142633204
Authors: Yeh, Cavour W. H.
Year: 1962
DOI: 10.7907/A13E-BB49
The problem of electromagnetic wave propagation along a dielectric cylinder of elliptical cross section is considered. Two infinite determinants representing the characteristic equations for the two types of hybrid waves (the _eHE_(mn) and the _oHE_(mn) waves) are derived.
These waves degenerate to the well-known HE_(mn) wave of the circular dielectric rod as the eccentricity of the elliptical rod approaches zero. It is found that there exist two dominant waves which possess zero cutoff frequencies. The characteristic roots of these two
dominant waves are computed for various values of eccentricity and relative dielectric constant. Also given are the attenuation characteristics and the field distribution of the dominant modes. It is shown that a flattened dielectric rod supporting the _eHE_(11) wave offers less loss than a circular rod having the same cross-sectional area and supporting the HE_(11) wave. Theoretical propagation characteristics (the guide wavelength, the field distribution and the attenuation constant) of the dominant waves are verified by experiments. The Q's of a dielectric rod cavity resonator supporting the dominant waves are also presented.
https://thesis.library.caltech.edu/id/eprint/6597A Study of cross-polarization effects in paraboloidal antennas
https://resolver.caltech.edu/CaltechETD:etd-09242002-083513
Authors: Kerdemelidis, Vassilios
Year: 1966
DOI: 10.7907/3SFB-WB47
In this report the induced surface current method is used to investigate the spatial structure of the radiated electric field for a number of paraboloidal antennas. The paraboloids are excited by three different types of feeds, namely, a small electric dipole, an elemental plane wave source, and a rectangular horn.
For the case of electric dipole excitation, formulas are derived that show the following characteristics:
(i) For a reflector of constant ratio of focal length to the aperture diameter the magnitude of the cross-polarized lobe nearest to the antenna axis (paraboloid axis) remains constant relative to the maximum of the main lobe of the principally-polarized wave and is independent of the aperture size.
(ii) For a given aperture size the magnitude of the cross-polarized component relative to its own principally-polarized maximum decreases with the focal length.
(iii) The position of the maximum of the cross-polarized lobe depends only on the aperture size and is independent of the focal length.
The problem of cross-polarization is also solved by using a simple model which gives results that are in surprisingly close agreement with those obtained by the more complete expressions. In addition this crude model explains the angular variation of the amplitude of cross-polarization component at angles not necessarily small from the paraboloid axis.
For a paraboloid excited by an elemental Huyghens source the cross-polarization in the forward direction is reduced but the component in the laterally-directed radiation is increased relative to that of an electric dipole.
In the case of the horn-excited paraboloid we obtain a formula that explains the experimentally-observed large crosspolarization.
Finally, we show that the problems of the paraboloids excited by a small electric dipole and a plane (Huyghens) source are merely particular cases of the horn excitation problem.https://thesis.library.caltech.edu/id/eprint/3738A study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas
https://resolver.caltech.edu/CaltechTHESIS:09102015-131924711
Authors: Chan, Tsiu Chiu
Year: 1966
DOI: 10.7907/E932-CW77
<p>This thesis is a study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas externally biased with a magnetostatic field. The present study is restricted to the nonlinear phenomena rising from the interaction of electromagnetic waves in the ionized gas. The important effects of nonlinearity are wave-form distortion leads to cross modulation of one wave by a second amplitude-modulated wave.</p>
<p>The nonlinear effects are assumed to be small so that a perturbation method can be used. Boltzmann’s kinetic equation with an appropriate expression for the collision term is solved by expanding the electron distribution function into spherical harmonics in velocity space. In turn, the electron convection current density and the conductivity tensors of the nonlinear ionized gas are found from the distribution function. Finally, the expression for the current density and Maxwell’s equations are employed to investigate the effects of nonlinearity on the propagation of electromagnetic waves in the ionized gas, and also on the reflection of waves from an ionized gas of semi-infinite extent. </p>
https://thesis.library.caltech.edu/id/eprint/9144Radiation of a point charge moving uniformly over an infinite array of conducting half planes
https://resolver.caltech.edu/CaltechETD:etd-09252002-122649
Authors: Lam, John Ling-Yee
Year: 1967
DOI: 10.7907/1BR2-6A78
The problem of the excitation of an infinite array of parallel, semi-infinite metallic plates by a uniformly moving point charge is studied by the Wiener-Hopf method. It is treated as a boundary value problem for the potentials of the diffracted electromagnetic fields. The formulation of this problem makes use of the well-known conditions on the electromagnetic fields at a metallic boundary. A method is used to translate these boundary conditions on the fields into boundary conditions on the potentials. In this way the problem is formulated in terms of a set of dual integral equations for the current densities induced on the plates by the point charge. These integral equations are exactly soluble by the Wiener-Hopf technique. The solutions are found to satisfy the famous edge conditions for diffraction problems, and are therefore unique. From these solutions exact expressions for the diffracted fields are derived in the form of Fourier integrals. It is seen that these fields represent a radiation of electromagnetic energy. The method of steepest descent is then used to obtain expressions for the radiation fields, the Poynting vector, the frequency spectrum and the radiation pattern. The radiation shows that the array of plates behaves both like a diffraction grating and a series of parallel-plate waveguides.https://thesis.library.caltech.edu/id/eprint/3755Electric dipole radiation in isotropic and uniaxial plasmas
https://resolver.caltech.edu/CaltechETD:etd-09242002-082113
Authors: Kenny, John J.
Year: 1968
DOI: 10.7907/2Q1Z-GS04
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This paper describes an investigation of radiation from an electric point dipole situated in a cold, collisionless, homogeneous, electronic plasma medium. Two limiting cases of a gyroelectric medium are studied. The magnetostatic biasing field [...] is first taken to be equal to zero, making the medium isotropic, and then it is taken to be infinite, causing a uniaxial anisotropy. The retarded electromagnetic fields and the instantaneous and averaged values of irreversibly radiated power [...] are calculated.
