[3] In 1897 Lord Rayleigh did a definitive analysis of waveguides; he solved the boundary value problem of electromagnetic waves propagating through both conducting tubes and dielectric rods of arbitrary shape.
In a June 1, 1894 lecture, "The work of Hertz", before the Royal Society, Oliver Lodge demonstrated the transmission of 3 inch radio waves from a spark gap through a short cylindrical copper duct.
[3][8] In his pioneering 1894-1900 research on microwaves, Jagadish Chandra Bose used short lengths of pipe to conduct the waves, so some sources credit him with inventing the waveguide.
[3][10] The waveguide was developed independently between 1932 and 1936 by George C. Southworth at Bell Telephone Laboratories[2] and Wilmer L. Barrow at the Massachusetts Institute of Technology, who worked without knowledge of one another.
He found that if he removed the Lecher line, the tank of water still showed resonance peaks, indicating it was acting as a dielectric waveguide.
[3] At MIT beginning in 1932 he worked on high frequency antennas to generate narrow beams of radio waves to locate aircraft in fog.
[10] The source he was using had a large wavelength of 40 cm, so for his first successful waveguide experiments he used a 16-foot section of air duct, 18 inches in diameter.
[3] Barrow and Southworth became aware of each other's work a few weeks before both were scheduled to present papers on waveguides to a combined meeting of the American Physical Society and the Institute of Radio Engineers in May 1936.
The development of centimeter radar during World War 2 and the first high power microwave tubes, the klystron (1938) and cavity magnetron (1940), resulted in the first widespread use of waveguide.
In the microwave region of the electromagnetic spectrum, a waveguide normally consists of a hollow metallic conductor.
Hollow waveguides must be one-half wavelength or more in diameter in order to support one or more transverse wave modes.
Waveguides may be filled with pressurized gas to inhibit arcing and prevent multipaction, allowing higher power transmission.
This structure has the capability of generating a radiation pattern to launch an electromagnetic wave in a specific relatively narrow and controllable direction.
Due to the skin effect at high frequencies, electric current along the walls penetrates typically only a few micrometers into the metal of the inner surface.
Voltage standing wave ratio (VSWR) measurements may be taken to ensure that a waveguide is contiguous and has no leaks or sharp bends.
If such bends or holes in the waveguide surface are present, this may diminish the performance of both transmitter and receiver equipment connected at either end.
Poor transmission through the waveguide may also occur as a result of moisture build up which corrodes and degrades conductivity of the inner surfaces, which is crucial for low loss propagation.
For this reason, waveguides are nominally fitted with microwave windows at the outer end that will not interfere with propagation but keep the elements out.
Moisture can also cause fungus build up or arcing in high power systems such as radio or radar transmitters.
Arcing may also occur if there is a hole, tear or bump in the conducting walls, if transmitting at high power (usually 200 watts or more).
Voltage standing waves occur when impedance mismatches in the waveguide cause energy to reflect back in the opposite direction of propagation.
In addition to limiting the effective transfer of energy, these reflections can cause higher voltages in the waveguide and damage equipment.
In practice, waveguides act as the equivalent of cables for super high frequency (SHF) systems.
The transverse modes are classified into different types: Waveguides with certain symmetries may be solved using the method of separation of variables.
Additionally, the propagating modes (i.e. TE and TM) inside the waveguide can be mathematically expressed as the superposition of two TEM waves.
[19][20] These confine the radio waves by total internal reflection from the step in refractive index due to the change in dielectric constant at the material surface.