PHYS 211 Experimental Physics
O6. Microwave Reflection, Scattering, and Diffraction
Purpose
The objective of this experiment is to help you to understand the principles of microwave
optics and become familiar with the basic operation of microwave experiment.
Equipment and components
Microwave transmitter and receiver with stands, goniometer, metal reflector with holder,
rotating table, polyethylene panel, cubic lattice, multimeter for receiver reading, power
supply for transmitter (specifications: 9 Volt DC, 500 mA, miniature phone jack connector
with a positive pin).
Background
There are many advantages to studying optical phenomena at microwave frequencies. Using
a microwave of wavelength of 2.85 cm, one can transform the scale of the experiment.
Nanometers (for X-ray) or micrometers (for laser light) become centimeters and variables
obscured by the small scale of traditional optical experiments are easily seen and
manipulated. In this experiment, you will learn the basic operation of microwave equipment
and carry out several exercises ranging from quantitative investigations of microwave
propagation, reflection, and diffraction to the measurement of the wavelength and Brewster's
angle.
When two electromagnetic waves meet in space, they superpose and the total electric field at
any point in space is the sum of the electric fields created by the two waves at that point. If
the two waves travel at the same frequency but in opposite direction they form a standing
wave. Nodes appear where the fields of the two waves cancel and antinodes appear where
the superposed field oscillates with maximal amplitude. The distance between the nodes in
the standing wave pattern is just one half of the wavelength of the two waves. This
phenomenon is utilized in Exercise 2 to measure the wavelength of the microwave.
When a plane wave is incident upon a periodic array of particles, part of the wave is
diffracted (or scattered) by the particles and part of the wave transmits through the sample.
The scattered wave consists of many sub-waves, which superpose in space beyond the
scattering sample. Similar to the interference pattern, there are points in space where a
maximal intensity is realized and others where a minimal intensity is found. Having a
periodic array of particles, a crystal sample can be considered as a grating with the same
period as the lattice constant. Therefore, if a plane wave is shone through the "crystal
grating,” one should see the diffraction spots of different orders.
According to Bragg’s law, the diffraction effect is significant only when the wavelength of
the wave becomes comparable to the period of the "grating." In particular, two criteria must
be met for a wave to be diffracted from a crystal into a particular angle. Namely, there is a
plane of atoms in the crystal oriented with respect to the incident wave, such that:
1. the angle of incidence equals the angle of reflection, and
2. Bragg's equation, 2dsin θ = n λ, is satisified; where d is the spacing between the
diffracting planes, θ is the grazing angle of the incident wave, n is an integer, and λ is the
wavelength of the radiation.
Scattering of coherent waves provides a powerful tool for measuring the structure of
materials. Examples include x-ray diffraction study of atomic crystals and laser light
scattering of various soft materials.
Revised: 28 May 2008
O6-1/7
Microwave Reflection, Scattering, and Diffraction
Procedure
Exercise 1: Microwave optics. This exercise provides a brief introduction to the microwave
optics and the basic operation of microwave equipment.
1.1 Gunn diode transmitter. The Gunn diode microwave transmitter provides a coherent,
linearly polarized microwave with wavelength of 2.85 cm and output power of 15 mW. The
unit consists of a Gunn diode in a 10.525 GHz resonant cavity, a microwave horn to direct
the output, and an 18 cm stand to help reduce table top reflections. The transmitter may be
powered directly from a standard 220/240 VAC, 50/60 Hz outlet by using the provided power
supply. Other features include an LED power-indicator light and a rotation scale that allows
easy measurement of the angle of polarization. The Gunn diode acts as a non-linear resistor
that oscillates in the microwave band. The output is linearly polarized along the axis of the
diode and the attached horn radiates a strong beam of microwave radiation centered along the
axis of the horn.
CAUTION: The output power of the microwave transmitter is well within the standard safety
levels. Nevertheless, one should never look directly into the microwave horn at close range
when the transmitter is on.
1.2 Microwave receiver. The microwave receiver provides a meter reading that, for low
amplitude signals, is approximately proportional to the intensity of the incoming microwave
signal. A microwave horn identical to that of the transmitter's collects the microwave signal
and channels it to a Schottky diode in a 10.525 GHz resonant cavity. The diode responds only
to the component of a microwave signal that is polarized along the diode axis, producing a
DC voltage that varies with the magnitude of the microwave signal.
Special features of the receiver include four attenuation ranges - from one to thirty - with a
variable sensitivity knob that allows fine tuning of the attenuation in each range. The receiver
is battery powered and has an LED battery indicator. As with the transmitter, an 18 cm high
mount minimizes table top reflections, and a rotation scale allows convenient measurements
of the polarization angle. A multimeter is provided to connect to the banana plug connector
for an output signal. Two 9-volt batteries are already installed inside the receiver.
NOTE: The detector diodes in the receiver (and the probe) are non-linear devices. This nonlinearity will not be a problem for most experiments. It is important to realize, however, that
the meter reading is not directly proportional to either the electric field (E) or the intensity
(I) of the incoming microwave. Instead, it generally reflects some intermediate value.