In each medium, the partial differential equations resulting from the two-sided Laplace transformation of Maxwell's equations with an oscillating electric dipole source and the constitutive equations (derived from the appropriate form of the Lorentz force equation) are solved. A particular path deformation of the Laplace inversion integral reveals that the electromagnetic fields and [...] are exactly expressible in terms of circular, cylindrical, and two-variabled Lommel functions. Asymptotic expressions and graphical results of numerical calculations of these quantities are presented.
For the isotropic case, it is shown that the retarded fields are well behaved for all space and time (excluding the origin, of course). [...] eventually settles down to the result derived from the conventional time-harmonic analysis when the dipole oscillation frequency [...] is greater than the plasma frequency [...] . When the value of [...] is less than that of [...], [...] eventually oscillates at a frequency [.....] with zero average value.
When the medium is uniaxial, the fields are finite everywhere except at the dipole. The amplitude of the fields does, however, increase with increasing time. This is quite different from the ordinary time-harmonic solution which ignores all time variations different from [...] and which is singular on a conical surface defined by [...] for [...]. The value of [...] in a uniaxial medium is found to be equal to the value of [.....] of a dipole in vacuum. It is also shown that the so-called conventional expression for time-averaged radiated power will not give a sensible result since it contains the retarded electric field which never settles down to a steady-state variation with time. The quantity [...], on the other hand, does not increase with time, oscillates only at the source frequency, and has a well-defined time average.
https://thesis.library.caltech.edu/id/eprint/3737The resolution of the thermodynamic paradox and the theory of guided wave propagation in anisotropic media
https://resolver.caltech.edu/CaltechTHESIS:12182015-135931289
Authors: Mrstik, Adolph Vincent
Year: 1968
DOI: 10.7907/5DAY-XC29
<p>The resolution of the so-called thermodynamic paradox is presented in this paper. It is shown, in direct contradiction to the results of several previously published papers, that the cutoff modes (evanescent modes having complex propagation constants) can carry power in a waveguide containing ferrite. The errors in all previous “proofs” which purport to show that the cutoff modes cannot carry power are uncovered. The boundary value problem underlying the paradox is studied in detail; it is shown that, although the solution is somewhat complicated, there is nothing paradoxical about it.</p>
<p>The general problem of electromagnetic wave propagation through rectangular guides filled inhomogeneously in cross-section with transversely magnetized ferrite is also studied. Application of the standard waveguide techniques reduces the TM part to the well-known self-adjoint Sturm Liouville eigenvalue equation. The TE part, however, leads in general to a non-self-adjoint eigenvalue equation. This equation and the associated expansion problem are studied in detail. Expansion coefficients and actual fields are determined for a particular problem. </p>
https://thesis.library.caltech.edu/id/eprint/9328Electromagnetic scattering from cylindrically and spherically stratified bodies
https://resolver.caltech.edu/CaltechTHESIS:12212015-110440537
Authors: Latham, Raymond Walter
Year: 1968
DOI: 10.7907/QGVG-1464
A method is developed for calculating the electromagnetic field scattered by certain types of bodies. The bodies consist of inhomogeneous media whose constitutive parameters vary only with the distance from some axis or point of symmetry. The method consists in an extension of the invariant imbedding method for treating wave problems. This method, which is familiar in the case of a one-dimensional inhomogeneity, is extended to handle special types of two and three-dimensional inhomogeneities. Comparisons are made with other methods which have been proposed for treating these kinds of problems. Examples of applications of the method are given, some of which are of interest in themselves.https://thesis.library.caltech.edu/id/eprint/9338A multiple scattering problem
https://resolver.caltech.edu/CaltechTHESIS:01142016-141500284
Authors: Varvatsis, Athanassios Demetrius
Year: 1968
DOI: 10.7907/02K5-V111
<p>The present work deals with the problem of the interaction of the electromagnetic radiation with a statistical distribution of nonmagnetic dielectric particles immersed in an infinite homogeneous isotropic, non-magnetic medium. The wavelength of the incident radiation can be less, equal or greater than the linear dimension of a particle. The distance between any two particles is several wavelengths. A single particle in the absence of the others is assumed to scatter like a Rayleigh-Gans particle, i.e. interaction between the volume elements (self-interaction) is neglected. The interaction of the particles is taken into account (multiple scattering) and conditions are set up for the case of a lossless medium which guarantee that the multiple scattering contribution is more important than the self-interaction one. These conditions relate the wavelength λ and the linear dimensions of a particle a and of the region occupied by the particles D. It is found that for constant λ/a, D is proportional to
λ and that |Δχ|, where Δχ is the difference in the dielectric susceptibilities between particle and medium, has to lie within a certain range.</p>
<p>The total scattering field is obtained as a series the several terms of which represent the corresponding multiple scattering orders. The first term is a single scattering term. The ensemble average of the total scattering intensity is then obtained as a series which does not involve terms due to products between terms of different orders. Thus the waves corresponding to different orders are independent and their Stokes parameters add.</p>
<p>The second and third order intensity terms are explicitly computed. The method used suggests a general approach for computing any order. It is found that in general the first order scattering intensity pattern (or phase function) peaks in the forward direction Θ = 0. The second order tends to smooth out the pattern giving a maximum in the Θ = π/2 direction and minima in the Θ = 0 , Θ = π directions. This ceases to be true if ka (where k = 2π/λ) becomes large (> 20). For large ka the forward direction is further enhanced. Similar features are expected from the higher orders even though the critical value of ka may increase with the order.</p>
