Electromagnetic Waveguides

Type of physical science: Waveguides, Electromagnetic, Microwaves, Electromagnetism, Electromagnetic waves, Classical physics

Field of study: Electromagnetism

An electromagnetic waveguide is a structure designed to guide the travel of electromagnetic waves (radio waves, microwaves, or light waves) along a prescribed path, usually with little loss of energy. Waveguides are used in microwave ovens, radar instruments, and microwave and optical communications systems.

Overview

To understand the structure and function of electromagnetic waveguides, it is necessary to understand certain properties of electromagnetic waves. An explanation of these properties will be followed by some examples of common waveguide structures and how they guide electromagnetic waves.

Light waves, microwaves, and radio waves are all examples of electromagnetic waves. These waves consist of electric and magnetic fields that travel at or near the speed of light. These fields are not "static" fields such as the magnetic field around a permanent magnet. Such a static field has a direction (for example, from the north pole to the south pole of the magnet) and a magnitude (strength) that does not change with time, although the field's direction and magnitude vary from point to point in space.

By contrast, an electromagnetic wave consists of a moving field pattern that travels through space, much as a periodic pattern of water waves travels along the surface of a pond. Since the fields move, an observer at a fixed location sees them change with time. The fields of an electromagnetic wave go through cycles of change in both magnitude and direction, from strongest in one direction (the "peak" of the wave), decreasing through zero, to strongest in the opposite direction, going through zero again, and increasing back to the starting value at the next peak. The number of times per second that the fields go through this complete cycle of change is called the "frequency" of the wave, expressed in a unit called "hertz." For example, a radio wave with fields that change at a rate of one million cycles per second is said to have a frequency of one million hertz (usually expressed as "one megahertz").

The frequency of an electromagnetic wave determines another important property of the wave called the "wavelength." The wavelength is the distance between two adjacent peaks of the wave. In empty space, a radio wave with a frequency of one megahertz has a wavelength of about 300 meters. The entire pattern of fields moves through space at the velocity of light, about 300,000 kilometers per second. As the frequency increases, more waves must fit into the distance that the fields travel in one second, so the wavelength becomes smaller. Microwaves are radio waves between 1 and 30 thirty centimeters long, and visible light waves are less than a millionth of a meter long.

The wavelength property of electromagnetic waves is important because waveguides can carry only waves that are shorter than a certain wavelength. The longest wavelength a waveguide can carry is called the "cutoff wavelength," because transmission of waves longer than that wavelength cannot occur (the transmission is "cut off"). One of the most common types of waveguide used for microwaves consists of a hollow rectangular pipe. The rectangular cross section of the waveguide has a width equal to about twice its height. The pipe is made of a metal such as copper that conducts electricity well. The high conductivity of the metal at the inside surface of the pipe imposes what is called a "boundary condition" on the electromagnetic fields inside. Specifically, the only electric field that can exist at the walls must be perpendicular to the walls. If one imagines the electric field to be expressed in terms of small arrows pointing in the direction of the field, the arrows can point head-on into the walls, or out of the walls, but cannot lie alongside the walls. This boundary condition determines the longest wavelength that can be carried efficiently by the waveguide.

For this particular kind of waveguide, the longest wavelength it can transmit is established by the width of the long dimension of the rectangular cross section. Unless the wavelength is shorter than twice the width of the waveguide, the waveguide will not transmit the wave. The exact explanation for this involves the fundamental equations of electromagnetism, called Maxwell's equations after their discoverer, James Clerk Maxwell (1831-1879). These are quite complicated, but a simple analogy can express the difficulty involved in transmitting waves with a wavelength that exceeds the waveguide's cutoff wavelength. In an electromagnetic wave traveling in free space, the smallest distance between two adjacent points where the electric field is zero is one-half of the wavelength, since there are two places where the field is zero for every full cycle of the wave. Such a wave can exactly fit inside a waveguide with a cross-sectional width of one half-wavelength, since its electric field satisfies the boundary conditions on all four walls. If the long dimension of the waveguide cross section is horizontal (left to right), the electric field direction must be vertical (up and down). Since the electric field goes to zero every half-wavelength, the boundary conditions at the left and right side of the waveguide wall will be satisfied. Since the electric field arrows run perpendicularly into the top and bottom walls of the waveguide, those boundary conditions are also satisfied. If the wavelength were any longer (the frequency lower), the electric field would not go to zero at the left and right walls of the waveguide, and the wave would not fit.

