10 cm microwaves are used for the demonstration of travelling and standing waves, reflection, interference, refraction, diffraction, absorption, polarization, tunneling, and waveguides.
What it shows:
The following is a sequence of experiments that can accompany a standard lecture on electromagnetic waves. One may wish to follow the "Radio Wave Properties" demonstrations with these microwave companions; at 3 GHz, they're a factor of 10 higher in frequency and that much shorter in wavelength. It's a small but dramatic step from radio waves to light waves. Indeed, the demonstrations can also be used in lectures on the wave nature of light—Young's double-slit experiment is particularly vivid with 10 cm microwaves.
(1) The direction of polarization of the microwaves and the radiation pattern emanating from the horn antenna can be explored.
(2) Malus's law: a skein of wires can be used to absorb or transmit the microwaves, depending on their orientation with respect to the the incident polarization.
(3) The absorption of microwaves by water
(4) Interferometer: interference can be demonstrated by reflecting microwaves from a stationary and movable "mirror" onto the detector.
(5) Standing waves can be produced by the superposition of incident and reflected microwaves.
(6) Refraction: a large paraffin prism refracts microwaves
(7) Young's double-slit experiment on a grand scale—15 degrees between intensity maxima produced by two slits having 45 cm separation.
(8) Stealth bomber: the reflections from an aluminum surface are cancelled by reflections from Z0 cloth positioned a distance of λ/4 in front of the aluminum.
(9) Microwave zone plate illustrates some of the principles of optical (visible light) Fresnel zone plates.
(10) Microwave tunneling phenomenon
(11) Waveguides: guiding microwaves with parallel conducting plates
How it works:
The microwave source is a 3 GHz oscillator module1 whose output is amplified by a 50 Watt power amplifier2 which, in turn, feeds a 20 dB gain horn antenna.3 The microwave beam diverges about ±20 degrees. The various components and ancillary power supplies all reside on a dedicated cart.
Several detectors are available. The simplest is a miniature incandescent light bulb4 glued to the end of a wooden dowel. Two short copper wires, soldered to it's base, form a 1/2-wave dipole antenna. The current induced in the dipole is large enough to light the bulb at close range.
For larger distances requiring more sensitivity, another detector is used. It also consists of a 1/2-wave dipole antenna, but it is connected to an RF diode.5 The output is a negative DC current that can be read directly on an analog meter.6 The meter, being physically small, is made visible to the audience by video camera/projection. This can be cumbersome, so another detection scheme has been developed—an audio detector.
The DC current from the dipole antenna is converted to a 0 - 2 kHz signal, which is then amplified by a 3 Watt audio amplifier to drive a speaker. The entire battery powered circuit is housed in a hand-held shielded box.7
And now the details of the various demonstrations possible with the apparatus:
(1) The microwave waveguide/horn is oriented with it's narrow dimension vertical, and that means the E-field is vertical and determines the direction of polarization. This is easily verified with the light bulb detector—the lightbulb glows brightly when the dipole is oriented vertically and goes out completely when oriented horizontally.
(2) Microwave polarizing filter: One way to produce a given polarization is to get rid of the undesired components of the waves by arranging to have them do work and use up their energy. A grid of wires serves that purpose as they absorb microwaves with E along the length of the wire.
Since the incident microwaves are already polarized in the vertical direction, orient the dipole detector vertically to maximize the signal. Interpose the wire grid between the microwave source and the dipole detector. When the grid is rotated so that the wires are vertical, the bulb goes out (the grid absorbs the incident radiation). When the grid wires are horizontal, the bulb is lit. Using the more sensitive audio detector, one can show that the radiation transmitted by the filter is polarized in a new direction which depends on the orientation of the grid. Two such filter grids can be used together to demonstrate the popular "3-polarizer puzzler," usually performed with light. In this case, we don't need three filters because the microwave source is already polarized. Proceed as follows: start with one filter grid horizontal (no microwaves are detected) and add a second filter grid between the first one and the source. If the intermediate grid is at 45˚, microwaves once more make it to the detector. When they are oriented 90˚ w.r.t. each other ("crossed" polarizers), no radiation passes through, regardless of the pair's orientation.
(3) Atmospheric absorption (due to water vapor) of radio signals at microwave frequencies begins around 2 GHz and increases dramatically with frequency8. Although our frequency is only 3 GHz, microwave absorption by water is easy to show—think "microwave oven." Simply putting your hand in front of the dipole antenna attenuates the signal. An aquarium full of water kills the signal. Radar exhibits severe interference problems when signals backscatter from rain cells. This kind of scattering interference can be simulated by a person moving around near the detector.