<p>The first order polarization of the scattered wave is determined. The ensemble average of the Stokes parameters of the scattered wave is explicitly computed for the second order. A similar method can be applied for any order. It is found that the polarization of the scattered wave depends on the polarization of the incident wave. If the latter is elliptically polarized then the first order scattered wave is elliptically polarized, but in the Θ = π/2 direction is linearly polarized. If the incident wave is circularly polarized the first order scattered wave is elliptically polarized except for the directions Θ = π/2 (linearly polarized) and Θ = 0, π (circularly polarized). The handedness of the Θ = 0 wave is the same as that of the incident whereas the handedness of the Θ = π wave is opposite. If the incident wave is linearly polarized the first order scattered wave is also linearly polarized. The second order makes the total scattered wave to be elliptically polarized for any Θ no matter what the incident wave is. However, the handedness of the total scattered wave is not altered by the second order. Higher orders have similar effects as the second order.</p>
<p>If the medium is lossy the general approach employed for the lossless case is still valid. Only the algebra increases in complexity. It is found that the results of the lossless case are insensitive in the first order of k<sub>im</sub>D where k<sub>im</sub> = imaginary part of the wave vector k and D a linear characteristic dimension of the region occupied by the particles. Thus moderately extended regions and small losses make (k<sub>im</sub>D)<sup>2</sup> ≪ 1 and the lossy character of the medium does not alter the results of the lossless case. In general the presence of the losses tends to reduce the forward scattering.</p>
https://thesis.library.caltech.edu/id/eprint/9534A scaling technique for the design of idealized electromagnetic lenses
https://resolver.caltech.edu/CaltechTHESIS:01252016-081748086
Authors: Baum, Carl Edward
Year: 1969
DOI: 10.7907/N9WZ-SP03
<p>A technique is developed for the design of lenses for transitioning TEM waves between conical and/or cylindrical transmission lines, ideally with no reflection or distortion of the waves. These lenses utilize isotropic but inhomogeneous media and are based on a solution of Maxwell's equations instead of just geometrical optics. The technique employs the expression of the constitutive parameters, ɛ and μ, plus Maxwell's equations, in a general orthogonal curvilinear coordinate system in tensor form, giving what we term as formal quantities. Solving the problem for certain types of formal constitutive parameters, these are transformed to give ɛ and μ as functions of position. Several examples of such lenses are considered in detail.</p>https://thesis.library.caltech.edu/id/eprint/9540Theory of Electrodynamics of Media in Non-Inertial Frames and Applications
https://resolver.caltech.edu/CaltechTHESIS:03282017-111748813
Authors: Mo, Tse Chin
Year: 1969
DOI: 10.7907/1Z64-YS50
<p>In the first half of this thesis a local electrodynamics of
media in given non-inertial frames*, within Maxwell-Einstein classical
field theory, is constructed in terms of observable EM fields and
co-moving local physical media parameters. Localization of tensors to
observables is introduced and justified, and a relation is obtained
connecting tensor transforms to instantaneous Lorentz transforms for
observers in different frames. A constitutive tensor, explicitly
expressed by the four-velocity and the local properties in co-moving
frame of a linear medium, is found for the first time. Previous mistakes
in confusing the tensors, in which forms the physical quantities
combine with the non- flatness of frames to be used in covariant equations
and thus make geometrical quantities, with observables are
cleared. Also a Lagrangian formulation for both lossless and lossy
media is constructed, and boundary conditions, local conservation laws,
and energy momentum tensor are obtained.</p>
<p>The second half concerns application to motions in SRT, such
as uniform linear (hyperbolic) acceleration and steady rotation. For
these local Maxwell equations in co-moving frames are obtained, and
approximate solutions are found for special cases. An EM wave
propagating in the direction of acceleration is studied in the
accelerating frame. The first order propagation shows a frequency
shift and amplitude change which have very simple physical significances
of instantaneous Doppler shift and photon density in media
and which agree with familiar results in the vacuum limit. A particle
model for this wave shows that the "mass dressed" photon is dragged by
the medium and does not follow a geodesic path. In the rotating medium
case a plane wave scattered by a rotating sphere is solved by an integral
iteration method in the laboratory frame. The scattered field
purely associated to the rotation of the medium is separated from the
Mie scattering. Its first order amplitudes are found and plotted for
incidences perpendicular and parallel to the rotation axis. Particular
synunetry and shapes of scattering amplitude in the results agree with
intuition and resemble radiation patterns of appropriately induced
traveling electric and magnetic dipole sheaths.</p>
<p>*The contribution of EM field to g<sub>µv</sub> is neglected.</p>https://thesis.library.caltech.edu/id/eprint/10111Radiation from an Antenna Entering the Martian Atmosphere
https://resolver.caltech.edu/CaltechTHESIS:03242017-095341798
Authors: Norgard, John Dennis
Year: 1969
DOI: 10.7907/pd64-rx94
<p>The interaction between the ionized wake of a capsule entering
the Martian atmosphere and the circularly polarized radiation emitted
by an antenna located on the aft part of the capsule is theoretically
investigated in this study. A simplified mathematical model of the
atmosphere of Mars, the entry-trajectory of the capsule, and the flow
field surrounding the capsule are used in the analysis. The near wake
of the capsule is approximated by a cylindrically stratified plasma
shell consisting of n plasma regions. The plasma in each region is
assumed to be homogeneous, anisotropic, and conducting, and moving at
a uniform velocity relative to the antenna. The antenna is represented
by a turnstile antenna located off-axis λ<sub>o</sub>/4 above an infinite ground
plane and operates at the signal frequencies of 400 MHz and 2.295 GHz.</p>
<p>Integral expressions for the cylindrical components of the
field vectors are obtained by a rigorous relativistic formulation of
the problem, and are evaluated using the techniques of asymptotic
expansions to yield the radiation patterns of the antenna. Radiation
patterns for the special case of an on-axis antenna radiating through
a uniform, lossless, and isotropic plasma shell are presented and are
compared with the free space patterns.</p>
<p>The analysis shows that blackout occurs during the entry of
a capsule into the Martian atmosphere, Before and after blackout,
the radiation patterns of the antenna exhibit an on-axis null region
whose angular extent is proportional to the electron concentration of
