Waveguide - AbsoluteAstronomy.com

A waveguide is a structure which guides waves, such as electromagnetic waves or sound

Sound

Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

waves. There are different types of waveguides for each type of wave. The original and most common meaning is a hollow conductive metal pipe used to carry high frequency radio wave

Radio Wave

Radio Wave may refer to:*Radio frequency*Radio Wave 96.5, a radio station in Blackpool, UK...

s, particularly microwave

Microwave

Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

s.

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

Optical fiber

An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...

guiding light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

(high frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

) will not guide microwaves (which have a much lower frequency). As a rule of thumb

Rule of thumb

A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...

, the width of a waveguide needs to be of the same order of magnitude

Order of magnitude

An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

as the wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

of the guided wave.

There are structures in nature which act as waveguides: for example, the SOFAR channel

Sofar channel

The SOFAR channel , or deep sound channel , is a horizontal layer of water in the ocean at which depth the speed of sound is minimal. The SOFAR channel acts as a waveguide for sound, and low frequency sound waves within the channel may travel thousands of miles before dissipating...

layer in the ocean can guide whale song

Whale song

Whale sounds are the sounds made by whales and which are used for different kinds of communication.The word "song" is used to describe the pattern of regular and predictable sounds made by some species of whales, notably the Humpback Whale...

enormous distances.

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

Reflection (physics)

Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

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 hollow metal tube with a rectangular or circular cross section.

History

The first structure for guiding waves was proposed by J. J. Thomson

J. J. Thomson

Sir Joseph John "J. J." Thomson, OM, FRS was a British physicist and Nobel laureate. He is credited for the discovery of the electron and of isotopes, and the invention of the mass spectrometer...

in 1893, and was first experimentally tested by Oliver Lodge in 1894. The first mathematical analysis of electromagnetic waves in a metal cylinder was performed by Lord Rayleigh

John Strutt, 3rd Baron Rayleigh

John William Strutt, 3rd Baron Rayleigh, OM was an English physicist who, with William Ramsay, discovered the element argon, an achievement for which he earned the Nobel Prize for Physics in 1904...

in 1897.
For sound waves, Lord Rayleigh published a full mathematical analysis of propagation modes in his seminal work, “The Theory of Sound”.

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

Arnold Sommerfeld

Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...

and Debye

Peter Debye

Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

.
Optical fiber began to receive special attention in the 1960s due to its importance to the communications industry.

Uses

The uses of waveguides for transmitting signals were known even before the term was coined. The phenomenon of sound waves guided through a taut wire have been known for a long time, as well as sound through a hollow pipe such as a cave

Cave

A cave or cavern is a natural underground space large enough for a human to enter. The term applies to natural cavities some part of which is in total darkness. The word cave also includes smaller spaces like rock shelters, sea caves, and grottos.Speleology is the science of exploration and study...

or medical stethoscope

Stethoscope

The stethoscope is an acoustic medical device for auscultation, or listening to the internal sounds of an animal body. It is often used to listen to lung and heart sounds. It is also used to listen to intestines and blood flow in arteries and veins...

. Other uses of waveguides are in transmitting power between the components of a system such as radio, radar or optical devices. Waveguides are the fundamental principle of guided wave testing

Guided wave testing

Guided Wave testing is one of latest methods in the field ofnon-destructive evaluation. The methodemploys mechanical stress waves that propagate along an elongatedstructure while guided by its boundaries. This allows the...

(GWT), one of the many methods of non-destructive evaluation

Nondestructive testing

Nondestructive testing or Non-destructive testing is a wide group of analysis techniques used in science and industry to evaluate the properties of a material, component or system without causing damage....

.

Specific examples:

Optical fibers transmit light and signals for long distances and with a high signal rate.
In a microwave oven
Microwave oven
A microwave oven is a kitchen appliance that heats food by dielectric heating, using microwave radiation to heat polarized molecules within the food...

a waveguide transfers power from the magnetron where waves are formed, to the cooking chamber.
In a radar, a waveguide transfers Radio Frequency energy to and from the antenna, where the impedance
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

needs to be matched for efficient power transmission (see below).
A waveguide called stripline
Stripline
Stripline is a transverse electromagnetic transmission line medium, that was invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s.- Description :...

can be created on a printed circuit board
Printed circuit board
A printed circuit board, or PCB, is used to mechanically support and electrically connect electronic components using conductive pathways, tracks or signal traces etched from copper sheets laminated onto a non-conductive substrate. It is also referred to as printed wiring board or etched wiring...

, and is used to transmit microwave signals on the board. This type of waveguide is very cheap to manufacture and has small dimensions which fit inside printed circuit boards.
Waveguides are used in scientific instruments to measure optical, acoustic and elastic properties of materials and objects. The waveguide can be put in contact with the specimen (as in a Medical ultrasonography
Medical ultrasonography
Diagnostic sonography is an ultrasound-based diagnostic imaging technique used for visualizing subcutaneous body structures including tendons, muscles, joints, vessels and internal organs for possible pathology or lesions...

), in which case the waveguide ensures that the power of the testing wave is conserved, or the specimen may be put inside the waveguide (as in a dielectric constant measurement), so that smaller objects can be tested and the accuracy is better.

A sketch of the theoretical analysis

Electromagnetic wave propagation along the axis of the waveguide is described by the wave equation

Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...

, which is derived from Maxwell's equations

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

, and where the wavelength

Wavelength

depends upon the structure of the waveguide, and the material within it (air, plastic, vacuum, etc.), as well as on the frequency

Frequency

of the wave.

