Electromagnetic radiation

Electromagnetic nature of radiation

Maxwell's equations and their solutions (Panofsky–Phillips equations) indicate that a component of the electric field and magnetic field has an amplitude that decreases inversely with the distance between the source and the observer (1/r), allowing it to be detectable at large distances.^[7] These components are transverse to the direction of propagation (n) of the radiation.

One has ${\displaystyle \mathbf {E} \perp \mathbf {B} \perp \mathbf {n} }$, with E and B related by: $${\displaystyle \mathbf {B} ={\frac {\mathbf {n} \times \mathbf {E} }{c}}}$$ Note also that these fields propagate through space at the speed of light, i.e. at 299,792,458 m/s.

Properties

Electromagnetic radiation is produced by accelerating charged particles and can be naturally emitted,^[8][9] as from the Sun and other celestial bodies, or artificially generated for various applications. The energy in electromagnetic waves is sometimes referred to as radiant energy.^[10][11] The electromagnetic waves' energy does not need a propagating medium to travel through space; they move through a vacuum at the speed of light.^[12]

Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition.^[13] For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves.^[14] The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in a linear medium such as a vacuum. However, in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields—these interactions include the Faraday effect and the Kerr effect.^[15][16]

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength-dependent refractive index of the prism material (dispersion); that is, each component wave within the composite light is bent a different amount.^[17]

EM radiation exhibits both wave properties and particle properties at the same time (known as wave–particle duality). Both wave and particle characteristics have been confirmed in many experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not so difficult to experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior. Rather, it reflects the quantum nature of matter.^[18] A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.

Electromagnetic waves can be polarized, reflected, refracted, or diffracted, and can interfere with each other.^[19][20][21] Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single photon.^[22] When a low intensity light is sent through an interferometer it will be detected by a photomultiplier or other sensitive detector only along one arm of the device, consistent with particle properties, and yet the accumulated effect of many such detections will be interference consistent with wave properties.

Wave model

In homogeneous, isotropic media, electromagnetic radiation is a transverse wave,^[23] meaning that its oscillations are perpendicular to the direction of energy transfer and travel. It comes from the following equations:$${\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &=0\\\nabla \cdot \mathbf {B} &=0\end{aligned}}}$$These equations predicate that any electromagnetic wave must be a transverse wave, where the electric field E and the magnetic field B are both perpendicular to the direction of wave propagation. The electric and magnetic parts of the field in an electromagnetic wave stand in a fixed ratio of strengths to satisfy the two Maxwell's equations that specify how one is produced from the other. In dissipation-less (lossless) media, these E and B fields are also in phase, with both reaching maxima and minima at the same points in space.

In the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a time-change in one type of field is proportional to the curl of the other. These derivatives require that the E and B fields in EMR are in phase. An important aspect of light's nature is its frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion.

A monochromatic wave (a wave of a single frequency) consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves longer than a continent to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:^[24]

${\displaystyle \displaystyle v=f\lambda }$

where v is the speed of the wave (c in a vacuum or less in other media), f is the frequency, and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation. Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum, or individual sinusoidal components, each of which contains a single frequency, amplitude, and phase. Such a component wave is said to be monochromatic.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which is known as parallel polarization state generation.^[25]

Maxwell's equations

James Clerk Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.^[26][27] Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves.^[28] Out of the four equations, two of the equations that Maxwell refined were Faraday's Law of Induction and Ampère's circuital law, which he extended by adding the displacement current term to the equations himself. Maxwell thought that the displacement current, which he viewed as the motion of bound charges, gave rise to the magnetic field.^[29] The other two equations are Gauss's law and Gauss's law for magnetism.

Near and far fields

Maxwell's equations established that some charges and currents (sources) produce local electromagnetic fields near them that do not radiate. Currents directly produce magnetic fields of a magnetic-dipole–type that die out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential (such as in an antenna) produce an electric-dipole–type electrical field, but this also declines with distance. These fields make up the near field. Neither of these behaviours is responsible for EM radiation. Instead, they only efficiently transfer energy to a receiver very close to the source, such as inside a transformer. The near field has strong effects on its source, with any energy withdrawn by a receiver causing increased load (decreased electrical reactance) on the source. The near field does not propagate freely into space, carrying energy away without a distance limit, but rather oscillates, returning its energy to the transmitter if it is not absorbed by a receiver.^[30]

By contrast, the far field is composed of radiation that is free of the transmitter, in the sense that the transmitter requires the same power to send changes in the field out regardless of whether anything absorbs the signal, e.g. a radio station does not need to increase its power when more receivers use the signal. This far part of the electromagnetic field is electromagnetic radiation. The far fields propagate (radiate) without allowing the transmitter to affect them. This causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Due to conservation of energy, the amount of power passing through any closed surface drawn around the source is the same. The power density of EM radiation from an isotropic source decreases with the inverse square of the distance from the source; this is called the inverse-square law. Field intensity due to dipole parts of the near field varies according to an inverse-cube law,^[31] and thus fades with distance.

