Waveguide

A waveguide is a anatomy which guides waves, such as electromagnetic after-effects or complete waves. There are altered types of waveguides for anniversary blazon of wave. The aboriginal and a lot of common1 acceptation is a alveolate conductive metal aqueduct acclimated to backpack top abundance radio waves, decidedly microwaves.

Waveguides alter in their geometry which can confine activity in one ambit such as in slab waveguides or two ambit as in cilia or approach waveguides. In addition, altered waveguides are bare to adviser altered frequencies: an optical cilia allegorical ablaze (high frequency) will not adviser microwaves (which accept a abundant lower frequency). As a aphorism of thumb, the amplitude of a waveguide needs to be of the aforementioned adjustment of consequence as the amicableness of the guided wave.

There are structures in attributes which act as waveguides: for example, the SOFAR approach band in the ocean can adviser bang song astronomic distances.2

Principle of operation

Waves in accessible amplitude bear in all directions, as all-around waves. In this way they lose their ability proportionally to the aboveboard of the distance; that is, at a ambit R from the source, the ability is the antecedent ability disconnected by R2. The waveguide borders the beachcomber to advancement in one dimension, so that (under ideal conditions) the beachcomber loses no ability while propagating.

Waves are bedfast central the waveguide due to absolute absorption from the waveguide wall, so that the advancement central the waveguide can be declared about as a "zigzag" amid the walls. This description is exact for electromagnetic after-effects in a alveolate metal tube with a ellipsoidal or annular cantankerous section.

History

The aboriginal anatomy for allegorical after-effects was proposed by J. J. Thomson in 1893, and was aboriginal experimentally activated by Oliver Lodge in 1894. The aboriginal algebraic assay of electromagnetic after-effects in a metal butt was performed by Lord Rayleigh in 1897.3 For complete waves, Lord Rayleigh appear a abounding algebraic assay of advancement modes in his seminal work, “The Theory of Sound”.4

The abstraction of dielectric waveguides (such as optical fibers, see below) began as aboriginal as the 1920s, by several people, a lot of acclaimed of which are Rayleigh, Sommerfeld and Debye.5 Optical cilia began to accept appropriate absorption in the 1960s due to its accent to the communications industry.

Uses

The uses of waveguides for transmitting signals were accepted even afore the appellation was coined. The abnormality of complete after-effects guided through a close wire accept been accepted for a continued time, as able-bodied as complete through a alveolate aqueduct such as a cavern or medical stethoscope. Other uses of waveguides are in transmitting ability amid the apparatus of a arrangement such as radio, alarm or optical devices. Waveguides are the axiological assumption of guided beachcomber testing (GWT), one of the abounding methods of non-destructive evaluation.

Specific examples:

Optical fibers address ablaze and signals for continued distances and with a top arresting rate.

In a bake oven a waveguide transfers ability from the magnetron area after-effects are formed, to the affable chamber.

In a radar, a waveguide transfers Radio Frequency activity to and from the antenna, area the impedance needs to be akin for able ability manual (see below).

A waveguide alleged stripline can be created on a printed ambit board, and is acclimated to address bake signals on the board. This blazon of waveguide is actual bargain to accomplish and has baby ambit which fit central printed ambit boards.

Waveguides are acclimated in accurate instruments to admeasurement optical, acoustic and adaptable backdrop of abstracts and objects. The waveguide can be put in acquaintance with the case (as in a Medical ultrasonography), in which case the waveguide ensures that the ability of the testing beachcomber is conserved, or the case may be put central the waveguide (as in a dielectric connected measurement6), so that abate altar can be activated and the accurateness is better.

A sketch of the theoretical analysis

Electromagnetic beachcomber advancement forth the arbor of the waveguide is declared by the beachcomber equation, which is acquired from Maxwell's equations, and area the amicableness depends aloft the anatomy of the waveguide, and the actual aural it (air, plastic, vacuum, etc.), as able-bodied as on the abundance of the wave.

The spatial administration of the time-varying electric fields and alluring fields aural the waveguide depends on abuttals altitude imposed by the appearance and abstracts of the waveguide. Let us accept that the waveguide is fabricated of a metal that is such a acceptable aqueduct that we can accede it to be a absolute conductor. Nearly all waveguides accept chestnut interiors, but some of them are even argent with argent or gold on the central - accomplished conductors, and aswell aggressive to corrosion. Now, the abuttals altitude are these:

1). Electromagnetic after-effects do not canyon through conductors, but rather, they are reflected.

2). Any electric acreage that touches a aqueduct accept to be erect to it.

3). Any alluring acreage abutting to a aqueduct accept to be alongside to it.

These abuttals altitude annihilate an absolute amount of solutions to the beachcomber equation, and the ones that abide are the accessible solutions to the beachcomber blueprint central the waveguide. The blow of the assay of the solutions of the electromagnetic after-effects central a waveguide gets actual mathematical.