the plasma. Also, sharp peaks which are attributed to leaky wave radiation,
are present in the null region of the patterns. For the non-null
region of the patterns, the values of the gain function of the antenna
oscillate about the free space values. As the electron concentration
of the plasma increases, the peaks in the radiation patterns become more
numerous and more sharply defined. The effects of the motion of the
plasma on the radiation emitted by the antenna are to shift the peaks
of the radiation patterns to smaller cone angles and to introduce more
peaks into the patterns.</p>
<p>For the low velocity case corresponding to an entry into the
Martian atmosphere, no serious motional or depolarization effects
occur, and communications with the capsule can be satisfactorily carried
out when the condition of blackout does not exist.</p>https://thesis.library.caltech.edu/id/eprint/10105Analysis of Aperture Antennas in Inhomogeneous Media
https://resolver.caltech.edu/CaltechTHESIS:04152011-101450645
Authors: Damlamayan, Dikran
Year: 1970
DOI: 10.7907/8GWH-NP26
<p>The object of this report is to calculate the admittance and the radiation pattern of aperture antennas fed by waveguides of arbitrary cross-section and radiating into dielectric slabs, whose constitutive parameters may be functions of position along the direction normal to the slab faces.</p>
<p>For a given aperture field distribution the antenna aperture admittance and the radiation field are expressed here, for the first time, in terms of two auxiliary quantities directly related to the plane wave reflection and transmission coefficients of the dielectric slab. These quantities are the input admittance of the dielectric slab and the ratio of the total electric field amplitude transmitted at one end of the slab to the transverse field at the other, both calculated for plane waves as a function of incident propagation direction. This approach introduces a great simplification in the solution of the problem, particularly in the case of an antenna radiating into an inhomogeneous dielectric slab.</p>
<p>A simple and powerful method has been devised for the computation of the input admittance of an inhomogeneous dielectric slab as well as for the electric field ratio. In this case the impracticability of obtaining analytical results has necessitated the use of numerical techniques.</p>
<p>Examples of the application of the theory to typical dielectric slabs are given and the results are discussed.</p>https://thesis.library.caltech.edu/id/eprint/6334Investigations in the theory of electromagnetic scattering from expanding dielectric obstacles
https://resolver.caltech.edu/CaltechTHESIS:08202015-163157997
Authors: Pogorzelski, Ronald J.
Year: 1970
DOI: 10.7907/G2F7-EJ85
<p>An equation for the reflection which results when an expanding dielectric slab scatters normally incident plane electromagnetic waves is derived using the invariant imbedding concept. The equation is solved approximately and the character of the solution is investigated. Also, an equation for the radiation transmitted through such a slab is similarly obtained. An alternative formulation of the slab problem is presented which is applicable to the analogous problem in spherical geometry. The form of an equation for the modal reflections from a nonrelativistically expanding sphere is obtained and some salient features of the solution are described. In all cases the material is assumed to be a nondispersive, nonmagnetic dielectric whose rest frame properties are slowly varying. </p>https://thesis.library.caltech.edu/id/eprint/9111Electromagnetic wave propagation and scattering in a randomly-inhomogeneous dielectric sphere
https://resolver.caltech.edu/CaltechTHESIS:08282015-131240078
Authors: Bilow, Henry Joel
Year: 1970
DOI: 10.7907/CMVZ-RR78
<p>Electromagnetic wave propagation and scattering in a sphere composed of an inhomogeneous medium having random variations in its permittivity are studied by utilizing the Born approximation in solving the vector wave equation. The variations in the permittivity are taken to be isotropic and homogeneous, and are spatially characterized by a Gaussian correlation function. Temporal variations in the medium are not considered.</p>
<p>Two particular problems are considered: i) finding the far-zone electric field when an electric or magnetic dipole is situated at the center of the sphere, and ii) finding the electric field at the sphere's center when a linearly polarized plane wave is incident upon it. Expressions are obtained for the mean-square magnitudes of the scattered field components; it is found that the mean of the product of any two transverse components vanishes. The cases where the wavelength is much shorter than correlation distance of the medium and where it is much longer than it are both considered.</p>
https://thesis.library.caltech.edu/id/eprint/9121Electromagnetic Wave Propagation and Source Radiation in Space-Time Periodic Media
https://resolver.caltech.edu/CaltechETD:etd-10302003-143115
Authors: Elachi, Charles
Year: 1971
DOI: 10.7907/WYFR-GR84
The electromagnetic wave equations for the fields, potentials and Hertz vectors are derived and a Lorentz gauge is given for space-time dependent media. Electromagnetic wave propagation, electric and magnetic dipole radiation, and Cerenkov and transition radiation in sinusoidally space-time periodic dielectric, plasma and uniaxial plasma are studied and numerous radiation patterns are given. A special radiation effect in the uniaxial plasma is investigated. Finally the study is extended to general space-time periodic media (i.e., ε = ε<sub>0</sub>ε<sub>r</sub> [1 + ε<sub>1</sub> f(Kz - Ωt)] where f(ξ) is a periodic function).https://thesis.library.caltech.edu/id/eprint/4318Plasma inverse scattering theory
https://resolver.caltech.edu/CaltechTHESIS:04012016-145403689
Authors: Balanis, George Nick
Year: 1972
DOI: 10.7907/7PTN-RV17
<p>The object of this report is to calculate the electron density profile of plane stratified inhomogeneous plasmas. The electron density profile is obtained through a numerical solution of the inverse scattering algorithm.</p>
<p>The inverse scattering algorithm connects the time dependent reflected field resulting from a δ-function field incident normally on the plasma to the inhomogeneous plasma density.</p>
<p>Examples show that the method produces uniquely the electron density on or behind maxima of the plasma frequency.</p>
<p>It is shown that the δ-function incident field used in the inverse scattering algorithm can be replaced by a thin square pulse.</p>
https://thesis.library.caltech.edu/id/eprint/9642Electromagnetic fields in nonuniform lossless transmission lines
https://resolver.caltech.edu/CaltechTHESIS:06062016-081741962
Authors: McGovern, Patrick Anthony
Year: 1972
DOI: 10.7907/S8QM-4Y57
