Waveguide

Without the physical constraint of a waveguide, waves would expand into three-dimensional space and their intensities would decrease according to the inverse square law.

The original and most common meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves.

The SOFAR channel layer in the ocean can guide the sound of whale song across enormous distances.

Waveguides are the fundamental principle of guided wave testing (GWT), one of the many methods of non-destructive evaluation.

[3] Specific examples: The first structure for guiding waves was proposed by J. J. Thomson in 1893, and was first experimentally tested by Oliver Lodge in 1894.

[8][9] The study of dielectric waveguides (such as optical fibers, see below) began as early as the 1920s, by several people, most famous of which are Rayleigh, Sommerfeld and Debye.

The development of radio communication initially occurred at the lower frequencies because these could be more easily propagated over large distances.

The long wavelengths made these frequencies unsuitable for use in hollow metal waveguides because of the impractically large diameter tubes required.

Consequently, research into hollow metal waveguides stalled and the work of Lord Rayleigh was forgotten for a time and had to be rediscovered by others.

Southworth at first took the theory from papers on waves in dielectric rods because the work of Lord Rayleigh was unknown to him.

This misled him somewhat; some of his experiments failed because he was not aware of the phenomenon of waveguide cutoff frequency already found in Lord Rayleigh's work.

This work led to the discovery that for the TE01 mode in circular waveguide losses go down with frequency and at one time this was a serious contender for the format for long-distance telecommunications.

[11]: 544–548 The importance of radar in World War II gave a great impetus to waveguide research, at least on the Allied side.

The magnetron, developed in 1940 by John Randall and Harry Boot at the University of Birmingham in the United Kingdom, provided a good power source and made microwave radar feasible.

His researchers included Julian Schwinger, Nathan Marcuvitz, Carol Gray Montgomery, and Robert H. Dicke.

So much so that when radar parts from a downed British plane were sent to Siemens & Halske for analysis, even though they were recognised as microwave components, their purpose could not be identified.

A shielded rectangular conductor can also be used and this has certain manufacturing advantages over coax and can be seen as the forerunner of the planar technologies (stripline and microstrip).

[10] Due to the constraints of the boundary conditions, there are only limited frequencies and forms for the wave function which can propagate in the waveguide.

[15]: 38 Propagation modes are computed by solving the Helmholtz equation alongside a set of boundary conditions depending on the geometrical shape and materials bounding the region.

For a lossless case, the propagation constant might be found to take on either real or imaginary values, depending on the chosen solution of the eigenvalue equation and on the angular frequency

is purely real, the mode is said to be "below cutoff", since the amplitude of the field phasors tends to exponentially decrease with propagation; an imaginary

[17] In circuit theory, the impedance is a generalization of electrical resistance in the case of alternating current, and is measured in ohms (

[18]: 2–3, 6–12 [19]: 14 [20] In other words, the impedance indicates the ratio of voltage to current of the circuit component (in this case a waveguide) during propagation of the wave.

In connecting a waveguide to an antenna a complete transmission is usually required, so an effort is made to match their impedances.

[20] Waveguides can be constructed to carry waves over a wide portion of the electromagnetic spectrum, but are especially useful in the microwave and optical frequency ranges.

[24] Other types of optical waveguide are also used, including photonic-crystal fiber, which guides waves by any of several distinct mechanisms.

Guides in the form of a hollow tube with a highly reflective inner surface have also been used as light pipes for illumination applications.

The inner surfaces may be polished metal, or may be covered with a multilayer film that guides light by Bragg reflection (this is a special case of a photonic-crystal fiber).

The term acoustic waveguide is also used to describe elastic waves guided in micro-scale devices, like those employed in piezoelectric delay lines and in stimulated Brillouin scattering.

An interesting result by Jeffrey Goldstone and Robert Jaffe is that any tube of constant width with a twist, admits a bound state.