In reality, waves longer than the cutoff wavelength do travel a short distance into the guide, but the intensity of the electric and magnetic fields falls off practically to zero in a distance of only a few wavelengths. In other words, the "loss" is very high for wavelengths longer than the cutoff wavelength. Loss refers to the weakening of a wave's intensity as it travels down a waveguide. For wavelengths shorter than the cutoff wavelength, the wave travels down the waveguide with very little loss. If the waveguide were made from a perfectly conducting material, the wave could travel an infinite distance without losing any intensity. Even the best available conductors cause some loss, however, and so no real waveguide can transmit a wave without any loss at all.

This property of low-loss transmission is the most important feature of electromagnetic waveguides from the standpoint of practical applications. Electromagnetic waves can be transmitted through long distances of open space without waveguides, but the loss involved is often greater than if a properly designed waveguide were used. The reason is that in transmission through unbounded space, all electromagnetic waves spread out in a way that is determined by the fundamental properties of waves. This spreading distributes the energy of the wave over a wider and wider area as the wave travels farther from its source. For this reason, the loss encountered in transmitting any electromagnetic wave through empty space increases at least as fast as the square of the distance involved. If the wave is transmitted through a waveguide, however, its energy is confined to the constant cross section of the waveguide and undergoes no spreading. An analogy can be made to water going through a flexible garden hose to a spray nozzle at the end. If the hose does not leak, all the water that goes in one end of the hose comes out the other end. If the water is then sprayed into the air, however, less water is available as one moves farther from the spray nozzle.

Returning to the example of the rectangular waveguide, if the wavelength of the transmitted wave becomes shorter than the cutoff wavelength, more than one half-wave can fit between the waveguide walls. At shorter wavelengths, there is more than one way that the wave can travel down the guide. Each way (called a "mode") has characteristic patterns of electric and magnetic fields that appear across the guide, but every mode satisfies the boundary conditions imposed by the walls. Different modes travel at different velocities down the guide. In most applications, multiple modes represent wasted energy that cannot be recovered, so it is customary to operate microwave waveguides in a frequency range where only one mode can be transmitted. This is called "single-mode" operation.

An unusual feature of waves inside a hollow electromagnetic waveguide is the phenomenon of "phase velocity." Because of the way the fields interact inside the waveguide, the field pattern of some modes creates the appearance that the wave travels faster than the speed of light. For example, a wave with a free-space wavelength slightly shorter than the cutoff wavelength will create field patterns inside a waveguide that have a very long "wavelength." The only way these field patterns could occur in free space would be if the wave traveled faster than the speed of light. However, this effect does not violate the fundamental physical law that no signal can travel faster than the speed of light. If one tries to send a signal by changing the intensity or frequency of the wave, the signal in the waveguide travels at a speed called the "group velocity," which in all cases is slower than the speed of light.

Hollow conducting tubes are not the only form of electromagnetic waveguide. Waveguides can also be made from electrical insulators (such as plastic or glass) in which the loss at the frequency of the transmitted wave is sufficiently low. Glass waveguides of this type designed to transmit infrared or visible light are called "fiber-optic waveguides" or, simply, "optical fibers." These are made by covering a small central core of glass with a different kind of glass in which light travels slightly faster than in the core. This sets up a boundary condition at the edges of the core that is satisfied by certain modes of light waves that travel down the fiber. The lowest loss and highest quality of transmission is provided by a single-mode fiber, the core diameter of which is on the order of a single wavelength of light and is small enough to transmit only one mode.

Applications

Probably the most familiar application of microwave waveguides is found in microwave ovens. A microwave oven works by subjecting food or beverages to strong microwave fields. The fields (primarily the electric field) agitate the water molecules in the food, and the resulting vibration becomes heat within the food. Unlike light waves, which penetrate less than a millimeter into most opaque objects, microwaves penetrate a distance of several centimeters into most items of food, so that heat is created quickly throughout the object's volume.

Heating food in a short time takes at least several hundred watts of microwave power. This power must be carried from the oven's microwave generator (usually a vacuum tube called a magnetron) to the chamber containing the food. A common method of transmitting longer radio waves is by a coaxial cable, which consists of an inner conducting wire surrounded by an insulating layer. The insulating layer is covered with a conducting outer layer. At shorter wavelengths, most of the energy in the wave passes through the insulating layer. If the wave is too powerful, its electric field becomes too high and sparks through the insulating layer, destroying it.