<p>Methods are developed for electromagnetic field calculations in nonuniform lossless transmission lines which support quasi-one dimensional propagation of a single baseband wave species. Approximate solutions are obtained in perturbation series for smoothly tapered lines by expanding Maxwell's equations and boundary conditions in the dimensionless parameter ƞ, given by the ratio of typical
cross-section dimension to the length of the tapered section. The method emphasizes construction of a single ''warped" field description rather than the local modal expansions of Schelkunoff's generalized telegraphist's equations. </p>
<p>Expansions in Cartesian coordinates yield the traditional distributed circuit parameter equations in the lowest approximation. Correction terms appear in even powers of ƞ, and their effects are shown most clearly by calculating waveform aberrations introduced by line transitions of nominally constant characteristic impedance. Improved field descriptions in nonuniform regions are obtained by reformulating the exact equations in special nonorthogonal coordinate systems more closely related to the essential structure of the field problem. The lowest term of the ordered expansion is now exact for a uniform finite angle taper. New circuit level nonuniform line equations are obtained which reduce to the well-known forms for gradual tapers. </p>
<p>These techniques are extended to treat tapered plate lines with curved center lines and then to give a description of coaxial lines in which the field pattern is locally dominated by the boundaries, and the electrical center line is located in the propagation region. Odd-sequence field distortion terms now appear in third and higher orders. In all the systems investigated, distributed circuit equations give results, outside the nonuniform region, that are valid to within second order terms in the taper scale parameter. </p>
https://thesis.library.caltech.edu/id/eprint/9847Electromagnetic Wave Propagation and Radiation in a Suddenly Created Plasma
https://resolver.caltech.edu/CaltechTHESIS:07112018-141856792
Authors: Jiang, Ching-Lin
Year: 1973
DOI: 10.7907/3TKY-YR40
<p>Propagation and radiation of electromagnetic waves from oscillating sources in a suddenly created plasma are studied in this investigation. Field expressions are derived through the use of Laplace transformations. The spatial distribution of sources is taken to be arbitrary but confined.</p>
<p>Two cases are considered in detail: (1) plane wave propagation in a source-free region, and (2) electric point dipole radiation. In the case of plane wave propagation, various aspects such as wave split, frequency shift, phase and group velocities, amplitude changes, power flows and energy relations are discussed. In the case of electric dipole radiation, the electromagnetic fields and instantaneous radiated power are calculated and expressed in terms of Lommel functions of two variables. Asymptotic expressions and graphical results of numerical calculations of these quantities are presented. Many interesting properties of the spherical waves and power radiation are discussed.</p>https://thesis.library.caltech.edu/id/eprint/11114Shielding Theory of Enclosures with Apertures
https://resolver.caltech.edu/CaltechTHESIS:10192017-142731943
Authors: Mendez, Horacio Augusto
Year: 1974
DOI: 10.7907/Z9KW5D7F
<p>Present methods for computing the shielding efficiency of metallic plates with apertures are based on the analysis of a plane wave incident on an infinite conducting sheet. When applied to actual enclosures with internal radiation sources, these methods lose all validity, and obviously fail to predict the measured results. Semi-empirical formulas are available for special cases,
but no serious analytic investigation has ever been conducted.</p>
<p>This dissertation develops the theory of electromaqnetic radiation from metallic enclosures with apertures, excited by an internal source at frequencies below the fundamental resonance
of the enclosure.</p>
<p>The enclosure with an aperture is analyzed from two different points of view: as a cavity with a small aperture in a wall; and as a waveguide section short-circuited at one end and open at the
other end.</p>
<p>Rectangular geometries are used throughout, since these are by far the most commonly encountered in practical enclosures and cabinets.</p>
<p>Using the corresponding dyadic Green's functions, the fields generated inside the enclosure by some simple sources are determined. In addition to the case of a Hertzian dipole - the building block for more complicated sources - a center-fed dipole and a square loop antenna are analyzed. The fields radiated through small apertures in a cavity are determined using Bethe's theory of diffraction by small holes. The radiation from an open waveguide is calculated with the help of field equivalence theorems, with assumptions applicable to the case of evanescent waves.</p>
<p>The final step is to derive expressions for the "Insertion Loss" of the shield, defined as the ratio of the field strength at a point external to the shield, before and after the insertion
of the enclosure. To accomplish this, the effect of the shield upon the input impedance of the antenna is analyzed, and expressions obtained for the applicable cases.</p>
<p>The resulting insertion loss expressions are numerically evaluated for some representative cases, and graphically compared with a series of measurements performed to obtain experimental
confirmation. Very good agreement is obtained in all cases, establishing the validity of the analysis.</p>
<p>Thus, this work provides accurate prediction capabilities for the design of shielded enclosures with apertures, in the presence of internal or external noise sources (the latter is a consequence
of applying the reciprocity theorem). Hence, it constitutes a useful tool in the solution of electromagnetic interference and susceptibility problems.</p>https://thesis.library.caltech.edu/id/eprint/10531Transient radiation from coaxial waveguide and cylindrical monopole antennas
https://resolver.caltech.edu/CaltechETD:etd-09302005-110310
Authors: Broome, Norval L.
Year: 1974
DOI: 10.7907/5MP2-DD24
In this work the coaxial waveguide antenna is treated by the Wiener-Hopf technique and the transient radiation from a cylindrical monopole is developed in the light of the rigorous results obtained from the Wiener-Hopf analysis. Analytic expressions are derived for (1) the electromagnetic fields in the feed line and (2) the far zone radiation fields of the coaxial waveguide antenna, with time harmonic excitation voltage. Complete characterization of the transient behavior is also found for (1) the fields interior to the feed line and (2) the radiated fields for excitation voltages arbitrary in their time dependence to the extent that kb,ka << 1. This corresponds to the case of a thin antenna and excitation voltage with a non-zero rise time, specifically chosen so that frequencies violating the restriction kb,ka << l are negligible.