The distinction between near field and radiated field is illustrated by the Panofsky–Phillips equations, which give the general expression of the electric and magnetic fields produced by an arbitrary distribution of charges and currents. The terms of the Panofsky–Phillips equations can be separated into near field terms and far field terms. The near field terms have a ${\displaystyle 1/r^{2}}$ dependence and are significant only in the immediate vicinity of the sources. The far field terms have a ${\displaystyle 1/r}$ dependence. Due to their slower decrease with distance, they dominate as one moves away from the sources.

${\displaystyle \definecolor {vert}{rgb}{0,0.6,0}\mathbf {E} ={\frac {1}{4\pi \varepsilon _{0}}}\,\displaystyle \iiint \left({\color {vert}{\frac {[\rho ]\mathbf {n} }{r^{2}}}+{\frac {\left(\left[\mathbf {J} \right]\cdot \mathbf {n} \right)\mathbf {n} +\left(\left[\mathbf {J} \right]\times \mathbf {n} \right)\times \mathbf {n} }{c\,r^{2}}}}\mathbin {\color {red}{+}} {\color {red}{\frac {\left(\left[{\dot {\mathbf {J} }}\right]\times \mathbf {n} \right)\times \mathbf {n} }{c^{2}r}}}\right)\,dV'}$

${\displaystyle \definecolor {vert}{rgb}{0,0.6,0}\mathbf {B} ={\frac {1}{4\pi \varepsilon _{0}}}\,\displaystyle \iiint \left({\color {vert}{\frac {\left[\mathbf {J} \right]\times \mathbf {n} }{c^{2}r^{2}}}}\mathbin {\color {red}{+}} {\color {red}{\frac {\left[{\dot {\mathbf {J} }}\right]\times \mathbf {n} }{c^{3}r}}}\right)\,dV'}$

• In green are the near fields (decaying as 1/r²).
• In red are the radiated fields (decaying as 1/r).

In the far-field region, near fields can be neglected and the expressions of the emitted fields reduce to:^[32][33]

${\displaystyle \mathbf {E} ={\frac {1}{4\pi \varepsilon _{0}c^{2}}}\,\displaystyle \iiint \left({\frac {\left(\left[{\dot {\mathbf {J} }}\right]\times \mathbf {n} \right)\times \mathbf {n} }{r}}\right)\,dV'}$

${\displaystyle \mathbf {B} ={\frac {1}{4\pi \varepsilon _{0}c^{3}}}\,\displaystyle \iiint \left({\frac {\left[{\dot {\mathbf {J} }}\right]\times \mathbf {n} }{r}}\right)\,dV'}$

In the Liénard–Wiechert potential formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast, the term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity are both associated with the near field, and do not comprise electromagnetic radiation.^[34]

Particle model and quantum theory

An anomaly arose in the late 19th century involving a contradiction between the wave theory of light and measurements of the electromagnetic spectra that were being emitted by thermal radiators known as black bodies. Physicists struggled with this problem unsuccessfully for many years, and it later became known as the ultraviolet catastrophe. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta. In 1905, Albert Einstein proposed that light quanta be regarded as real particles. Later the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by

${\displaystyle E=hf={\frac {hc}{\lambda }}\,\!}$

where h is the Planck constant, ${\displaystyle \lambda }$ is the wavelength and c is the speed of light. This is sometimes known as the Planck–Einstein equation.^[35] In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency of the EMR wave.^[36] Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:

${\displaystyle p={E \over c}={hf \over c}={h \over \lambda }.}$

The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances) was an experimental anomaly not explained by the wave theory: the photoelectric effect, in which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency, rather than the intensity, of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried to find an explanation. In 1905, Einstein explained this phenomenon by resurrecting the particle theory of light. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the Compton effect.^[37][38]

As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence, a type of photoluminescence. An example is visible light emitted from fluorescent paints, in response to ultraviolet (blacklight). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called phosphorescence.^[39][40]

