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# Waveguide (electromagnetism)

Electromagnetism
Electricity · Magnetism
Electrical Network
Conduction
Resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
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In electromagnetics and communications engineering, the term waveguide may refer to any linear structure that guides electromagnetic waves. However, the original and most common meaning is a hollow metal pipe used for this purpose.

A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe. An optical fibre is a dielectric guide designed to work at optical frequencies. Transmission lines such as microstrip, coplanar waveguide, stripline or coax may also be considered to be waveguides.

The electromagnetic waves in (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected between opposite walls of the guide. For the particular case of rectangular waveguide, it is possible to base an exact analysis on this view. Propagation in dielectric waveguide, may be viewed in the same way, with the waves confined to the dielectric by total internal reflection at its surface. Some structures, such as nonradiative dielectric waveguide [NRD], and the Goubau line, use both metal walls and dielectric surfaces to confine the wave.

## History

The first waveguide was proposed by J. J. Thomson in 1893 and experimentally verified by O. J. Lodge in 1894; the mathematical analysis of the propagating modes within a hollow metal cylinder was first performed by Lord Rayleigh in 1897. (McLachan, 1947.)

## Principles of operation

Depending on the frequency, waveguides can be constructed from either conductive or dielectric materials. Generally, the lower the frequency to be passed the larger the waveguide is. For example the natural waveguide[1] the earth forms given by the dimensions between the conductive Ionosphere and the ground as well as the circumference at the median altitude of the earth is resonant at 7.83 Hz. This is also known as Schumann resonance. Waveguides can also be less than a millimeter in width. An example might be those that are used in extremely high frequency (EHF) Satellite Communications(SATCOM). There is a formula for calculating waveguide dimensions, more information may be found at this website[2].

## Analysis

Electromagnetic waveguides are analyzed by solving Maxwell's equations, or their reduced form, the electromagnetic wave equation, with boundary conditions determined by the properties of the materials and their interfaces. These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is therefore characterized by an eigenvalue, which corresponds to the axial propagation velocity of the wave in the guide.

Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide. The longitudinal mode of a waveguide is a particular standing wave pattern formed by waves confined in the cavity. The transverse modes are classified into different types:

• TE modes (Transverse Electric) have no electric field in the direction of propagation.
• TM modes (Transverse Magnetic) have no magnetic field in the direction of propagation.
• TEM modes (Transverse ElectroMagnetic) have no electric nor magnetic field in the direction of propagation.
• Hybrid modes are those which have both electric and magnetic field components in the direction of propagation.

In hollow metallic waveguides, the fundamental modes are derived from the transverse electric TE1,0 mode for rectangular and TE1,1 for circular waveguides. Also, in hollow waveguides, TEM waves are not possible, since Maxwell's Equations will give that the electric field must then have zero divergence and zero curl and be equal to zero at boundaries, resulting in a zero field. (or, equivalently, $\nabla^2 \boldsymbol{E}=0$ with boundary conditions guaranteeing only the trivial solution). However, TEM waves can propagate in coaxial cable.

## Hollow metallic waveguides

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 are often pressurized to inhibit arcing/multipaction, allowing higher power. Conversely, waveguides may be required to be evacuated as part of evacuated systems. (e.g. electron beam systems)

A slotted waveguide is generally used for radar and other similar applications. The waveguide structure has the capability of confining and supporting the energy of an electromagnetic wave to a specific relatively narrow and controllable path.

A closed waveguide is an electromagnetic waveguide (a) that is tubular, usually with a circular or rectangular cross section, (b) that has electrically conducting walls, (c) that may be hollow or filled with a dielectric material, (d) that can support a large number of discrete propagating modes, though only a few may be practical, (e) in which each discrete mode defines the propagation constant for that mode, (f) in which the field at any point is describable in terms of the supported modes, (g) in which there is no radiation field, and (h) in which discontinuities and bends cause mode conversion but not radiation.

Hollow metallic waveguides are far narrower than the wavelength of operation. They can take the form of single conductors with or without a dielectric coating, e.g. the Goubou line and helical waveguides.

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 TX and RX equipment strings. Arcing may occur if there is a hole, if transmitting at high power, usually 200 watts or more. Waveguide plumbing[3] is crucial for proper waveguide performance. Reflected power may occur and damage equipment as well. Another cause for a bad VSWR in a waveguide is moisture build up and can typically be prevented with silica gel which is a desiccant. Due to the negative effect of moisture buildup within the waveguide desiccant silica gel canisters may attached with screw-on nibs.

## Dielectric rods for microwaves

Dielectric rod waveguides, in linear arrays of short transverse conductors, and planar resistive conductors use the same principle as optical waveguides.

These function via a refractive index effect where the waveguide slows the EM wave velocity below the free space velocity, continuously bending the relatively wide EM wavefronts towards the narrow waveguide and keeping them entrained. Helical waveguides and linear arrays of short conductors are used as part of "end-fire" antennas such as the helical antenna and Yagi antenna. Planar resistive waveguides are used in Over-The-Horizon radar and the Ground Wave Emergency Network, where the resistive surface of the Earth or ocean serves to slow the waves below free space velocity; entraining them and forcing them to follow the curvature of the Earth. Several waveguides based on entrainment of EM waves also exist.

## Applications

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. Waveguides are used for transferring both power and communication signals, usually for short distances. Bell Labs in the 1970s built a waveguide line several miles long, to study possible use for intercity communication, but advances in optical fiber disrupted the plan.

## References

• J. J. Thomson, Recent Researches (1893).
• O. J. Lodge, Proc. Roy. Inst. 14, p. 321 (1894).
• Lord Rayleigh, Phil. Mag. 43, p. 125 (1897).
• N. W. McLachlan, Theory and Applications of Mathieu Functions, p. 8 (1947) (reprinted by Dover: New York, 1964).