The transient radiation from the cylindrical monopole is developed in a closed analytic form which is relatively easy to interpret and apply. The expressions found offer an alternative to transient analysis by conventional methods requiring numerical techniques involving extensive computer calculations. They are also the basis for an uncomplicated procedure to synthesize a desired behavior of the transient radiation from cylindrical monopole antennas.
https://thesis.library.caltech.edu/id/eprint/3836Electromagnetic Pulses at the Boundary of a Nonlinear Plasma
https://resolver.caltech.edu/CaltechTHESIS:09172021-215240263
Authors: Satorius, Edgar Harry
Year: 1975
DOI: 10.7907/d6ww-a643
<p>This paper describes an investigation of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collision-less, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma.</p>
<p>Two cases are studied. First, we consider the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, we consider the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found.</p>
<p>In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found.</p>https://thesis.library.caltech.edu/id/eprint/14366Electromagnetic theory of distributed feedback lasers in periodic dielectric waveguides
https://resolver.caltech.edu/CaltechETD:etd-12052007-100020
Authors: Evans, Gary A.
Year: 1975
DOI: 10.7907/QMW8-1287
A theory for distributed feedback lasers in transversely bounded structures is developed. The space harmonics approach is used to discuss the general properties of periodic structures. The coupled mode approach is used to develop expressions for the threshold gain, longitudinal mode structure, and electromagnetic field distribution for distributed feedback lasers.
Three basic structures are considered for distributed feedback lasers--thin film waveguides, diffusion waveguides, and fiber wave-guides.
Equations for the amplification of a waveguide mode that extends transversely over both regions with and without gain are derived.
Analytical expressions are derived for coupling between modes in periodically perturbed dielectric waveguides. Sinusoidal perturbations of the electric permittivity and of the waveguide boundary are considered.
Theoretical results indicate that an optimum design of distributed feedback lasers can be achieved by an appropriate choice of geometrical parameters. Regions of optimum design are illustrated in numerous plots of normalized threshold gain versus normalized laser frequency.
https://thesis.library.caltech.edu/id/eprint/4799An Analysis of Linear Induction Motors for Propulsion and Suspension of Magnetically Levitated Vehicles
https://resolver.caltech.edu/CaltechTHESIS:11092017-124408265
Authors: Yang, Fang-Chou
Year: 1976
DOI: 10.7907/DM0P-XW77
A four-layer single-sided LIM used for propulsion and suspension of magnetically levitated vehicles is studied. The track is assumed to be made of conductors with uniaxial μ and σ. A general analysis allows us to exclude unsuitable geometries. The machine performance is given for the promising geometries. A possible way of computing the effective μ and σ for a composite track is sketched. From the analysis of an extremely simplified geometry, the conditions for the validity of the effective μ and σ concept are given. Finally, a three-dimensional correction is introduced.https://thesis.library.caltech.edu/id/eprint/10553Electromagnetic wave propagation in almost periodic media
https://resolver.caltech.edu/CaltechTHESIS:03122012-112325331
Authors: Mickelson, Alan Rolf
Year: 1978
DOI: 10.7907/SZMY-A964
The problem of electromagnetic wave propagation in almost periodic
media is investigated and a solution is obtained directly from Maxwell's
equations. Techniques to evaluate this solution are developed. These
techniques involve a generalization to almost periodic media of the
Brillouin diagram of periodic media. The method of invariant imbedding
is applied to the coupled mode equations which determine the Brillouin
diagram for the purpose of transforming them to coupled Riccati equations.
These coupled Riccati equations, when subjected to a single boundary condition,
determine the solutions to both the periodic and almost periodic
boundary value problems. These evaluation techniques are used to place
in evidence similarities and differences of wave propagation in periodic
and almost periodic media. It is shown that although the periodic and
almost periodic theories agree in many cases of interest, there exist
cases in which distinct differences appear. In cases of multi-tone perturbations,
the almost periodic theory yields both simpler and more reasonable
results than the periodic theory.https://thesis.library.caltech.edu/id/eprint/6849The Influence of Random Media on the Propagation and Depolarization of Electromagnetic Waves
https://resolver.caltech.edu/CaltechETD:etd-10162006-082641
Authors: Harris, Jerry Michael
Year: 1980
DOI: 10.7907/XH76-NK15
<p>Electromagnetic wave propagation and depolarization in an inhomogeneous medium having random fluctuations in its permittivity are studied. The continuous space-time permittivity fluctuations are taken to be frozen-in, homogeneous, and isotropic. We find that the essential effect of the random permittivity is to destroy the time coherence and spatial orthogonality of the vector components of an electromagnetic wave penetrating the medium.</p>
<p>To study this problem, we develop a unique discrete model for the continuous random medium by dividing the volume occupied by the random inhomogeneities into independent elementary scattering volumes. Scattering by each of these elementary volumes is analyzed to obtain the complex amplitude and polarization of the single scattered field. Then multiple scattering among the many elementary volumes is used to estimate the composite values for scattering per unit length and depolarization per unit length of the medium. The manifestation of scattering in the medium is the generation of an incoherent or fluctuating electric wavefield and a coherent or average electric wavefield. It is shown that the total electric wavefield propagating in the medium satisfies an integral equation which is directly reducible to the classical equation for radiation transfer.</p>
<p>A novel result of this study is that only two phenomenological parameters are needed to describe the penetration of the wave into a plane-parallel medium, when a polarized plane wave is normally incident. These two parameters appear as diffusion constants in expressions for the solution for the coherency and Stokes matrices. These solutions simply describe how wave energy is progressively converted from the initially coherent and polarized field to an incoherent and unpolarized field as the wave propagates. An initially polarized wave is gradually depolarized, yielding a completely unpolarized wave deep into the medium.</p>
https://thesis.library.caltech.edu/id/eprint/4109Investigations of Near-Zone Doppler Effects
https://resolver.caltech.edu/CaltechETD:etd-09142006-111227
Authors: Prouty, Dale Austen
Year: 1982
DOI: 10.7907/vfzj-7d74