Quantum mechanics also governs emission, which is seen when an emitting gas glows due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation.^[41] An example is the emission spectrum of nebulae.^[42] Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature. These phenomena can be used to detect the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements comprise a particular star. Shifts in the frequency of the spectral lines for an element, called a redshift, can be used to determine the star's cosmological distance.^[43]: 181

Wave–particle duality

The modern theory that explains the nature of light includes the notion of wave–particle duality. The theory is based on the concept that every quantum entity can show wave-like or particle-like behaviors, depending on observation. The observation led to the collapse of the entity's wave function. If it is based on the Copenhagen interpretation, the observation does really collapse the wave function; for the many-worlds interpretation, all possible outcomes of the collapse happened in parallel universes; for the pilot wave theory, the particle behaviour is simply determined by waves. The duality nature of a real photon has been observed in the double-slit experiment.

Together, wave and particle effects fully explain the emission and absorption spectra of EM radiation. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in the atoms. Dark bands in the absorption spectrum are due to the atoms in an intervening medium between source and observer. The atoms absorb certain frequencies of the light between emitter and detector/eye, then emit them in all directions. A dark band appears to the detector, due to the radiation scattered out of the light beam. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere.

Propagation speed

In empty space (vacuum), electromagnetic radiation travels at the speed of light, ${\displaystyle c}$, 299,792,458 meters per second (approximately 186,000 miles per second). In a medium other than vacuum it travels at a lower velocity ${\displaystyle v}$, given by a dimensionless parameter between 0 and 1 characteristic of the medium called the velocity factor ${\displaystyle {\mathit {VF}}}$ or its reciprocal, the refractive index ${\displaystyle n}$:

${\displaystyle v={\mathit {VF}}\cdot c={c \over n}}$.

The reason for this is that in matter the electric and magnetic fields of the wave are slowed because they polarize the charged particles in the medium they pass through.^[44]: 401 The oscillating electric field causes nearby positive and negative charges in atoms to move slightly apart and together, inducing an oscillating polarization, creating an electric polarization field. The oscillating magnetic field moves nearby magnetic dipoles, inducing an oscillating magnetization, creating an induced oscillating magnetic field. These induced fields, superposed on the original wave fields, slow the wave (Ewald–Oseen extinction theorem). The amount of slowing depends on the electromagnetic properties of the medium, the electric permittivity and magnetic permeability. In the SI system of units, empty space has a vacuum permittivity of ${\displaystyle \epsilon _{\text{0}}=}$ 8.854×10⁻¹² F/m (farads per meter) and a vacuum permeability of ${\displaystyle \mu _{\text{0}}=}$ 1.257×10⁻⁶ H/m (henries per meter). These universal constants determine the speed of light in a vacuum:

${\displaystyle c={1 \over {\sqrt {\epsilon _{\text{0}}\mu _{\text{0}}}}}}$

In a medium that is isotropic and linear, which means the electric polarization is proportional to the electric field ${\displaystyle \mathbf {D} =\epsilon \mathbf {E} }$ and the magnetization is proportional to the magnetic field ${\displaystyle \mathbf {H} ={1 \over \mu }\mathbf {B} }$. The speed of the waves, the ${\displaystyle {\mathit {VF}}}$, and the refractive index are determined by only two parameters: the electric permittivity ${\displaystyle \epsilon }$ of the medium in farads per meter, and the magnetic permeability of the medium ${\displaystyle \mu }$ in henrys per meter^[44]: 401

${\displaystyle v={1 \over {\sqrt {\epsilon \mu }}}}$

${\displaystyle n={1 \over {\mathit {VF}}}=c{\sqrt {\epsilon \mu }}={\sqrt {\epsilon \mu \over \epsilon _{\text{0}}\mu _{\text{0}}}}}$

If the permittivity and permeability of the medium is constant for different frequency EM waves, this is called a non-dispersive medium.^{[44]: 417–418} In this case all EM wave frequencies would travel at the same velocity, and the waveshape stays constant as it travels. However in real matter ${\displaystyle \epsilon }$ and ${\displaystyle \mu }$ typically vary with frequency, this is called a dispersive medium. In dispersive media different spectral bands have different propagation characteristics, and an arbitrary wave changes shape as it travels through the medium.

Radio and microwave

Electromagnetic radiation phenomena with wavelengths ranging from one meter to one millimeter are called microwaves; with frequencies between 300 MHz (0.3 GHz) and 300 GHz. When radio waves impinge upon a conductor, they couple to the conductor, travel along it, and induce an electric current on the conductor surface by moving the electrons of the conducting material in correlated bunches of charge. At radio and microwave frequencies, EMR interacts with matter largely as a bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors, such induced bulk movement of charges (electric currents) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside a microwave oven. These interactions produce either electric currents or heat, or both.

