# Waveguide

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A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguide for each type of wave. The original and most common[1] meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves.

Waveguides differ in their geometry which can confine energy in one dimension such as in slab waveguides or two dimensions as in fiber or channel waveguides. In addition, different waveguides are needed to guide different frequencies: an optical fiber guiding light (high frequency) will not guide microwaves (which have a much lower frequency). As a rule of thumb, the width of a waveguide needs to be of the same order of magnitude as the wavelength of the guided wave.

There are structures in nature which act as waveguides: for example, a layer in the ocean can guide whale song to enormous distances.[2]

## Contents

### Principle of operation

Waves in open space propagate in all directions, as spherical waves. In this way they lose their power proportionally to the square of the distance; that is, at a distance R from the source, the power is the source power divided by R2. The waveguide confines the wave to propagation in one dimension, so that (under ideal conditions) the wave loses no power while propagating.

Waves are confined inside the waveguide due to total reflection from the waveguide wall, so that the propagation inside the waveguide can be described approximately as a "zigzag" between the walls. This description is exact for electromagnetic waves in a rectangular or circular hollow metal tube.

### History

The first structure for guiding waves was proposed by J. J. Thomson in 1893, and was first experimentally tested by O. J. Lodge in 1894. The first mathematical analysis of electromagnetic waves in a metal cylinder was performed by Lord Rayleigh in 1897[3]. For sound waves, Lord Rayleigh published a full mathematical analysis of propagation modes in his seminal work, “The Theory of Sound”[4].

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