The spatial distribution of the time-varying electric field

Electric field

In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

s and magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s within the waveguide depends on boundary conditions imposed by the shape and materials of the waveguide. Let us assume that the waveguide is made of a metal that is such a good conductor that we can consider it to be a perfect conductor. Nearly all waveguides have copper interiors, but some of them are even plated with silver

Silver

Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

or gold

Gold

Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...

on the inside - excellent conductors, and also resistant to corrosion. Now, the boundary conditions are these:

1). Electromagnetic waves do not pass through conductors, but rather, they are reflected.

2). Any electric field that touches a conductor must be perpendicular to it.

3). Any magnetic field close to a conductor must be parallel to it.

These boundary conditions eliminate an infinite number of solutions to the wave equation, and the ones that remain are the possible solutions to the wave equation inside the waveguide. The rest of the analysis of the solutions of the electromagnetic waves inside a waveguide gets very mathematical.

All that remains that can be said without getting very mathematical is that commonly-used waveguides are only of a few categories. The most common kind of waveguide is one that has a rectangular cross-section, one that is usually not square. It is common for the long side of this cross-section to be twice as long as its short side. These are useful for carrying electromagnetic waves that have a horizontal or vertical polarization to them.

The second most commonly used kind of waveguide has a circular cross-section. These turn out to be quite useful when carrying electromagnetic waves with a rotating, circular polarization

Circular polarization

In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....

to them. Then, its electrical field traces out a helical pattern as a function of time.

The third kind of a waveguide - actually a seldom-used one - has an elliptical cross-section.

Propagation modes and cutoff frequencies

A propagation mode in a waveguide is one solution of the wave equations, or, in other words, the form of the wave. 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. The lowest frequency in which a certain mode can propagate is the cutoff frequency

Cutoff frequency

In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced rather than passing through.Typically in electronic systems such as filters and...

of that mode. The mode with the lowest cutoff frequency is the basic mode of the waveguide, and its cutoff frequency is the waveguide cutoff frequency.

Impedance matching

In circuit theory, the impedance

Electrical impedance

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

is a generalization of electrical resistivity in the case of alternating current

Alternating current

In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

, and is measured in ohm

Ohm

The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

s (

).
A waveguide in circuit theory is described by a transmission line

Transmission line

In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...

having a length and self impedance. In other words the impedance is the resistance of the circuit component (in this case a waveguide) to the propagation of the wave. This description of the waveguide was originally intended for alternating current, but is also suitable for electromagnetic and sound waves, once the wave and material properties (such as pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

, density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, dielectric constant

Dielectric constant

The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...

) are properly converted into electrical terms (current

Electric current

Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

and impedance for example).

Impedance matching is important when components of an electric circuit are connected (waveguide to antenna for example): The impedance ratio determines how much of the wave is transmitted forward and how much is reflected. In connecting a waveguide to an antenna a complete transmission is usually required, so that their impedances are matched.

The reflection coefficient can be calculated using:

, where

is the reflection coefficient (0 denotes full transmission, 1 full reflection, and 0.5 is a reflection of half the incoming voltage),

and

are the impedance of the first component (from which the wave enters) and the second component, respectively.

An impedance mismatch creates a reflected wave, which added to the incoming waves creates a standing wave. An impedance mismatch can be also quantified with the standing wave ratio

Standing wave ratio

In telecommunications, standing wave ratio is the ratio of the amplitude of a partial standing wave at an antinode to the amplitude at an adjacent node , in an electrical transmission line....

(SWR or VSWR for voltage), which is connected to the impedance ratio and reflection coefficient by:

, where

are the minimum and maximum values of the voltage absolute value

Absolute value

In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...

, and the VSWR is the voltage standing wave ratio, which value of 1 denotes full transmission, without reflection and thus no standing wave, while very large values mean high reflection and standing wave pattern.

Electromagnetic waveguides

Waveguides can be constructed to carry waves over a wide portion of the electromagnetic spectrum

Electromagnetic spectrum

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

, but are especially useful in the microwave

Microwave

and optical

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

frequency ranges. Depending on the frequency, they can be constructed from either conductive or dielectric

Dielectric

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

materials. Waveguides are used for transferring both power

Power (physics)

In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

and communication signals.

Optical waveguides

Waveguides used at optical frequencies are typically dielectric waveguides, structures in which a dielectric

Dielectric

material with high permittivity

Permittivity

In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

, and thus high index of refraction, is surrounded by a material with lower permittivity. The structure guides optical waves by total internal reflection

Total internal reflection

Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

. An example of an optical waveguide is optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...

.

Other types of optical waveguide are also used, including photonic-crystal fiber

Photonic-crystal fiber

Photonic-crystal fiber is a new class of optical fiber based on the properties of photonic crystals. Because of its ability to confine light in hollow cores or with confinement characteristics not possible in conventional optical fiber, PCF is now finding applications in fiber-optic...

, 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). One can also use small prism

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

s around the pipe which reflect light via total internal reflection http://www.physics.ubc.ca/ssp/research/lightpipe.htm—such confinement is necessarily imperfect, however, since total internal reflection can never truly guide light within a lower-index core (in the prism case, some light leaks out at the prism corners).

Acoustic waveguides

An acoustic waveguide is a physical structure for guiding sound waves. A duct for sound propagation also behaves like a transmission line

Transmission line

. The duct contains some medium, such as air, that supports sound propagation.

Sound synthesis

Sound synthesis uses digital delay line

Digital delay line

A digital delay line is a discrete element in digital filter theory, which allows a signal to be delayed by a number of samples. If the delay is an integer multiple of samples digital delay lines are often implemented as circular buffers...

s as computational elements to simulate wave propagation

Wave propagation

Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....

in tubes of wind instruments and the vibrating strings of string instruments.

External links

Francesco Errante, The behaviour of RF balanced transmission lines in a progressive wave regime
Waveguide basics Multiple pages giving detailed tutorial

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.