Optics 101

# An Introduction to Waveguides

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Waveguides are used in everything from the transmission of sound waves to optical communications. Every application that uses a waveguide requires a waveguide with a specifically designed structure, as this it what determines the waveguide’s function.

In this article, we look at what waveguides are, and how the various  types differ.

## What are Waveguides?

A waveguide is an instrument or material which can be used to guide waves along a defined path. By doing this, waveguides facilitate wave propogation from a source to another defined point without any loss in wave intensity. During this process the wave is confined along a set dimensional path, so propagation in all directions is inhibited.

Waveguides are crucial components in much modern technology. They are used in the fibreoptic cables which deliver broadband internet, they guide the microwaves within microwave ovens, and are also used in the complex scientific equipment found in the physical sciences and medicine.

Waveguides are not a single type of technology. In fact, there are many different wave-types, e.g. optical, sonic or electromagnetic, which can be guided, and each type requires a completely different waveguide structure.

Without a waveguide, waves propagate in all directions once transmitted. Additionally, waves without a waveguide are bound by the inverse square law. This means that as the waves move away from the source, the intensity becomes inversely proportional to the distance travelled. As waveguides result in no loss in intensity, and as electromagnetic waves propagate so rapidly, they are extremely popular tools for communication technologies.

The geometry of a waveguide is an essential factor for it to perform its designed function. Whilst there are many different geometries used in the construction of waveguides, there are three main types. The first of these is a slab geometry, which confines the energy of the wave to a single transverse dimension. The second and third, are the fiber and strip geometries which both both transmit waves in two transverse directions.

For many waveguides, the frequency of the transmitted wavelength is often the driving factor for the choice of geometry, because the frequency often determines the shape of the waveguide. One key thing for all waveguides, regardless of the geometry, is that the width of the waveguide needs to be of the same order of magnitude as the transmitted wave.

## Acoustic Waveguides

Acoustic waveguides are the simplest form of waveguide. They can range from microphones being implemented directly into an instrument, to the string that holds together two cans in primitive communication devices. Most acoustic waveguides are used to transmit audible sound waves, but others have been specifically designed for ultrasonic waves.

Most acoustic waveguides are made of simple materials such as metal or wood, and have a tube like shape. However, sound waves can move in various ways, so the waveguide needs to match the type of wave for each application. Ultrasonic waves, one the other hand, usually take the form of a shear wave, and whilst a simple construction is still possible with ultrasonic waves, the waveguide needs to be designed so that it can propagate a shear wave.

## Electromagnetic Waveguides

Electromagnetic waveguides are used for the transmission of microwaves and radio waves. Electromagnetic waves propagate transversely to the direction of the electromagnetic field and can only be directed when there are two conductors. Waveguides for electromagnetic waves can be as simple as a hollow tube, although many are more complicated with structures involving dielectric materials, conductive surfaces or specific geometries to guide the waves.

Whilst the electromagnetic wave propagates, only one of the fields (either the electric or magnetic field) will be transverse to the wave’s direction of travel. The other field “loops” longitudinally to the direction of the wave, whilst remaining perpendicular to the other field. Depending on which field stays transverse, the wave can propagate in either a transverse electric (TE) or transverse magnetic mode (TM).

## Optical Waveguides

Optical waveguides are perhaps one of the most complex waveguides out there and are used to guide electromagnetic waves in the optical spectrum. The most popular optical waveguides are in optical fibers – a common way of delivering high speed broadband.

Optical waveguides come in many forms. 2D dimensional waveguides such as strip and rectangular waveguides are common, as are dielectric waveguides in the form of slab and planar waveguides. Regardless of the geometry, optical waveguides guide light using a series of internal reflections. This can be through utilizing the surrounding materials refractive index, a sandwich material possessing a much larger dielectric index than the surrounding layers, or by using the photorefractive index of transparent materials.

Overall, the total internal reflection of a waveguide is a key factor to not only helping the light waves propagate efficiently, but for also containing the light waves within the given dimension of the waveguide geometry. Depending on the required geometry, optical waveguides can be made from a range of materials including silicon-based materials, 2D materials, polymers or semiconductors.

## Sources & Further Reading

• Caltech: http://www.feynmanlectures.caltech.edu/II_24.html
• All About Circuits: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-14/waveguides/
• Antenna Theory: http://www.antenna-theory.com/tutorial/waveguides/waveguide.php
• University of Colorado: http://spot.colorado.edu/~pricej/downloads/AcousticWaveguides.pdf
• University of Rochester: http://www2.optics.rochester.edu/users/gpa/opt468a.pdf
• Optiwave: https://optiwave.com/optibpm-manuals/bpm-introduction-to-optical-waveguides/
• RP Photonics: https://www.rp-photonics.com/waveguides.html
• “Acoustic waveguides: An attractive alternative for accurate and robust contact thermometry”- Wang Y., et al, Sensors and Actuators A: Physical, 2018, DOI: 10.1016/j.sna.2017.12.049

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Written by

### Liam Critchley

Liam Critchley is a writer and journalist who specializes in Chemistry and Nanotechnology, with a MChem in Chemistry and Nanotechnology and M.Sc. Research in Chemical Engineering.

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