Infrared

Like radio and microwave, infrared (IR) is reflected by metals (and also most EMR, well into the ultraviolet range). However, unlike lower-frequency radio and microwave radiation, infrared EMR commonly interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. It is consequently absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. The same process, run in reverse, causes bulk substances to radiate in the infrared spontaneously (see thermal radiation section below).

Infrared radiation is divided into spectral subregions. While different subdivision schemes exist,^{[50][51][new archival link needed]} the spectrum is commonly divided as near-infrared (0.75–1.4 μm), short-wavelength infrared (1.4–3 μm), mid-wavelength infrared (3–8 μm), long-wavelength infrared (8–15 μm) and far infrared (15–1000 μm).^[52]

Some animals, such as snakes, have thermo-sensitive membranes (pit organs) that can detect temperature differences, allowing them to sense infrared radiation.^[53]

Visible light

Natural sources produce EM radiation across the spectrum. EM radiation with a wavelength between approximately 400 nm and 700 nm is directly detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light.

As frequency increases into the visible range, photons have enough energy to change the bond structure of some individual molecules. It is not a coincidence that this happens in the visible range, as the mechanism of vision involves the change in bonding of a single molecule, retinal, which absorbs a single photon. The change in retinal causes a change in the shape of the rhodopsin protein it is contained in, which starts the biochemical process that causes the retina of the human eye to sense the light.

Visible light is able to affect only a tiny percentage of all molecules. Usually not in a permanent or damaging way, rather the photon excites an electron which then emits another photon when returning to its original position. This is the source of color produced by most dyes. Retinal is an exception. When a photon is absorbed, the retinal permanently changes structure from cis to trans, and requires a protein to convert it back, i.e. reset it to be able to function as a light detector again.

Photosynthesis becomes possible in this range as well, for the same reason. A single molecule of chlorophyll is excited by a single photon. In plant tissues that conduct photosynthesis, carotenoids act to quench electronically excited chlorophyll produced by visible light in a process called non-photochemical quenching, to prevent reactions that would otherwise interfere with photosynthesis at high light levels.

Limited evidence indicate that some reactive oxygen species are created by visible light in skin, and that these may have some role in photoaging, in the same manner as ultraviolet A.^[54]

Infrared, microwaves, and radio waves are known to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation.

Ultraviolet

As frequency increases into the ultraviolet, photons now carry enough energy (about three electron volts or more) to excite certain doubly bonded molecules into permanent chemical rearrangement. In DNA, this causes lasting damage. DNA is also indirectly damaged by reactive oxygen species produced by ultraviolet A (UVA), which has energy too low to damage DNA directly. This is why ultraviolet at all wavelengths can damage DNA, and is capable of causing cancer, and (for UVB) skin burns (sunburn) that are far worse than would be produced by simple heating (temperature increase) effects.

At the higher end of the ultraviolet range, the energy of photons becomes large enough to impart enough energy to electrons to cause them to be liberated from the atom, in a process called photoionisation. The energy required for this is always larger than about 10 electron volt (eV) corresponding with wavelengths smaller than 124 nm (some sources suggest a more realistic cutoff of 33 eV, which is the energy required to ionize water). This high end of the ultraviolet spectrum with energies in the approximate ionization range, is sometimes called "extreme UV". Ionizing UV is strongly filtered by the Earth's atmosphere.^[55]

X-rays and gamma rays

Electromagnetic radiation composed of photons that carry minimum-ionization energy, or more (which includes the entire spectrum with shorter wavelengths), is therefore termed ionizing radiation. (Many other kinds of ionizing radiation are made of non-EM particles.) Electromagnetic-type ionizing radiation extends from the extreme ultraviolet to all higher frequencies and shorter wavelengths, which means that all X-rays and gamma rays qualify. These are capable of the most severe types of molecular damage, which can happen in biology to any type of biomolecule, including mutation and cancer,^[56] and often at great depths below the skin, since the higher end of the X-ray spectrum, and all of the gamma ray spectrum, penetrate matter.

Use as a weapon

The heat ray is an application of EMR that makes use of microwave frequencies to create an unpleasant heating effect in the upper layer of the skin. The heat ray weapon Active Denial System was developed by the US military as an experimental weapon to deny the enemy access to an area.^[74]