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# Evanescent Waves

Definition: waves with rapidly decaying amplitude and no power transport

Opposite term: traveling waves

German: evaneszente Wellen

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In the area of optics, one often encounters the phenomenon of evanescent waves. In contrast to traveling waves, they exhibit a rapidly decaying field amplitude in a certain spatial direction. Also, they do not contribute to energy transport in that direction, although the Poynting vector (averaged over one oscillation cycle) may have non-zero components in other directions.

Evanescent waves also occur in the context of other types of waves, such as sound waves and quantum-mechanical waves (associated e.g. with tunneling phenomena), but this article focuses on evanescent waves in optics.

There are also cases where a light field can be decomposed into an evanescent and a propagating part.

## Example: Total Internal Reflection

A classical example (and a particularly simple case to analyze) is that of a plane wave which hits a plane interface between two different transparent media at an angle against the surface normal such that total internal reflection occurs. For example, a laser beam in some glass may hit an interface to air. The light field then slightly extends into the air, but with an amplitude which exponentially decays with increasing distance from the interface.

Mathematically, this can be understood by considering the involved wave vectors:

• The original incident traveling wave in the glass, for simplicity described as a plane wave, has a certain vector component along the surface, which must be matched by the same vector component on the air side.
• The magnitude of the wave vector is smaller on the side of the air compared with the glass side because of the lower refractive index of air.
• Total internal reflection occurs when the magnitude of the wave vector in air is smaller than the required wave vector component along the surface. In that case, the wave vector component perpendicular to the surface must become imaginary, which implies that its square is negative. Only that way, it is possible to meet the boundary condition despite the small wave vector in air.
• The imaginary wave vector component in air now leads to an exponentially decaying field on that side. At the same time, the oscillation phase does not depend on the distance from the interface.

In typical situations, the magnitude of the imaginary wave vector component is not that small, so that the penetration depth is only of the order of the wavelength. Therefore, evanescent optical fields are often not easy to observe. A larger penetration depth is achieved only when the incidence angle is close to the critical angle for total internal reflection. Larger penetration depths can also occur in cases with a small refractive index contrast.

For more details, see the article on total internal reflection.

## Other Examples and Applications

Evanescent optical waves also occur under various other circumstances; some examples:

### Optical Fibers and Fiber Couplers

An optical waveguide can confine an optical field to a certain region – for example, light propagating in an optical fiber can be confined to its fiber core. However, the light is not completely inside the fiber core, but somewhat penetrates into the fiber cladding – usually with a very rapid decay of amplitude with increasing distance from the core.

It is possible to utilize such evanescent waves e.g. in fiber couplers: these waves allow light to couple from one core to a closely neighbored core (obtained e.g. by fusing together to single-core fibers over some length), despite a tiny distance between the cores.

Similar coupling effects can also be exploited with other types of waveguides.

### Evanescent Wave Coupling to Resonators

There are monolithic optical ring resonators where light can be coupled in and out using an evanescent type of coupler. This can be a tiny prism which is approach to a point where total internal reflection would normally occur. When the coupling prism penetrates the evanescent field, some light can couple over; one has frustrated total internal reflection, which actually means that the reflection is no longer total.

A special example for such ring resonators are spheres in which whispering gallery modes are exploited.

The strength of evanescent coupling critically depends on the position of the coupling prism, which can be a problem for practical applications.

### Evanescent Wave Sensing

There are optical sensors for certain chemical species where one exploits the fact that a light field, which is essentially guided e.g. in some glass structure, is associated with an evanescent field outside the glass (e.g. in a liquid). Atoms or molecules in that region can then interact with the light field; for example, they can emit fluorescence after being excited by the light.

### Near-field Optical Microscopy

When light is scattered e.g. at tiny features of an observed object, the scattered light can have both traveling and evanescent components. In an ordinary optical microscope, only traveling light components can get through the objective to the observer or a film, while evanescent components cannot contribute to image generation. However, there are different kinds of near-field microscopes, which can access evanescent fields with some kind of probes penetrating those fields. Such microscopes often achieve superior image resolution beyond the classical optical limits.

## Questions and Comments from Users

2021-05-06

How can it be said that the evanescent wave has no energy transport? It must transport energy if it is capable of exciting fluorescence in an adjacent medium.

You are right – if you insert some absorbing medium, for example atoms or molecules which can exhibit fluorescence, into the originally evanescent field, it transmits some power and is thus no longer purely evanescent. However, in practice the field may still be very close to not transporting energy if there are only a few fluorescing atoms.

2022-02-13

If I am trying to optimize the power transmission through an optical fiber and want to minimize the loss of power to the evanescent fields, would it make sense to construct a fiber with cladding thickness equal to the depth penetration of the evanescent wave? Suppose I do this – what happens to the evanescent waves which are now within the cladding? Will they eventually return into the core or do they just stop at the outer cladding boundary?

The usual situation in an optical fiber is that there is an evanescent field around the core, extending somewhat into the fiber cladding, which however goes much further. The evanescent field does then not constitute any power loss. The Poynting vector is fully in the direction of the fiber axis, assuming that there are no absorption and scattering in the core and in the region of the evanescent field.

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