A coaxial cable rugged enough to carry the high-power microwave energy from a microwave oven's magnetron to the food chamber might have to be more than a centimeter thick. Its loss would also be fairly high, meaning that a substantial amount of the energy intended to heat the food would instead be wasted in heating the cable. This is why most microwave ovens use a short section of waveguide to transmit microwave energy from the generator to the food. A hollow metal pipe a few centimeters across is less expensive to build and install than a coaxial cable, and the loss is much lower.

In general, electromagnetic waveguides are used whenever microwaves must be transmitted with very little loss. Radar systems use microwaves to locate remote objects by bouncing a beam of microwaves off the target. The farthest distance over which a radar can operate is determined by the strongest microwave beam it can transmit and the weakest beam it can receive. For this reason, radar systems usually contain powerful microwave transmitters and sensitive microwave receivers. In transmission, the wave must travel from the transmitter to the antenna, which sends it toward the target. The weak returning wave must travel from the antenna to the receiver. The use of a waveguide between the transmitter/receiver unit and the antenna minimizes the loss of transmitted and received energy and maximizes the radar's range.

One specialized use of waveguides is in radioastronomy. Stars and other astronomical objects emit microwaves, but these waves are very weak when they arrive on the earth's surface. Radioastronomers construct large antennae to gather as much of the weak microwave energy as possible. Waveguides are often used to carry the weak signals to sensitive receivers with low loss.

Electromagnetic waveguides are also used in communications systems in two major ways. One application is in the field of microwave communications. Since microwaves travel through the air or space with relative ease, they are used in both satellite communications systems and point-to-point ground-based systems. In these systems, free space carries the microwave signals for most of the distance, but as in radar systems, low-loss waveguides often connect the antennae to transmission and reception equipment.

The second major application of waveguides in communications is fiber optics. As mentioned above, an optical fiber is a type of electromagnetic waveguide. For use in communications, optical fibers have two great advantages over microwave waveguides. One advantage is that optical fibers can transmit infrared light waves with much lower loss than is shown by the same length of waveguide in transmitting a microwave. For example, if a light wave travels over a 10-kilometer length of communications-quality optical fiber, more than half of the energy that goes into one end emerges at the other end. If the same experiment were tried with a 10-kilometer length of microwave waveguide of the type used in microwave ovens, the fraction of incoming power that would reach the far end would be only 1/10¹⁵ (10¹⁵ equals 1 followed by 15 zeros). This is one reason why optical fibers are used for long-distance point-to-point communications instead of microwave waveguides or coaxial cables, both of which have much higher loss.

The other advantage has to do with how much information each medium can carry per second. The rate of information transmission is called "bandwidth." It is related to the highest frequency of electromagnetic wave that the system can transmit. Since the light waves carried by optical fibers are about ten thousand times shorter than microwaves, their frequency is about ten thousand times higher. Consequently, a light wave can be used to transmit thousands of times as many voice or data channels as a microwave can. This is another reason that fiber-optic waveguides have superseded microwave communications systems for many fixed-site applications.

Context

Following Maxwell's theoretical description of the fundamental laws underlying all electromagnetic radiation in 1864, Heinrich Hertz (1857-1894) demonstrated the existence of radio waves in the laboratory. One of Hertz's experiments showed how these waves traveled along a system of wires that was similar to a coaxial cable. A theoretical study in 1897 by Lord Rayleigh (John William Strutt, 1842-1919) pointed out the possibility that electromagnetic waves could travel inside a completely empty conducting cylinder, or waveguide.

Experimental work on waveguides was hampered before about 1925 by the great difficulty of generating the very short waves that could be transmitted by waveguides of convenient size. Eventually, these problems were overcome, and workers at Bell Telephone Laboratories and other locations began to explore the possibility of using waveguides as a long-distance transmission medium in the 1930's.

The need for compact, efficient radar sets during World War II stimulated vigorous growth in the science and technology of microwave waveguides. During the war, waveguides were developed from laboratory curiosities into a mature technology that has changed relatively little since. In the decades following the war, considerable effort was expended to develop a special kind of waveguide in which loss theoretically decreased indefinitely as the frequency increased. Researchers hoped that this kind of waveguide would be useful for long-distance communications in telephone networks. These efforts were curtailed about 1975 when it became obvious that fiber-optic waveguides were superior to microwave waveguides for this application.

