The wave propagation inside a cylindrical waveguide, coated with lossy dielectric material due to the incidence of a plane wave at the open end of the guide, was studied. The general properties of the normal mode propagation were investigated

Lee, S. W.

Lo, Y. T.

English

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r{NASA-CR-175U23) NUMERICAL METHODS FOfi N84-19620
ANALYZING ELECTROMAGNETIC SCATTERING
Semiannual Report, 25 Sep. 1983 - 24 Mar.
11984 ' iIllinois Oniv.) 21 p HC A02/MF A01 Onclas
V, CSCL 20N G3/32 11934
Semi-Annual Report for
NUMERICAL METHODS FOR ANALYZING ELECTROMAGNETIC SCATTERING
September 25, 1983 to March 24, 1984
Submitted to
Dr. Y. C. Cho
National Aeronautics and Space Administration
Lewis Research Center (MS 54-3)
Cleveland, OH 44113
Grant No. NAG-3-475
Prepared by
Professor Y. T. Lo
Electromagnetics Laboratory
Department of Electrical and Computer Engineering
University of Illinois
Urbana, IL 61801
and
Professor S. W. Lee
Electromagnetics Laboratory
Department of Electrical and Computer Engineering
University of Illinois
Urbana, IL 61801
March 23, 1984
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TABLE OF CONTENTS
Page
I. INTRODUCTION 1
II. TECHNICAL PERSONNEL 1
III. PRESENTATION AND PUBLICATIONS 1
IV. TECHNICAL PROGRESS 2
PRECEDING PAGE BLANK NOT FILMEU
ii
LIST OF FIGURES
Figure Page
1. An open-ended cylinder illuminated by an incident plane
wave 3
2. Attenuation constant with variation of frequency . 5
3. Real part of propagation constant 6
4. Attenuation constant with variation of e (TE..) 7
5. Attenuation constant with variation of e (TM. ) 8
6. Attenuation along the waveguide from normal incident wave
(polystyrene 70% and carbon 30%) 11
7. Attenuation along the waveguide from normal incident wave
(catalin 700 base) 12
8. Attenuation along the waveguide from normal incident wave
(pyralin) 13
n
9. Attenuation constant with variation of B(TE..,e = 3) .... 14
U
10. Attenuation constant with variation of B(TE..,e = 1.5) ... 15
t>
11. Attenuation constant with variation of B(TMj.,e = 3) .... 16
t)
12. Attenuation constant with variation of B(TM. .,e = 1.5) ... 17
iii
I. INTRODUCTION
The research grant NAG 3-475 entitled "Numerical Methods for Analyzing
Electromagnetic Scattering" was awarded to the University of Illinois by
NASA-Lewis Research Center on September 28, 1983. Dr. Y. C. Cho of NASA's
Microwave Amplifier Section Is the Technical Officer, and Mr. Boyd M. Bane
is the contracting officer. The total amount of funds received by the
University is
$22,385 + $52,600 - $74,985
to cover the period from
September 25, 1983 to November 25, 1984 (14 months).
This report is the first semi-annual report for the period September 25,
1983 to March 24, 1984.
II. TECHNICAL PERSONNEL
S. W. Lee Professor of Electrical and Computer Engineering
Y. T. Lo Professor of Electrical and Computer Engineering
S. L. Chuang Assistant Professor of Electrical and Computer
Engineering
C. S. Lee Research Assistant of the Department of Electrical and
Computer Engineering
III. PRESENTATION AND PUBLICATIONS
1. Professors S. W. Lee and Y. T. Lo traveled to NASA Lewis on
.November 1, 1983 to present a talk entitled "Electromagnetic
Scattering by Cylinders and Spheres." Viewgraphs of the presentation
are published as Electromagnetic Laboratory Report 83-1 under the
same title.
1
2. S. L. Chuang, S. W. Lee and Y. C. Cho, "Approximate Solutions for
Reflection from an Open-ended Waveguide," 1984 IEEE AP-S/URSI
Symposium, Boston, MA, June 25-28, 1984.
3. C. S. Lee, S. L. Chuang and S. W. Lee, "Wave Attenuation and Mode
Dispersion in a Waveguide Coated with Lossy Dielectric Material,"
paper to be presented in the Sixth Annual Workshop of the Industrial
Affiliates Program on Communication, Antennas, and Propagation (CAP),
Urbana-Champaign, IL, April 5-6, 1984.
IV. TECHNICAL PROGRESS
In the past six-month period, we studied the wave propagation inside a
cylindrical waveguide coated with lossy dielectric material due to the
incidence of a plane wave at the open end of the guide (Figure 1).
The first step for this problem is to obtain the propagation constants
of the normal modes in the lossy waveguide. Before we select any practical
material for the lossy dielectric, we have investigated the general proper-
ties of the normal mode propagation.
The characteristic equation for the propagation constant of a normal
mode in the lossy cylindrical waveguide can be derived by matching the
boundary conditions on the conducting surface and the interface between the
lossy dielectric and the air region in the cylinder. Then this charac-
teristic equation is solved numerically. In the cylindrically symmetric
geometry, mode coupling is largest between TE and TM modes with the same
mode indices, e.g., TE and TM . Though the normal mode in this case is
no longer pure TE or TM, it is closer to one of two modes when the thickness
ORIGINAL PAGE 88
OF POOR QUALITY
