Radiation pressure (also known as light pressure) is mechanical pressure exerted upon a surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted (e.g. black-body radiation) by matter on any scale (from macroscopic objects to dust particles to gas molecules).Stellar Atmospheres, D. Mihalas (1978), Second edition, W. H. Freeman & Co.Eddington, A. S., & Eddington, A. S. (1988). The internal constitution of the stars. Cambridge University Press.Chandrasekhar, S. (2013). Radiative transfer. Courier Corporation. The associated force is called the radiation pressure force, or sometimes just the force of light.
The forces generated by radiation pressure are generally too small to be noticed under everyday circumstances; however, they are important in some physical processes and technologies. This particularly includes objects in outer space, where it is usually the main force acting on objects besides gravity, and where the net effect of a tiny force may have a large cumulative effect over long periods of time. For example, had the effects of the Sun's radiation pressure on the spacecraft of the Viking program been ignored, the spacecraft would have missed Mars orbit by about .Eugene Hecht, "Optics", 4th edition, p. 57. Radiation pressure from starlight is crucial in a number of astrophysical processes as well. The significance of radiation pressure increases rapidly at extremely high temperatures and can sometimes dwarf the usual gas pressure, for instance, in stellar interiors and thermonuclear weapons. Furthermore, large lasers operating in space have been suggested as a means of propelling sail craft in beam-powered propulsion.
Radiation pressure forces are the bedrock of laser technology and the branches of science that rely heavily on lasers and other optical technologies. That includes, but is not limited to, biomicroscopy (where light is used to irradiate and observe microbes, cells, and molecules), quantum optics, and optomechanics (where light is used to probe and control objects like atoms, qubits and macroscopic quantum objects). Direct applications of the radiation pressure force in these fields are, for example, laser cooling (the subject of the 1997 Nobel Prize in Physics), quantum control of macroscopic objects and atoms (2012 Nobel Prize in Physics), interferometry (2017 Nobel Prize in Physics) and optical tweezers (2018 Nobel Prize in Physics).
Radiation pressure can equally well be accounted for by considering the momentum of a classical electromagnetic field or in terms of the momenta of photons, particles of light. The interaction of electromagnetic waves or photons with matter may involve an exchange of momentum. Due to the law of conservation of momentum, any change in the total momentum of the waves or photons must involve an equal and opposite change in the momentum of the matter it interacted with (Newton's third law of motion), as is illustrated in the accompanying figure for the case of light being perfectly reflected by a surface. This transfer of momentum is the general explanation for what we term radiation pressure.
Discovery
Johannes Kepler put forward the concept of radiation pressure in 1619 to explain the observation that a tail of a comet always points away from the Sun.
The assertion that light, as electromagnetic radiation, has the property of momentum and thus exerts a pressure upon any surface that is exposed to it was published by James Clerk Maxwell in 1862, and proven experimentally by Russian physicist Pyotr Lebedev in 1900P. Lebedew, 1901, "Untersuchungen über die Druckkräfte des Lichtes", Annalen der Physik, 1901 Series 4 6, 433-458. and by Ernest Fox Nichols and Gordon Ferrie Hull in 1901.Nichols, E. F & Hull, G. F. (1903) The Pressure due to Radiation, The Astrophysical Journal, Vol.17 No.5, p.315-351 The pressure is very small, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal in a Nichols radiometer (this should not be confused with the Crookes radiometer, whose characteristic motion is not caused by radiation pressure but by air flow caused by temperature differentials.)
Theory
Radiation pressure can be viewed as a consequence of the conservation of momentum given the momentum attributed to electromagnetic radiation. That momentum can be equally well calculated on the basis of electromagnetic theory or from the combined momenta of a stream of photons, giving identical results as is shown below.
Physical origin
Electromagnetic radiation consists of an electric field E and a magnetic field B related by:
where n is the unit vector directed along the propagation direction of the radiation, and c is the speed of light in vacuum. The fields are transverse and satisfy the relation . These properties are notably reflected in the Panofsky–Phillips equations.
When this electromagnetic field reaches an electric charge q initially at restThe Feynman Lectures on Physics, Vol. II, Section 34.9: The momentum of light, the electric field exerts a force (F = qE) on it, setting it into motion. Once the charge is in motion, it is also subject to a magnetic force exerted by the magnetic component of the radiation. Since the velocity v acquired by the charge is directed along E, and the magnetic force is given by , it follows that this force is directed along n.
Moreover, one can note that the electric field exchanges energy with the charge, while the magnetic field imparts momentum to it.