<p>Far away from an electromagnetic source the normal Doppler shifts in frequency occur – a red shift for receding and a blue shift for approaching. As indicated by previous work with an infinitesimal dipole, different frequency shifts occur when the source and observer move closer together, into the near-zone. These "near-zone Doppler effects" are investigated for general sources and subsequently two specific examples are presented.</p>
<p>The general results show that near-zone shifts are similar to far-zone shifts, but the local phase velocity must be used, i.e. ω' ≃ ω(1 ± (v/v<sub>ph</sub>)). In the far zone the phase velocity is the speed of light; in the near zone it differs. Fundamentally, the distance between surfaces of constant phase in the near zone is changed. The surfaces of constant phase for the waves are no longer spherical, but more ellipsoidal or spheroidal, so that a moving observer sees a different frequency shift.</p>
<p>Two specific examples are presented to indicate the actual magnitude of near-zone effects. The examples include a prolate spheroidal antenna and a circular aperture.</p>
<p>Once the magnitude of the effects is determined, the measurability of near-zone Doppler effects is discussed. The investigation concentrates on Fresnel zone effects due to the measurement problem.</p>
<p>Finally, it is shown that for an electrically large wire antenna (the spheroidal example) near-zone Doppler effects are measurable.</p>https://thesis.library.caltech.edu/id/eprint/3536On the Radiation Patterns of Interfacial Antennas
https://resolver.caltech.edu/CaltechETD:etd-09142006-080653
Authors: Engheta, Nader
Year: 1982
DOI: 10.7907/y86x-2709
<p>The radiation pattern of an interfacial radiating source is obtained for the case where the source is an infinitely long line source lying along the plane interface of two dielectric half-spaces; for the case where the source is an infinitesimal electric dipole vertically located on the interface; and for the case where the dipole is lying horizontally along the interface. For all the three cases, it is found that the radiation pattern at the interface has a null (interface extinction). For the infinitely long line source, it is obtained that the pattern in the upper half-space, whose index of refraction is taken to be less than that of the lower half-space, has a single lobe with a maximum normal to the interface, and that the pattern in the lower half-space (subsurface region) has two maxima straddling symmetrically a minimum. Interpretation of these results in terms of ray optics, Oseen's extinction theorem, and the Cerenkov effect are given. For the vertical dipole, it is found that the radiation pattern along the dipole axis has a null. For the horizontal dipole, it is obtained that the pattern in the upper half-space has a single lobe whose maximum is normal to the interface; that in the lower half-space, in the plane normal to the interface and containing the dipole, the pattern has three lobes; whereas in the plane normal to the interface and normally bisecting the dipole, the pattern has two maxima located symmetrically about a minimum. Interpretation of these results in terms of the Cerenkov effect is also given.</p>https://thesis.library.caltech.edu/id/eprint/3533An Analytical Study of Electromagnetic Vector Field Propagation in a Nonlinear Electron Plasma
https://resolver.caltech.edu/CaltechETD:etd-10312005-133116
Authors: Tatoian, James Zareh
Year: 1983
DOI: 10.7907/hzt3-s585
<p>From the equations of hydrodynamics and electrodynamics, a system of a coupled nonlinear equations governing the propagation of plane electromagnetic waves in a collisionless electron plasma is obtained. It is shown that solitary wave solutions exist for both the longitudinal and transverse components of the electromagnetic field. It is found that the velocity of the electromagnetic vector solitary wave depends on the amplitudes of all components of the field linearly. The relations among the longitudinal and transverse components that support the solitary waves are determined for different values of plasma temperature. It is shown that while transverse solitary waves cannot exist, except when they are supported by longitudinal waves, the latter can exist by themselves. The dynamics of the plasma electrons during the passage of a longitudinal wave is analyzed and the interaction of such waves with each other is studied. An upper bound on the amplitudes of these waves is obtained. The uniqueness and stability of the longitudinal waves are demonstrated. A Lagrangian density function and two conservation laws for the longitudinal wave equation are found. Frequency spectra of the solitary waves are calculated and their low frequency content is emphasized.</p>
https://thesis.library.caltech.edu/id/eprint/4338Electromagnetic Radiation and Scattering in a Plasma with an Azimuthal Biasing Field
https://resolver.caltech.edu/CaltechETD:etd-01232007-143259
Authors: Warne, Larry Kevin
Year: 1984
DOI: 10.7907/tja8-zp12
<p>The problem of radiation from an electric line source in a homogeneous, cold, incompressible electron plasma is considered when a large static current is superposed. The static axial current gives rise to a magnetostatic biasing field which is oriented in the azimuthal direction and varies with radial distance. When the driving frequency is greater than the plasma frequency, and the medium is assumed to be unbounded, the presence of the static current reduces the amount of radiation. On the other hand, if the driving frequency is less than the plasma frequency and the medium is assumed to be bounded, the amount of radiation is increased.</p>
<p>The problem of scattering from an axial current in a plasma is also considered. The medium in this problem is taken to be a bounded column of plasma containing a radially distributed axial current. At normal incidence the scattered wave contains a cross polarized field component due to the gyrotropic nature of the column. The scattered cross polarized component vanishes in the incident direction as well as in the backward direction. This null is explained by considering the effect of Faraday rotation on various rays traversing the column. Solutions to the scattering problem when the axial current density varies inversely with radial distance are considered in some detail. This case is labeled "homogeneous" since the dielectric tensor does not vary with radial distance and the resulting field equations are thus simplified. The field behavior in the vicinity of the origin is also considered in detail since phenomena similar to those encountered in wedge type media (unbounded fields) occur.</p>https://thesis.library.caltech.edu/id/eprint/297On the Importance of Polarization in Radar Scattering Problems
https://resolver.caltech.edu/CaltechETD:etd-06262006-133025
Authors: van Zyl, Jakob Johannes
Year: 1986
DOI: 10.7907/QRD0-YE09