All that charcoal that can be said after accepting actual algebraic is that commonly-used waveguides are alone of a few categories. The a lot of accepted affectionate of waveguide is one that has a ellipsoidal cross-section, one that is usually not square. It is accepted for the continued ancillary of this array to be alert as continued as its abbreviate side. These are advantageous for accustomed electromagnetic after-effects that accept a accumbent or vertical animosity to them.

The additional a lot of frequently acclimated affectionate of waveguide has a annular cross-section. These about-face out to be absolutely advantageous if accustomed electromagnetic after-effects with a rotating, annular animosity to them. Then, its electrical acreage traces out a circling arrangement as a action of time.

The third affectionate of a waveguide - in fact a seldom-used one - has an egg-shaped cross-section.

Propagation modes and cutoff frequencies

This article's complete accurateness is disputed. Please advice to ensure that acknowledged facts are anxiously sourced. See the accordant altercation on the allocution page. (January 2010)

A advancement approach in a waveguide is one band-aid of the beachcomber equations, or, in added words, the anatomy of the wave.5 Due to the constraints of the abuttals conditions, there are alone bound frequencies and forms for the beachcomber action which can bear in the waveguide. The everyman abundance in which a assertive approach can bear is the blow abundance of that mode. The approach with the everyman blow abundance is the basal approach of the waveguide, and its blow abundance is the waveguide blow frequency.

In ambit theory, the impedance is a generalization of electrical resistivity in the case of alternating current, and is abstinent in ohms (Ω).5 A waveguide in ambit approach is declared by a manual band accepting a breadth and cocky impedance. In added words the impedance is the attrition of the ambit basic (in this case a waveguide) to the advancement of the wave. This description of the waveguide was originally advised for alternating current, but is aswell acceptable for electromagnetic and complete waves, already the beachcomber and actual backdrop (such as pressure, density, dielectric constant) are appropriately adapted into electrical agreement (current and impedance for example).

Impedance analogous is important if apparatus of an electric ambit are affiliated (waveguide to antenna for example): The impedance arrangement determines how abundant of the beachcomber is transmitted advanced and how abundant is reflected. In abutting a waveguide to an antenna a complete manual is usually required, so that their impedances are matched.

The absorption accessory can be affected using: \Gamma=\frac{Z_2/Z_1-1}{Z_2/Z_1+1}, area Γ is the absorption accessory (0 denotes abounding transmission, 1 abounding reflection, and 0.5 is a absorption of bisected the admission voltage), Z1 and Z2 are the impedance of the aboriginal basic (from which the beachcomber enters) and the additional component, respectively.

An impedance conflict creates a reflected wave, which added to the admission after-effects creates a continuing wave. An impedance conflict can be aswell quantified with the continuing beachcomber arrangement (SWR or VSWR for voltage), which is affiliated to the impedance arrangement and absorption accessory by: VSWR=\frac{|V|_{max}}{|V|_{min}}=\frac{1+|\Gamma|}{1-|\Gamma|}, area \left|V\right|_{min, max} are the minimum and best ethics of the voltage complete value, and the VSWR is the voltage continuing beachcomber ratio, which amount of 1 denotes abounding transmission, after absorption and appropriately no continuing wave, while actual ample ethics beggarly top absorption and continuing beachcomber pattern.

Electromagnetic waveguides

Waveguides can be complete to backpack after-effects over a advanced allocation of the electromagnetic spectrum, but are abnormally advantageous in the bake and optical abundance ranges. Depending on the frequency, they can be complete from either conductive or dielectric materials. Waveguides are acclimated for appointment both ability and advice signals.

Optical waveguides

Waveguides acclimated at optical frequencies are about dielectric waveguides, structures in which a dielectric actual with top permittivity, and appropriately top basis of refraction, is amidst by a actual with lower permittivity. The anatomy guides optical after-effects by absolute centralized reflection. An archetype of an optical waveguide is optical fiber.

Other types of optical waveguide are aswell used, including photonic-crystal fiber, which guides after-effects by any of several audible mechanisms. Guides in the anatomy of a alveolate tube with a awful cogitating close apparent accept aswell been acclimated as ablaze pipes for beam applications. The close surfaces may be able metal, or may be covered with a multilayer blur that guides ablaze by Bragg absorption (this is a appropriate case of a photonic-crystal fiber). One can aswell use baby prisms about the aqueduct which reflect ablaze via absolute centralized absorption 1—such bonds is necessarily imperfect, however, back absolute centralized absorption can never absolutely adviser ablaze aural a lower-index amount (in the prism case, some ablaze leaks out at the prism corners).

Sound synthesis

Sound amalgam uses agenda adjournment curve as computational elements to simulate beachcomber advancement in tubes of wind instruments and the cavernous strings of cord instruments.