Fig. 1. An open-ended cylinder illuminated by an incident
plane wave.
of the dielectric layer is small. We call this mode "quasi" TE or TM mode,
and will use the same notation as in the unperturbed waveguide.
Figures 2 and 3 show the real and imaginary parts of the propagation
constants of the TE,. and TM., modes as a function of frequency in a
waveguide coated with a thin dielectric material. The exact numerical
solutions are compared with the results based on the perturbation theory
which we have applied to derive the attenuation constant following
Harrington*. We can see that the perturbation theory is valid only at the
low frequency region even though the thickness of the dielectric layer is
small. At the high frequency region, the TE mode shows much higher
attenuation than the TM1 mode. This is due to the fact that the TE
modal field moves closer to the surface of the cylinder than the TM1 . mode
as frequency increases.
Figures 4 and 5 show the attenuation constants as a function of the
complex dielectric constant e of the lossy dielectric material. We
observe two interesting features in these graphs. First, there is a clear
"resonance" effect of the imaginary part e of e on the attenuation
j^constant when the real part e of e is small « 1.5). Second, a smaller
n
e gives a larger attenuation constant except for those with a "dielectric
resonance." • To understand the results, consider: The attenuation constant
to be proportional to the power loss within the dielectric layer, which is
related to e and the magnitude of the electric field within the dielectric
layer. The angular E field E is small in the dielectric region when the
<P
dielectric layer is thin, because the tangential E field vanishes on the
surface of a perfect conductor. Thus the radial E field E is responsible
*R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill,
New York, 1961.
4
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for most of the power loss when |e j is not too large. Since E is inver-
sely proportional to |e | at the dielectric region, increasing the real
part of c actually decreases the power loss, and subsequently, the atten-
uation constant. Since the power loss is also proportional to e , the
attenuation constant becomes saturated as e becomes very large because
those two effects of e on the attenuation constant are about the same.
From the above results, it is natural to choose the lossy dielectric
p T
material with a small e and a large e (i.e., a large loss tangent) for
large attenuation within the waveguide. Plastics are in this category* and
three materials are chosen for further analysis (Table 1). Figures 6, 7,
and 8 show the power attenuation of the transmitted wave from the normally
incident plane wave with a unit power on the aperture. In order to calcu-
late the transmitted power, we use the Kirchhoff's approximation to find
the equivalent aperture source at the waveguide opening from the incident
field. Even though only two modes (TE.. and TE,«) are propagating in this
particular geometry, 85% of the incident power is transmitted. There are
two interesting features to be observed. Most of the power is carried by
the dominant mode (TE..) and the attenuation constant of the dominant mode
is usually larger than that of the higher mode. As those two modes propa-
gate through the waveguide, eventually the higher mode will carry most of
the power, but when this happens the total power has already decayed to a
small fraction of the initialpower at z = 0.
When the dielectric layer is thick, the behavior of the propagation
constant is different from the one for the thin dielectric layer. These
features are shown in Figures 9, 10, 11 and 12. We observe the following
*A. R. Von Hippel, ed., Dielectric Materials and Applications, Technology
Press,•M.I.T., Cambridge, Mass., 1954. •
9
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Table 1. The dielectric constants of the lossy dielectric
materials and the propagation constants of TEin and TE1?
modes when these materials are used in the waveguide.
ni ure
Material
IflUM €
* B
TEu
TEn
8
Catali*
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3.1 4.H4
3.3513
X1D "3
A=9.7 cm, B=10 cnn
*
A. R. Von Hippel, ed.,
Dielectric Materials and Applications,
Technology Press, M.I.T., Cambridge,
, 1954. •
10
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Interesting points: 1) There may exist a spatial resonance effect as the
R Ilayer thickness increases. 2) When we keep the ratio of e to e constant,
the basic dependence of the attenuation constant on the layer thickness
remains similar. 3) As e increases, the attenuation constant of the
TM.. mode increases, but the attenuation constant of the TE.. mode
decreases. In other words, they are mutually exclusive in attaining a
large attenuation constant.
18


Numerical methods for analyzing electromagnetic scattering

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