(4) Speaking of interference, a room-size interferometer can easily be set up with two metallic reflectors. Position the detector off to the side of the microwave source horn (out of the beam). Place a thin sheet of aluminum in the beam and angle it to reflect microwaves onto the detector. Put a second sheet in the beam (also aimed to reflect onto the detector) and move it back-and-forth. The detector will scream out interference maxima and minima as the second reflecting sheet is moved. This is our microwave analog to the Hear The Wall Bend demonstration, which uses laser light.
(5) The superposition of two waves having the same frequency and amplitude, but traveling in opposite directions, results in a standing wave. That situation is secured by using just one metallic reflector—interference between incident and reflected waves results in a standing wave, evidenced by exploring the space in front of the reflecting surface with the detector. Intense maxima show up every 5 cm.
(6) Paraffin is an excellent refracting medium of microwaves. A large equilateral triangular prism shows the effect. Position the detector out of the direct beam. Rotate the prism so that it refracts the beam onto the detector.
(7) Young's double-slit experiment on a grand scale: 45 cm between the two 10-cm-wide slits. Due to weak signal strength, the dipole/audio detector should be used for this demonstration. The intensity maxima are loud and clear, and occur roughly every 15˚. Note that the dsinθ = nλ condition for constructive interference does not apply to this geometry—the two "rays" from the slits to the detector are clearly not parallel (the approximation one invokes in deriving this formula). However, one can use two wooden dowels (with λ/2 markings on them) to simulate those rays converging on the detector and show the change in signal strength every time the path-length difference between the two rays changes by λ/2.
(8) One can create an anti-reflective surface by arranging to have two reflections that interfere destructively, not unlike an anti-reflective coating on optical lenses. We start with an aluminum sheet which readily reflects microwaves. Positioned a distance λ/4 in front of the metal sheet is a sheet of "space cloth" (a.k.a. Z0 cloth).9 It is partially reflective and lets the remainder pass through. The microwaves that pass through the cloth reflect off the metal sheet and pass through the cloth again. Having traveled an extra λ/2 in distance, these waves interfere destructively with waves that are reflected by the cloth. The result is no reflection.
To perform the demonstration, have the detector off to the side, out of the microwave beam. Show how a sheet of aluminum (positioned in the beam) reflects microwaves onto the detector. Next show how the sheet of space cloth reflects microwaves onto the detector. Show how a sheet of Styrofoam does not reflect and therefore only acts as a passive support for the space cloth. Finally, make a "sandwich" of the three and show how the combination does not reflect. If you add an additional 1"-thick sheet of Styrofoam to the sandwich, then the combination will reflect because the 2" separation between the space cloth and aluminum is close to ½λ, making the additional path length equal to λ.
(9) Microwaves can be "focused" with a zone plate to illustrate some of the principles of visible light Fresnel zone plates. An understanding of Fresnel zone plates helps understand holographic plates, making this demonstration relevant to that subject.
The photo shows an aluminum sheet with rings cut out of it. These rings can be removed. If a plane wave is incident on this sheet, annular wave fronts emanate from the opposite side. One can ask how the intensity varies along the "optical axis." To answer that question, consider a point on the axis. The distance from this point to each annular opening increases with increasing ring radius. If the ring radii are cunningly chosen so that these distances increase by integral numbers of wavelengths, then one will have constructiive interference at that point. We may speak of the illuminated point as its focus, and the distance of the point to the sheet as the focal length. As one moves further away from the sheet along the axis, one encounters other points for which the condition of constructive interference is satisfied. The intensity is less at these points and thus the first one is called the primary focus, and is given by the relation f = R2/mλ, where R is the radius of the m-th ring (or zone) and m is, of course, an integer.
The ring radii (measured to the outer edge) are 11, 15.3, 18.9, and 21.75 cm, giving a primary focal length of 11.9 cm for plane waves of λ=10 cm. As is the case with lenses, if the source is closer, the image is further from the plate.
(10) Microwave tunneling can be demonstrated with two paraffin right-angle prisms as shown in the photographs. When the prisms are well separated, microwaves undergo total internal reflection in the first prism and exit out the side, as is evidenced by the glowing light bulb. When the prisms are close together (less than 1/2 wavelength or so), the microwaves are able to tunnel through to the second prism and exit out the front. This is evidenced by the glowing of the second light bulb while the first one is no longer lit.