To operate the receiver,
1. Turn the INTENSITY selection switch from OFF to 30X, the highest attenuation level.
The battery indicator LED should light, indicating that the battery is okay. NOTE: The
INTENSITY selection settings (30X, 10X, 3X, 1X) are the values you must multiply the
meter reading by to normalize your measurements. 30X, for example, means that you
must multiply the meter reading by 30 to get the same value you would measure for the
same signal with the INTENSITY selection set to 1X. Of course, this is true only if you do
not change the position of the VARIABLE SENSITIVITY knob between the two
measurements.
2. Point the microwave horn toward the incoming microwave signal. Unless polarization
effects are under investigation, adjust the polarization angles of the transmitter and
receiver to the same orientation.
3. Adjust the VARIABLE SENSITIVITY knob to attain a multimeter reading about 0.5
volt. If the reading cannot reach 0.5 volt, decrease the attenuation by turning the
INTENSITY selection switch clockwise. Remember, always multiply your meter reading
by the appropriate INTENSITY selection and do not adjust the VARIABLE
SENSITIVITY once it is already set within each exercise.
Revised: 28 May 2008
O6-2/7
Microwave Reflection, Scattering, and Diffraction
1.3 Microwave intensity measurement.
1. Arrange the transmitter and receiver on the goniometer, as shown in Figure 1.1, with the
transmitter attached to the fixed arm. Be sure to adjust both transmitter and receiver to
the same polarity—the horns should have the same orientation, as shown. Plug in the
transmitter and turn the INTENSITY selection switch on the receiver from OFF to 30X.
The LEDs should light up on both units.
Figure 1.1 Experimental setup
2. Adjust the transmitter and receiver so that the distance R between the effective points of
transmission and reception is 50 cm. Figure 1.2 shows the effective point of emission
and reception of the transmitter signal. Adjust the INTENSITY and VARIABLE
SENSITIVITY dials on the receiver so that the meter reads 1.0V.
Figure 1.2 Location of effective point of transmission and reception
3. Measure the microwave intensity with varying distance R from 50 to 80 cm with 5 cm in
each step. Record the meter readings in your lab notebook. Do not adjust the receiver
controls between the measurements. After making the measurements, plot the measured
intensity as a function of R and R2.
4. Set R to some value between 60 and 80 cm. While watching the meter, slowly decrease
the distance R. Does the meter reading increase steadily as the distance decreases?
5. Set R to a value between 50 and 80 cm. Move the metal reflector, with its plane parallel
to the axis of the microwave beam, toward and away from the beam axis (see Figure 1.3).
Observe the meter readings. Explain your observations in steps 4 and 5. Note that
reflections from nearby objects, including the table top, can affect the results of your
microwave experiments. To reduce the effects of extraneous reflections, keep your
experiment table clear of all objects, especially metal objects, other than those
components required for the current experiment.
6. Loosen the hand screw on the back of the receiver and rotate the receiver. This varies the
polarity of maximum detection. (Look into the receiver horn and notice the alignment of
the detector diode.) Observe the meter readings through a full 3600 rotation of the horn.
At what polarity does the receiver detect no signal? Try rotating the transmitter horn as
well. When finished, reset the transmitter and receiver so that their polarities remain the
same.
Revised: 28 May 2008
O6-3/7
Microwave Reflection, Scattering, and Diffraction
Figure 1.3 Setup for metal reflector
7. Position the transmitter such that the output surface of the horn is centered directly over
the center of the degree plate of the goniometer arm (see Figure 1.4). With the receiver
directly facing the transmitter and as far back on the goniometer arm as possible, record
the multimeter reading of the receiver. Then rotate the goniometer arm as shown in
Figure 1.4. Measure the microwave intensity with varying scattering angle θ from -900
to +900 with 50 in each step. Record the meter readings in your lab notebook. Do not
adjust the receiver controls between the measurements. After making the measurements,
plot the measured intensity as a function of θ.
Figure 1.4 Intensity measurements as a function of the scattering angle θ
Questions
1.
The amplitude of an electromagnetic wave is inversely proportional to the distance from
the wave source. From your measurements in step 3, determine whether the meter
reading of the receiver is directly proportional to the electric field or to the intensity of
the wave. Explain.
Exercise 2: Standing waves - measurement of wavelength. The microwave horns are not
perfect collectors of microwave radiation. Instead, they act as partial reflectors, so that the
radiation from the transmitter reflects back and forth between the transmitter and reflector
horns, diminishing in amplitude at each pass. However, if the distance between the
transmitter and receiver diodes is equal to nλ/2, where n is an integer and λ is the wavelength
of the radiation, all the multiply-reflected waves entering the receiver horn will then be in
phase with the primary transmitted wave. When this occurs, the meter reading will be at
maximum. The distance between adjacent positions in order to see a maximum is therefore
λ/2.
1. Setup the experiment as shown in Figure 2. Adjust the receiver controls to get a meter
reading of 1 Volt. You may need to modify the separation between the transmitter and
the receiver to achieve this.