<p>In this thesis, the importance of polarization in radar scattering problems is investigated. The different matrix characterizations of scatterers are discussed in detail. The problem of finding the polarizations which would yield an optimum amount of power received from the scatterer is solved for the most general case. This shows that for certain classes of scatterers six optimum polarizations exist. The concept of a polarization spectrum to characterize a scatterer is introduced. The usefulness of these spectrums is illustrated when results, using measured multipolarization synthetic aperture radar data, are discussed. Another useful parameter, the coefficient of variation, is introduced. Measured results show that this parameter may be used to form an idea of the scale over which the scattering properties of the scene being imaged vary. The problem of finding the effective scattering operator of a slab filled with different scatterers is formulated. Detailed expressions are given for the effective single scattering operators. This formulation is illustrated by calculating the effective single scattering operators for models of different types of vegetation.</p>https://thesis.library.caltech.edu/id/eprint/2734Electromagnetic Wave Propagation and Radiation in Chiral Media
https://resolver.caltech.edu/CaltechETD:etd-02282008-090141
Authors: Bassiri, Sassan
Year: 1987
DOI: 10.7907/RFST-5K65
<p>Propagation and radiation of electromagnetic waves in a lossless, reciprocal, chiral medium is studied in this thesis. Such a medium is described electromagnetically by the constitutive relations D = εE + iγB and H = iγE + (1/µ)B. The constants ε, µ, γ are real and have values that are fixed by the size, shape, and the spatial distribution of the elements that collectively compose the medium. The plane wave propagation in an unbounded chiral medium is considered. The propagation constants are obtained and the polarization properties of electromagnetic waves in such a medium are discussed in detail. The problem of reflection from, and transmission through a semi-infinite chiral medium is solved by obtaining the Fresnel equations. The conditions for the total internal reflection of the incident wave from the interface, and the existance of the Brewster angle are obtained. The effects of the chirality on the polarization and intensity of the reflected wave from the chiral half-space are discussed and illustrated by employing the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence. The radiation emitted by an oscillating dipole in an unbounded, lossless, chiral medium is calculated. From the constitutive relations and from the time-harmonic Maxwell equations ∇ x E = iωB and ∇ x H = J - iωD, it is seen that the wave equation for such a medium is given by ∇ x ∇ x E - ω<sup>2</sup>µεE - 2ωµγ∇ x E = iωµJ where the source term J is the current density of the oscillating dipole and where E is the electric vector of the radiated field. The desired solution of this wave equation is found by the dyadic Green's function method, that is, by first constructing the dyadic Green's function Γ and then evaluating the expression E = iωµ∫Γ(r,r')•J(r')dV'. The dyadic Green's function Γ and the components of the radiated electric field E are obtained in closed form. The components of the radiated B, D, and H fields can be derived from knowledge of E by using the Maxwell equation B = (1/iω)∇ x E and the constitutive relations. The wave impedance of the medium and the radiation resistance of the dipole are also obtained. The effects of the chiral medium on the polarization and intensity of the dipole radiation are discussed.</p>https://thesis.library.caltech.edu/id/eprint/808The Critical Points of Poynting Vector Fields
https://resolver.caltech.edu/CaltechETD:etd-11082007-131130
Authors: Rizvi, Syed Azhar Abbas
Year: 1988
DOI: 10.7907/gj18-eq28
<p>In a thought provoking paper Maxwell [The Scientific Papers of James Clerk Maxwell, ed. W. D. Niven, vol. 2, 233-240, Dover Publications, New York (1952)] studied the flow of water on the Earth's surface and how this flow is affected by the local geography. His results linking number of hills and lake bottoms to valleys are simple and the conclusions elegant. Critical points such as summits and lake bottoms play a key role in the overall organization and structuring of the flow lines. This is the spirit in which electromagnetic power flow represented by the Poynting vector field (S) is studied in this thesis. The specialized case of a planar S field which arises due to a single electromagnetic field component <i>E<sup>z</sup></i> or <i>H<sup>z</sup></i> is dealt with here in considerable detail.</p>
<p>In order to analyse the behaviour of the flow lines of a plane Poynting vector field in the neighbourhood of a critical point, the S field is expanded in a Taylor series. Critical points can be classified according to their order, degeneracy or structural stability. The order of a critical point refers to the degree of the leading non zero term in the Taylor series. A critical point is non degenerate if this leading term is sufficient to give a qualitative description of the flow lines in the neighbourhood. A critical point is structurally stable if the flow lines in the neighbourhood do not change drastically when there is a small perturbation of the electromagnetic field. It is found that lowest order critical points, i.e., elementary center point and elementary saddle point, are the only structurally stable critical points. These critical points are always non degenerate. All degenerate and non elementary critical points are found to be structurally unstable. A formula for the index of rotation of the S field at a critical point is derived. The behaviour of the electric or the magnetic field component which lies in the <i>x-y</i> plane is also studied. It is shown that structurally unstable configurations of flow lines change into structurally stable configurations under small perturbations in such a way that the index of rotation is conserved. The statements made above in connection with the behaviour of flow lines and structural stability are illustrated with the help of examples involving linearly polarized system of interfering plane and/or cylindrical waves.</p>
<p>The flow lines of the S field in the vicinity of a perfectly conducting surface are studied. It is found that in structurally stable situations these lines are either parallel to the surface or they form critical points of half saddle type on this surface. Two types of problems involving flow lines and conducting surfaces are identified. The interior problem deals with the situations where all the flow lines are inside a region bounded by a perfect conductor. In the exterior problems all the flow lines are outside a region bounded by a perfectly conducting surface. Conclusions regarding the existence of critical points and the behaviour of flow lines are drawn in the two above mentioned problems. These conclusions are verified by computation of flow lines in a few well known problems of scattering and diffraction.</p>
<p>Finally the critical points of three dimensional Poynting vector fields are considered. A complete classification of these critical points requires further study at this time. In this thesis only structurally stable critical points are classified for these S fields. An example demonstrating the existence of such critical points is given.</p>https://thesis.library.caltech.edu/id/eprint/4465