The history of waveguides for light waves began in 1854, when John Tyndall (1820-1893) showed that a beam of light could be conducted inside a cylindrical stream of water by means of total internal reflection. Each time the light wave encountered the boundary between water and air, it was completely reflected and remained within the water stream. Understanding of the theoretical reasons for this had to await the discovery of Maxwell's equations. Such "light guides" saw little practical use during the first half of the twentieth century. By 1960, glass optical fibers were developed for short-distance light transmission, but the loss in long fibers was too high for their use in communications systems. In 1970, workers at Corning Glass prepared glass fibers that transmitted light with a loss of less than 50 percent over a distance of 100 meters. Since then, fibers with losses hundreds of times less than that have been manufactured, and many thousands of kilometers of optical-fiber cables for long-distance communications have been laid both on land and under the oceans.

Principal terms

BANDWIDTH: In communications, a measure of the amount of information that can be transmitted per second

BOUNDARY CONDITION: In waveguides, a requirement imposed on electric or magnetic fields by the physical structure and material characteristics at boundaries in the waveguide

CUTOFF WAVELENGTH: The wavelength (in open space) of the longest wave that a waveguide is capable of transmitting without excessive loss; related to the size and shape of the waveguide's cross section

ELECTRIC FIELD: A region in which an electric charge experiences a force; the direction and magnitude of the force is proportional to the direction and magnitude of the field

FREQUENCY: The number of times per second a wave's field undergoes a complete cycle of alternation; measured in hertz

GROUP VELOCITY: The speed at which a signal carried by an electromagnetic wave can travel; always less than the speed of light

MODE: The way a particular electromagnetic wave travels along a waveguide; each mode is characterized by a unique set of field patterns

PHASE VELOCITY: The apparent speed at which an electromagnetic wave in free space would have to travel in order to reproduce certain field patterns observed in waveguides; can be greater than the speed of light

Bibliography

Halliday, David, and Robert Resnick. Physics. 3d ed. New York: Wiley, 1978. This introductory physics textbook contains a discussion of electromagnetic waveguides and compares their operation to acoustical waveguides such as speaking tubes and organ pipes. Simple equations for the characteristics of rectangular waveguides are given. Includes several illustrations of waveguide field patterns.

Marcuvitz, Nathan, ed. Waveguide Handbook. Vol. 10 in the Radiation Laboratory Series. New York: McGraw-Hill, 1951. After World War II, members of the MIT Radiation Laboratory compiled a series of books on radar and microwave techniques developed during the war. This volume summarized wartime work on waveguides. Although parts of it are technical, it contains many illustrations and photographs of waveguides, waveguide fields, and auxiliary equipment.

Pierce, John R. Electrons, Waves, and Messages. Garden City, N.Y.: Hanover House, 1956. The author, for many years associated with Bell Telephone Laboratories, gives a nontechnical treatment of Maxwell's equations, electromagnetic waves, and their use in communications technology. While there is little material on waveguides as such, the clear, accurate explanation of electromagnetic waves makes this book particularly valuable.

Pierce, John R., and A. M. Noll. Signals: The Science of Telecommunications. New York: Scientific American Library, 1990. A panoramic view of the history, science, and technology of electrical communications from the telegraph to fiber-optical communications systems. Numerous figures vividly portray electromagnetic waves in both guided and unguided media, and the accompanying text blends scientific explanations with history to make a uniquely clear and appealing book. Contains excellent illustrations and historical photographs.

Ramo, Simon, J. R. Whinnery, and T. Van Duzer. Fields and Waves in Communication Electronics. New York: John Wiley & Sons, 1965. Published when microwave waveguides appeared to have an increasingly prominent role in future communications systems, this college-level textbook is unusual for its detailed and not over-technical explanations of waveguide characteristics and uses. Includes numerous illlustrations of waveguide types and field patterns.

Southworth, George C. Principles and Applications of Waveguide Transmission. New York: D. Van Nostrand, 1950. The author was one of the first researchers to perform extensive experimental investigation of radio-frequency waveguides at Bell Telephone Laboratories in the 1930's. Although written at an advanced level, the book has many illustrations of how fields in waveguides can be visualized.