of EM waves
Updated April 4,
This web page is part of a three-part
tutorial on radar absorbing materials used for RCS reduction.
Part one is on the fundamentals
of electromagnetic waves (you are here!)
two is on radar cross-section physics.
three is on radar absorbers and absorption mechanisms.
Here is the index to this page:
of electromagnetic waves
here to go to our main page on absorbing materials.
Chemical agent resistive coating.
When you get far enough from an antenna so that its radiated field
wave can be considered planar. Also called the Fraunhoffer
Region. See rule of thumb below.
Magnetic radar absorbing material, made of a synthetic rubber
material loaded with iron particles.
When you are close enough to an antenna so that its radiated field
must be considered mathematically spherical rather than planar.
Also called the Fresnel Region. See rule
of thumb below.
Perfect electrical conductor.
Perfect magnetic conductor.
The cross-product of the E-field and H-field, it "points"
in the direction that energy is moving. Units are power/area (W/m2).
The area of a perfect "mirror" that would give the same
radar return as a complex object in the far field.
Radar absorbing structures.
The object that you are trying to reduce the radar cross-section
Mirror-like reflection, the worst kind when you are trying to
reduce RCS. Similar to when an SUV behind your car nails your
rearview mirror with its headlights while you are driving at night.
of EM waves
Electromagnetic (EM) waves are
created by time-varying currents and charges. Their interactions
with materials obey the boundary conditions of Maxwell’s equations.
EM waves can be guided by structures (transmission lines) or by
free space. An antenna is a material structure that directs EM fields
from a source into space, or, by reciprocity, from space to a receiver.
The shape and size of the antenna controls the transition from the
near field to the far field.
Near-field behavior is most clearly
seen surrounding small antennas; the electric dipole is a capacitive
Update April 2013: Yulong Zhao correctly pointed out that the red arrows on the left figure above are pointing the wrong way, the E-field lines should go from positive charge to negative charge. Thanks!
The near field consists of the
reactive near field, also known as the quasi-static near field,
and the radiating near field also known as the Fresnel zone or Fresnel
region. In the quasi-static near field we see fields that strongly
resemble the electrostatic fields of a charge dipole for a dipole
antenna and the fields of a magnetic dipole for a loop antenna.
In large antennas the quasi-static field can be seen near edges.
In the Fresnel zone the waves
are clearly not plane and may have phase shifts that do not vary
linearly with distance from a (fictitious) phase center.
From the near field to the far
field, EM radiation changes from spherical waves to plane waves.
The far-field is sometimes called the Fraunhoffer region.
Microwaves101 Rule of Thumb
You are in the far-field if your
distance from the source is greater than 2d2/.
The small loop is the magnetic
dipole, an inductive object.
Common to all electrically small
(less than a wavelength) antennas is that the near field excites
the environment in which the antenna resides. It’s the antenna combined
with its environment that radiates EM waves. Electrically small
Before tackling the near field,
it’s best to understand the behavior of the far field. Far from
the source, the spherical EM waves flatten out and can be treated
like plane waves. The power density is given by:
spread out = W/m2
In the far field, E-field and
H-field are proportional to 1/radius. The Poynting vector (power/area)
is given by E x H. Therefore, power density drops as 1/radius2.
Electrically large antennas are
good sources of plane waves in the laboratory. A large antenna focuses
the power, this is called directivity, or directive gain. Here are
some large antenna examples:
The antenna creates a large (D>>)
area of electromagnetic field, with nearly uniform phase.
The paragraph below was updated
February 16, 2009 for clarity:
Below are two pairs of field
pattern plots of a 1 x 1 foot aperture, at one GHz and then at five
GHz, representing an "electrically small" aperture and
an "electrically large" aperture. The left plots are amplitude
while the right plots show phase. Note that the 5 GHz signal becomes
"far-field" in a shorter distance than the 1 GHz signal
(that is, the phase lines become flatter). The large aperture (5
GHz) quickly allows plane wave fronts to form, but there is interference
inside the Fresnel zone (the peaks and valleys you see in the amplitude).
The small aperture (1 GHz) generates a wave much like a small point
radiator, so the wave is spherical near the aperture (there is no
clear transition to a Fraunhoffer region).
Footnote: the computation
that generated the figures beyond the 1x1 foot aperture is credited
to PhD student Zhichao Zhang of ASU.
Much of the technical material
on this page was prepared by Dr. Rudy Diaz of Arizona State University,
for ARC Technologies, Inc.