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In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. The perturbing photon is not destroyed in the process (cf. absorption), and the second photon is created with the same phase, frequency, polarization, and direction of travel as the original. Stimulated emission is really a quantum mechanical phenomenon but it can be understood in terms of a classical field and a quantum mechanical atom. The process can be thought of as optical amplification, and it forms the basis of the laser and maser. Table of Opticks, 1728 Cyclopaedia Optics (appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ...
In physics, the photon (from Greek φως, phÅs, meaning light) is the quantum of the electromagnetic field; for instance, light. ...
Matter is commonly defined as the substance of which physical objects are composed. ...
Look up absorption in Wiktionary, the free dictionary Absorption may refer to: In physics: absorption (chemistry) - absorption of particles of gas or liquid in liquid or solid material as studied in physical chemistry absorption (optics) - absorption of photons by a material Absorption (acoustics) - absorption of sound waves by a material...
Waves with the same phase Waves with different phases The phase of a wave relates the position of a feature, typically a peak or a trough of the waveform, to that same feature in another part of the waveform (or, which amounts to the same, on a second waveform). ...
Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...
In electrodynamics, polarization (also spelled polarisation) is a property of waves, such as light and other electromagnetic radiation. ...
A simple introduction to this subject is provided in Basics of quantum mechanics. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Lasers range in size from microscopic diode lasers (top) with numerous applications, to football field sized neodymium glass lasers (bottom) used for inertial confinement fusion, nuclear weapons research and other physics experiments. ...
A Hydrogen RF discharge, the first element inside an Hydrogen Maser (see description below), courtesy NASA/JPL-Caltech. ...
Electrons and how they interact with each other and electromagnetic fields form the basis for most of our understanding of chemistry and physics. Electrons have energy in proportion to how far they are on average from the nucleus of an atom. The Pauli exclusion principle forces some electrons to be farther from the nucleus than others (that's why all the electrons don't just hang around in the 1 s orbital.) When electrons absorb energy either from light (photons) or from heat (phonons), they move farther away from the atomic nuclei but they are only allowed to absorb energy that will land them into specific energy levels. This leads to emission lines and absorption lines. Properties The electron is a fundamental subatomic particle that carries a negative electric charge. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Multicolored chemicals are frequent hallmarks of chemistry. ...
A Superconductor demonstrating the Meissner Effect. ...
A stylized representation of a lithium atom. ...
Properties Mass: || ≈ 1. ...
The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state. ...
It has been suggested that Energy level be merged into this article or section. ...
Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. ...
In physics, the photon (from Greek φως, phÅs, meaning light) is the quantum of the electromagnetic field; for instance, light. ...
In physics, heat is defined as energy in transit. ...
In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. ...
A stylized representation of a lithium atom. ...
A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ...
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ...
When an electron is excited, it will not stay that way forever. On average there is a lifetime for any particular energy level after which half of the electrons initially in that state will have decayed into a lower state. When such a decay occurs, the energy difference between the level the electron was at and the new level must be released either as a photon or a phonon. When an electron decays due to "timeout" it is said to be due to "spontaneous emission." The phase associated with the photon that is emitted is random and has to do with some quantum mechanical ideas concerning the atom's internal state. If a bunch of electrons were put into an excited state somehow and then left to relax, the resulting radiation would be very spectrally limited (only one wavelength of light would be present) but the individual photons would not be in phase with one another. This is also called fluorescence. Properties The electron is a fundamental subatomic particle that carries a negative electric charge. ...
In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). ...
Lifetime can refer to: Life expectancy, the length of time a person is alive One of the American media ventures owned by Lifetime Entertainment Services Lifetime (TV network), a cable television network Lifetime Movie Network, a cable movie network Lifetime (band), an American melodic hardcore punk band from New Jersey...
A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ...
Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles (radiation). ...
Spontaneous emission is the process by which a molecule in an excited state drops to the ground state, resulting in the creation of a photon. ...
Look up Phase in Wiktionary, the free dictionary Phase may refer to: Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter Phase (waves), the time position (or angle in the complex plane) within a cycle of a periodic waveform...
A simple introduction to this subject is provided in Basics of quantum mechanics. ...
Radiation has a variety of different meanings. ...
The wavelength is the distance between repeating units of a wave pattern. ...
Fluorescence induced by exposure to ultraviolet light in vials containing various sized Cadmium selenide (CdSe) quantum dots. ...
Other photons (i.e. an external electromagnetic field) will affect an atom's state. The quantum mechanical variables mentioned above are changed. Specifically the atom will act like a small electric dipole which will oscillate with the external field. One of the consequences of this oscillation is it encourages electrons to decay to the lower energy state. When it does this due to the presence of other photons, the released photon is in phase with the other photons and in the same direction as the other photons. This is known as stimulated emission. The Earths magnetic field, which is approximately a dipole. ...
A periodic signal (usually electromagnetic in nature) is in phase if its period is synchronized with another signal. ...
Stimulated emission can be modelled mathematically by considering an atom which may be in two electronic energy states, the ground state (1) and the excited state (2), with energies E1 and E2 respectively. Properties Mass: || ≈ 1. ...
Properties The electron is a fundamental subatomic particle that carries a negative electric charge. ...