The magnitude of the power P transferred by the electric field to the charge is given by:
which implies:
The magnitude of the force F transmitted by the magnetic field to the charge is, according to , given by:
Since the magnitude of B is related to that of E by B = E/c, one obtains:
which implies that at any time t, the instantaneous relation is:
Integrating this relation with respect to time yields:
where p and E are respectively the momentum and energy exchanged by the electromagnetic field with the charge q.
This result shows that, in addition to transporting energy, electromagnetic radiation also carries momentum, and that the momentum exchanged with matter is always equal to the energy exchanged divided by the factor c.
Furthermore, since electromagnetic radiation carries a momentum p, and since p = mv, it is also possible to assign it an equivalent mass m, such that m = p/v. As the propagation velocity of the radiation is equal to the speed of light c, the momentum of the radiation can be written as p = mc. Using the previous result, this gives:
That is,
This equivalence between energy and equivalent inertia of electromagnetic radiation was notably studied by Henri Poincaré in the early 1900s. The 1906 publication by Albert Einstein on the relation E = mc² is closely related to the above results (his 1905 work relies on the relativistic Doppler effect).
Radiation pressure from momentum of an electromagnetic wave
According to Maxwell's theory of electromagnetism, an electromagnetic wave carries momentum. Momentum will be transferred to any surface it strikes that absorbs or reflects the radiation.
Consider the momentum transferred to a perfectly absorbing (black) surface. The energy flux (irradiance) of a plane wave is calculated using the Poynting vector , which is the cross product of the electric field vector E and the magnetic field's auxiliary field vector (or magnetizing field) H. The magnitude, denoted by S, divided by the speed of light is the density of the linear momentum per unit area (pressure) of the electromagnetic field. So, dimensionally, the Poynting vector is , which is the speed of light, , times pressure, . That pressure is experienced as radiation pressure on the surface:
where is pressure (usually in pascals), is the incident irradiance (usually in W/m2) and is the speed of light in vacuum. Here, .
If the surface is planar at an angle α to the incident wave, the intensity across the surface will be geometrically reduced by the cosine of that angle and the component of the radiation force against the surface will also be reduced by the cosine of α, resulting in a pressure:
The momentum from the incident wave is in the same direction of that wave. But only the component of that momentum normal to the surface contributes to the pressure on the surface, as given above. The component of that force tangent to the surface is not called pressure.
Radiation pressure from reflection The above treatment for an incident wave accounts for the radiation pressure experienced by a black (totally absorbing) body. If the wave is specularly reflected, then the recoil due to the reflected wave will further contribute to the radiation pressure. In the case of a perfect reflector, this pressure will be identical to the pressure caused by the incident wave:
thus doubling the net radiation pressure on the surface:
For a partially reflective surface, the second term must be multiplied by the reflectivity (also known as the reflection coefficient of intensity), so that the increase is less than double. For a diffusely reflective surface, the details of the reflection and geometry must be taken into account, again resulting in an increased net radiation pressure of less than double.
If a reflection rate is then the net radiation pressure on the surface:
Radiation pressure by emission Just as a wave reflected from a body contributes to the net radiation pressure experienced, a body that emits radiation of its own (rather than reflected) obtains a radiation pressure again given by the irradiance of that emission in the direction normal to the surface Ie:
The emission can be from black-body radiation or any other radiative mechanism. Since all materials emit black-body radiation (unless they are totally reflective or at absolute zero), this source for radiation pressure is ubiquitous but usually tiny. However, because black-body radiation increases rapidly with temperature (as the fourth power of temperature, given by the Stefan–Boltzmann law), radiation pressure due to the temperature of a very hot object (or due to incoming black-body radiation from similarly hot surroundings) can become significant. This is important in stellar interiors.
Radiation pressure in terms of photons
Electromagnetic radiation can be viewed in terms of particles rather than waves; these particles are known as photons. Photons do not have a rest-mass; however, photons are never at rest (they move at the speed of light) and acquire a momentum nonetheless which is given by:
where is momentum, is the Planck constant, is wavelength, and is speed of light in vacuum. And is the energy of a single photon given by:
The radiation pressure again can be seen as the transfer of each photon's momentum to the opaque surface, plus the momentum due to a (possible) recoil photon for a (partially) reflecting surface. Since an incident wave of irradiance over an area has a power of , this implies a flux of photons per second per unit area striking the surface. Combining this with the above expression for the momentum of a single photon, results in the same relationships between irradiance and radiation pressure described above using classical electromagnetics. And again, reflected or otherwise emitted photons will contribute to the net radiation pressure identically.
Compression in a uniform radiation field
In general, the pressure of electromagnetic waves can be obtained from the vanishing of the trace of the electromagnetic stress tensor: since this trace equals 3P − u, we get
where is the radiation energy per unit volume.