2. Slide the receiver along the goniometer arm (no more than a centimeter or two) until the
meter shows a relative maximum reading. Record the receiver position along the metric
scale of the goniometer arm.
Revised: 28 May 2008
O6-4/7
Microwave Reflection, Scattering, and Diffraction
3.
While watching the meter, slide the receiver away from the transmitter. Do not stop until
the receiver passes through at least 10 pairs of minimum and maximum readings. Record
the final position of the receiver and the number of minima that the receiver has passed.
Figure 2 Experimental setup
4.
Use your data to calculate the wavelength λ of the microwave radiation. Repeat your
measurements and recalculate λ.
Questions
What is the experimental uncertainty for λ in your measurements?
8
2. Calculate the frequency of the microwave signal (assuming its velocity c = 3×10 m/sec).
Does your result agree with the expected frequency of the microwave radiation
(= 10.525 GHz)?
1.
Exercise 3: Brewster's angle. In this exercise, you will carry out a surface reflection
experiment and measure Brewster’s angle, at which the horizontally polarized wave does not
reflect.
1.
Arrange the equipment as shown in Figure 3, and set both the transmitter and the receiver
for horizontal polarization (90°). Adjust the transmitter and receiver so that the distance
R (as shown in fig. 1.1) between the effective points of transmission and reception is
about 80 cm. Adjust the polyethylene panel so that the angle of incidence of the
microwave is 35°. Rotate the goniometer arm until the receiver is positioned where it can
detect the maximum signal reflected from the panel. Adjust the receiver INTENSITY and
VARIABLE SENSITIVITY controls for full-scale reading (1V) and record the meter
reading in your lab notebook.
Figure 3. Experimental setup
0
0
0
2. Vary the incident angles ranged from 30 to 66 with 2 in each step and record the
receiver reading.
3. Repeat steps 1 and 2 for vertical polarization, that is, by rotating both the transmitter and
the receiver horns so that they align for the vertical polarization (0°).
NOTE: Please keep the receiver VARIABLE SENSITIVITY control unchanged, you
can still adjust the INTENSITY control if the reading is larger than 1V or too small.
Revised: 28 May 2008
O6-5/7
Microwave Reflection, Scattering, and Diffraction
4.
Plot the measured intensity as a function of the incidence angle for each polarization.
Find the Brewster’s angle - the angle at which the horizontally polarized wave does not
reflect.
Questions
Explain how Polaroid sun glasses can be used to reduce the glare caused by the sun
setting over a lake or the ocean. Should one design the glasses to block vertically or
horizontally polarized light?
2. Could you use the microwave apparatus to locate Brewster’s angle by examining the
transmitted wave rather than the reflected wave? How?
1.
Exercise 4: Bragg diffraction. In this exercise, Bragg diffraction is demonstrated on a
macroscopic scale using a cubic “crystal” consisting of 10-mm metal spheres embedded in an
ethafoam cube.
1. Mount the transmitter, the receiver and the “crystal” sample as shown in Figure 4.1. Set
both the transmitter and the receiver for vertical polarization (0°).
Figure 4.1 Experimental setup
2. There are three families of “crystal” planes indicated in Figure 4.2. These sets of planes
are designated as {100}, {110}, and {120} planes by the Miller indices. Adjust the
transmitter and receiver so that they directly face each other. Align the crystal so that the
{100} planes are parallel to the incident microwave beam. Adjust the receiver controls to
provide a readable signal. Record the meter reading.
Figure 4.2 "Atomic" planes of a crystal sample
3. Rotate the crystal (with the rotating table) one degree clockwise and the goniometer arm
two degrees clockwise. Record the grazing angle of the incident beam and the meter
reading. As shown in Fig. 4.3, the grazing angle is the complement of the angle of
incidence. It is measured with respect to the plane under investigation, not the face of the
cube.
Revised: 28 May 2008
O6-6/7
Microwave Reflection, Scattering, and Diffraction
Figure 4.3 Grazing angle for a “crystal” plane
4. Continue in this manner, rotating the goniometer
eter arm two degrees for every one degree
rotation of the crystal. Record the angle and meter reading at each position. If you need
to adjust the INTENSITY setting on the receiver, be sure to indicate that in your
notebook.
5. Plot the relative intensity of the diffracted signal as a function of the grazing angle of the
incident beam. How many intensity peaks are found in your measurements? At what
angles? Use Bragg’s law together with your data and the measured wavelength of the
microwave in Exercise 2 to determine the spacing between the {100} planes of the
crystal sample. Measure the spacing between the planes directly and compare it with
your diffraction result.
6. Repeat the measurements for the {110} or {120} planes.
Questions
1. What other families of planes might you expect to show diffraction in this cubic crystal?
Would you expect the diffraction to be observable with this apparatus? Why?
2. Suppose you did not know beforehand the orientation of the “inter-atomic planes” in the
crystal, how would this affect the complexity of the experiment? How would you go
about locating the planes?
3. What kind of electromagnetic wave is needed in order to measure the structure of a single
crystal silicon wafer?
Revised: 28 May 2008
O6-7/7