(11) A parallel plate wave guide is constructed with two 24" x 48" (61cm x 122 cm) sheets of aluminum. The general layout is as shown in the photograph. Vertically polarized microwaves from the transmitting horn antenna (at the right) are intercepted by a second horn antenna which, in turn, directs them into the space between the parallel plates:
To the left in the photo is a 1/2-wave dipole antenna light bulb, which serves as the detector:
The spacing between the two plates can be varied from 0 to 23 cm. If the spacing between the two plates is less than 6 cm, the 10-cm wavelength microwaves will not propagate between the plates and the light bulb will not light. The plate separation can be increased (this is easily done as one of the plates rides on two guide rails) to show that there are larger separations that meet the boundary conditions for transmission. A video camera trained on the light bulb enables a large class to see the light bulb glow. A disadvantage of the light bulb detector is that it is not sensitive enough to show maximum and minimum transmission for the larger plate separations. The audio detector (described above) is ideal for that: it is completely silent for plate separations less that 6 cm; slowly sliding the plates apart, the audio detector will squeal loudly every time the plate separation meets the boundary conditions for transmission. Obviously one doesn't need a video camera when using the audio detector.
As to understanding what's going on, Feynman presents a nice (as usual) qualitative explanation which he calls "another way of looking at the guided waves" ( R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics, Volume II (Addison-Wesley, Reading MA, 1964) pp 24-10 — 24-12). The electromagnetic field betweeen two reflecting plates is obtained by the repeated use of the method of images wherein the reflecting plates are replaced by an infinite sequence of image sources and the field between the plates is a superposition of the fields from these image sources. This is analogous to the problem in optics in which one considers a plane wave impinging on a transmission grating. The condition for constructive interference turns out to be the same and from this one can deduce the conditions for wave propagation through the parallel plates. A full mathematical analysis has been published by Smith (Glen S. Smith, "A different introduction to the guiding of electromagnetic waves," Am J Phys 79(3), 282-290 (2011).
Setting it up:
All the pieces of apparatus are on their own dedicated carts. You will need a lot of floor space.
The demonstrations suggested above are rich in content. Clearly, they cannot all be done in one lecture as they do take some time, but the time is well worth spent.
The most common criteria for human exposure to electromagnetic fields are those developed by the Institute of Electrical & Electronics Engineers (IEEE) and the National Council of Radiation Protection & Measurements (NCRP). The limit is expressed in terms of equivalent plane-wave power density. The International Commission on Non-Ionizing Radiation Protection (ICNIRP) limit is set at 50 W/m2 for 2.4 GHz radiation. Exposure from the horn antenna is well below this level at distances greater than 1 meter.
1. Kuhne Electronic GmbH model KU LO 3000 PLL-207
2. Kuhne Electronic GmbH model KU PA 3050 A
3. Flann Microwave UK model 10240-20
4. Chicago miniature lamp #338: 2.6 VDC, 60 mA, 162 mW, 0.5 lm
5. Telenic RF Detector XD-23E
6. The choice of meter (10's of μA, or 100's of μA, full scale) will depend on the distance of the dipole antenna from the mircrowave source as well as the particular phenomenon one wishes to demonstrate.
7. The largest dipole current (when the antenna is close to the microwave source) is about 1 mA and the circuit has been designed to produce a 2 kHz tone at that level. The frequency decreases linearly with current down to about 100 nA. The linear response is augmented by our perception of sound intensity. For exmple, a 60 dB tone at 100 Hz is perceived to be 20 dB lounder (roughly 4 times as loud) at 2 kHz. For this reason, 2 kHz was chosen to be the upper frequency — the perception of the intensity level is enhanced at this frequency. At the lower end of the range, the audio signal is no longer a "tone" once you get down into the 1-10 μA range. Nevertheless, the individual 2-20 Hz oscillations are still perceived as a "signal strength." Again, the dynamic range is enhanced by our hearing abilities. Since we are sensitive to percentage changes in frequency, changes in low level signals are readily perceived — we can easily detect changes of a few Hertz when the absolute frequency is in the 10s of Hertz. Changes in microwave signal strength can be detected at the back of hall B with the source down near the blackboard (a distance of about 25 m). One can even detect the normal (albeit small) microwave leakage around the door of a microwave oven.
8. Microwave communications above about 10 GHz suffer an increasingly severe attenuation because of water vapor and oxygen in the atmosphere. Rain and other weather conditions worsen the attenuation.
9. The space cloth is stretched over, and supported by, a 1"-thick sheet of Styrofoam. 1" thickness is chosen because it's very close to ¼λ. Space cloth can be made by painting Aquadag (a colloidal suspension of fine carbon powder) on canvas. Repeat applications until the impedance is 377 Ω / square (the impedance of free space). Commercially available Uskon cloth and Polyiron microwave absorber sheets could also be used for this application.