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Radiation Pressure

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Definition: a mechanical pressure resulting from incident light or other radiation

German: Strahlungsdruck

Categories: physical foundations, quantum optics

How to cite the article; suggest additional literature

When light is reflected on a mirror, for example, the mirror is subject to some radiation pressure – i.e., to a small mechanical force which is related to the transfer of momentum from the radiation to the solid material. (Strictly speaking, the pressure is the force per unit area; it is related to the optical intensity rather than to the optical power.) Such forces have been first predicted by James Clerk Maxwell, the creator of the famous Maxwell equations.

As the simplest case, light with normal incidence on a perfectly reflecting mirror can be considered. The propagation direction of each photon of the light is reversed, which implies that twice the momentum of each incident photon is transferred to the mirror. The momentum of a photon is hν / c. For non-normal incidence (but still complete reflection) with an angle of incidence θ, the radiative force is reduced by the factor cos θ; in total, the resulting force can be calculated with the following equation:

radiative force from radiation pressure

where P is the incident optical power. For the radiation pressure (force per unit area), we have

radiation pressure

with the optical intensity I. This equation contains the factor cos2θ rather than cos θ, because the angled incidence also increases the illuminated area on the mirror.

Modified equations can be derived for other situations; for example, if radiation is fully absorbed on a solid body, the radiative force is F = P / c. The factors of 2 and also cos θ are missing here, since photons are not reflected with the opposite momentum, and the angle of incidence can obviously not be relevant – except for the radiation pressure due to the above-mentioned increase of the illuminated area, here resulting in a factor cos θ (without the square).

Radiation forces can also result from the emission of light, e.g. thermal emission or laser emission.

Weakness of Light Forces

Essentially due to the very high velocity of light c, the radiative force e.g. for normally reflecting a laser beam with 1000 W is rather small: only ≈ 3.3 μN. Therefore, it is not easy to measure the radiation pressure. However, modern technology, e.g. based on microelectromechanical systems (MEMS), provides some powerful means.

Note also that the actual radiation pressure can occur together with other mechanical effects, which may be stronger. For example, they can result from the interaction of a heated surface with surrounding air. That effect and not the radiative pressure has been found to be essential for the workings of a Crookes radiometer, containing lightweight mirrors fixed to a rotating part.

Applications of Radiation Pressure

Even though radiation pressure is usually very weak effect, there are some real or at least proposed applications:

Bibliography

[1]P. Williams et al., “Portable, high-accuracy, non-absorbing laser power measurement at kilowatt levels by means of radiation pressure”, Opt. Express 25 (4), 4382 (2017)

(Suggest additional literature!)

See also: light forces, laser cooling, photons, optical intensity
and other articles in the categories physical foundations, quantum optics

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