If the atom is in the excited state, it may decay into the ground state by the process of spontaneous emission, releasing the difference in energies between the two states as a photon. The photon will have frequency ν and energy hν, given by: Spontaneous emission is the process by which a molecule in an excited state drops to the ground state, resulting in the creation of a photon. ...
Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...
- E2 − E1 = hν,
where h is Planck's constant. In science, a physical constant is a physical quantity whose numerical value does not change. ...
Alternatively, if the excited-state atom is perturbed by the electric field of a photon with frequency ν, it may release a second photon of the same frequency, in phase with the first photon. The atom will again decay into the ground state. This process is known as stimulated emission.
An energy level diagram illustrating the process is shown below:
 Image File history File links Stimulated emission File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which stimulated emission occurs is given by:
 , where B21 is a proportionality constant for this particular transition in this particular atom (referred to as an Einstein B coefficient), and ρ(ν) is the radiation density of photons of frequency ν. The rate of emission is thus proportional to the number of atoms in the excited state, N, and the density of the perturbing photons. The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ...
In physics, atomic spectral lines are formed when an electron makes a transition from a particular energy level of an atom, to a lower energy state. ...
The critical detail of stimulated emission is that the emitted photon is identical to the stimulating photon in that it has the same frequency, phase, polarisation, and direction of propagation. The two photons, as a result, are totally coherent. It is this property that allows optical amplification to take place. Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...
Look up Phase in Wiktionary, the free dictionary Phase may refer to: Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter Phase (waves), the time position (or angle in the complex plane) within a cycle of a periodic waveform...
This article treats polarization in electrodynamics. ...
Coherence is the property of wave-like states that enables them to exhibit interference. ...
Although most directly related to the discussion of how lasers work, stimulated emission touches on some of the most basic concepts in physics and the interaction of light and matter. It is a very important and key understanding to the understanding of optics specifically and physics in general. Lasers range in size from microscopic diode lasers (top) with numerous applications, to football field sized neodymium glass lasers (bottom) used for inertial confinement fusion, nuclear weapons research and other physics experiments. ...
Spectral line shape function Although there are many possible line shapes, it is common to model the spectral line shape function as a Lorentzian distribution: In physics, atomic spectral lines are formed when an electron makes a transition from a particular energy level of an atom, to a lower energy state. ...
The Cauchy-Lorentz distribution, named after Augustin Cauchy, is a continuous probability distribution with probability density function where x0 is the location parameter, specifying the location of the peak of the distribution, and γ is the scale parameter which specifies the half-width at half-maximum (HWHM). ...
 where  is the full width at half maximum, or FWHM, in hertz. This model is generally valid as long as A full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. ...
The hertz (symbol: Hz) is the SI unit of frequency. ...
 and  The line shape function, regardless of the form that it takes, must satisfy the normalization condition of any probability distribution:  which the Lorentzian satisfies.
The peak value of the Lorentzian line shape occurs at the line center:
 It is also convenient to define the normalized line shape function:  which is dimensionless, and which has a peak value, also at the line center, of 
Stimulated emission cross section The stimulated emission cross section (in square meters) is A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ...
 where - A21 is the Einstein A coefficient (in radians per second),
- λ is the wavelength (in meters),
- n is the refractive index of the medium (dimensionless), and
- g(ν) is the spectral line shape function (in seconds).
The wavelength is the distance between repeating units of a wave pattern. ...
The refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum. ...
Optical amplification Under certain conditions, stimulated emission can provide a physical mechanism for optical amplification. An external source of energy stimulates atoms in the ground state to transition to the excited state, creating what is called a population inversion. When light of the appropriate frequency passes through the inverted medium, the photons stimulate the excited atoms to emit additional photons of the same frequency, phase, and direction, resulting in an amplification of the input intensity. In optics, an optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal, then amplify it electrically, and finally reconvert it to an optical signal. ...
In physics, specifically statistical mechanics, the concept of population inversion is of fundamental importance in laser science because the production of a population inversion is a necessary step in the workings of a laser. ...
The population inversion, in units of atoms per cubic meter, is The cubic metre (symbol m³) is the SI derived unit of volume. ...
 where g1 and g2 are the degeneracies of energy levels 1 and 2, respectively. The energy levels of two or more physical states are said to be degenerate when they have the same value. ...
Small signal gain equation The intensity of the stimulated emission is governed by the following differential equation:  as long as the intensity I(z) is small enough so that it does not have a significant effect on the magnitude of the population inversion. Grouping the first two factors together, this equation simplifies as  where  is the small-signal gain coefficient (in units of radians per meter). We can solve the differential equation using separation of variables: In mathematics, separation of variables is any of several methods of solving ordinary and partial differential equations. ...
 Integrating, we find:  or  where  is the optical intensity of the input signal (in watts per square meter).
Saturation intensity The saturation intensity IS is defined as the input intensity at which the gain of the optical amplifier drops to exactly half of the small-signal gain. We can compute the saturation intensity as  where - h is Planck's constant, and
- τS is the saturation time constant, which depends on the spontaneous emission lifetimes of the various transitions between the energy levels related to the amplification.
A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...
General gain equation The general form of the gain equation, which applies regardless of the input intensity, derives from the general differential equation for the intensity:  where IS is the saturation intensity. The solution of this equation is the general gain equation: 
References - Saleh, Bahaa E. A. and Teich, Malvin Carl (1991). Fundamentals of Photonics, New York: John Wiley & Sons. ISBN 0471839655.
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