![Two photons absorption energy scheme](https://upload.wikimedia.org/wikipedia/commons/9/92/Two_photons_absorption_energy_scheme.png)
Two-photon absorption (TPA or 2PA) or two-photon excitation or non-linear absorption is the simultaneous absorption of two
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s of identical or different frequencies in order to excite a
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
from one state (usually the
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
) to a higher energy, most commonly an
excited electronic state. Absorption of two photons with different frequencies is called
non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the square of the light
intensity, thus it is a
nonlinear optical
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in ''nonlinear media'', that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typic ...
process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the
photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with
absorption cross section
Absorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagne ...
typically several orders of magnitude smaller than one-photon absorption cross section.
Two-photon excitation of a
fluorophore
A fluorophore (or fluorochrome, similarly to a chromophore) is a fluorescent chemical compound that can re-emit light upon light excitation. Fluorophores typically contain several combined aromatic groups, or planar or cyclic molecules with se ...
(a
fluorescent
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
molecule) leads to two-photon-excited
fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
where the excited state produced by TPA decays by spontaneous emission of a photon to a lower energy state.
Background
The phenomenon was originally predicted by
Maria Goeppert-Mayer
Maria Goeppert Mayer (; June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus. She was the second woman to win a Nobel Pri ...
in 1931 in her doctoral dissertation.
Thirty years later, the invention of the
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
permitted the first experimental verification of TPA when
two-photon-excited fluorescence was detected in a
europium
Europium is a chemical element with the symbol Eu and atomic number 63. Europium is the most reactive lanthanide by far, having to be stored under an inert fluid to protect it from atmospheric oxygen or moisture. Europium is also the softest lanth ...
-doped crystal. Soon afterwards, the effect was observed in cesium vapor and then in CdS, a semiconductor.
![Two photons excited fluorescence energy levels](https://upload.wikimedia.org/wikipedia/commons/4/45/Two_photons_excited_fluorescence_energy_levels.png)
TPA is a
nonlinear optical
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in ''nonlinear media'', that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typic ...
process. In particular, the imaginary part of the third-order nonlinear
susceptibility is related to the extent of TPA in a given molecule. The
selection rule
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in ...
s for TPA are therefore different from one-photon absorption (OPA), which is dependent on the first-order susceptibility. The relationship between the selection rules for one- and two-photon absorption is analogous to those of
Raman and
IR spectroscopies. For example, in a
centrosymmetric molecule
Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain ...
, one- and two-photon allowed transitions are mutually exclusive, an optical transition allowed in one of the spectroscopies is forbidden in the other. However, for non-centrosymmetric molecules there is no formal mutual exclusion between the selection rules for OPA and TPA. In
quantum mechanical
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
terms, this difference results from the fact that the quantum states of such molecules have either + or - inversion symmetry, usually labelled by g (for +) and u (for -). One photon transitions are only allowed between states that differ in the inversion symmetry, i.e. g <-> u, while two photon transitions are only allowed between states that have the same inversion symmetry, i.e. g <-> g and u <-> u.
The relation between the number of photons - or, equivalently, order of the electronic transitions - involved in a TPA process (two) and the order of the corresponding nonlinear susceptibility (three) may be understood using the
optical theorem
In physics, the optical theorem is a general law of wave scattering theory, which relates the forward scattering amplitude to the total cross section of the scatterer. It is usually written in the form
:\sigma_\mathrm=\frac~\mathrm\,f(0),
where (0 ...
. This theorem relates the imaginary part of an all-optical process of a given perturbation order
with a process involving charge carriers with half the perturbation order, i.e.
. To apply this theorem it is important to consider that the order in perturbation theory to calculate the probability amplitude of an all-optical
process is
. Since in the case of TPA there are electronic transitions of the second order involved (
), it results from the optical theorem that the order of the nonlinear susceptibility is
, i.e. it is a
process.
Phenomenologically, TPA can be thought of as the third term in a conventional
anharmonic oscillator
In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmo ...
model for depicting vibrational behavior of molecules. Another view is to think of light as
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s. In nonresonant TPA, neither photon is at resonance with the system energy gap, and two photons combine to bridge the energy gap larger than the energies of each photon individually. If there were an intermediate electronic state in the gap, this could happen via two separate one-photon transitions in a process described as "resonant TPA", "sequential TPA", or "1+1 absorption" where the absorption alone is a first order process and the generated fluorescence will rise as the square of the incoming intensity. In nonresonant TPA the transition occurs without the presence of the intermediate state. This can be viewed as being due to a "virtual" state created by the interaction of the photons with the molecule. The
virtual state argument is quite orthogonal to the anharmonic oscillator argument. It states for example that in a semiconductor, absorption at high energies is impossible if two photons cannot bridge the band gap. So, many materials can be used for the Kerr effect that do not show any absorption and thus have a high damage threshold.
The "nonlinear" in the description of this process means that the strength of the interaction increases faster than linearly with the electric field of the light. In fact, under ideal conditions the rate of TPA is proportional to the square of the field intensity. This dependence can be derived quantum mechanically, but is intuitively obvious when one considers that it requires two photons to coincide in time and space. This requirement for high light intensity means that lasers are required to study TPA phenomena. Further, in order to understand the TPA
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
,
monochromatic
A monochrome or monochromatic image, object or color scheme, palette is composed of one color (or lightness, values of one color). Images using only Tint, shade and tone, shades of grey are called grayscale (typically digital) or Black and wh ...
light is also desired in order to measure the TPA cross section at different
wavelengths
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
. Hence, tunable pulsed lasers (such as frequency-doubled Nd:YAG-pumped
OPOs OPOS, full name OLE for Retail POS, a platform specific implementation of UnifiedPOS, is a point of sale device standard for Microsoft Windows operating systems that was initiated by Microsoft, NCR, Epson, and Fujitsu-ICL and is managed by the A ...
and
OPAs) are the choice of excitation.
Measurements
Two-photon absorption can be measured by several techniques. Some of them are two-photon excited fluorescence (TPEF), z-scan, self-diffraction or nonlinear transmission (NLT).
Pulsed laser Pulsed operation of lasers refers to any laser not classified as continuous wave, so that the optical power appears in pulses of some duration at some repetition rate. Silfvast, William T. (1996). ''Laser Fundamentals'', Cambridge University Press. ...
s are most often used because TPA is a third-order nonlinear optical process, and therefore is most efficient at very high
intensities.
Absorption rate
Beer's law describes the decay in intensity due to one-photon absorption:
:
where
are the distance that light travelled through a sample,
is the light intensity after travelling a distance
,
is the light intensity where the light enters the sample and
is the one-photon absorption coefficient of the sample. In two-photon absorption, for an incident plane wave of radiation, the light intensity versus distance changes to
:
for TPA with light intensity as a function of path length or cross section
as a function of
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
and the initial light intensity
. The
absorption coefficient
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
now becomes the TPA coefficient
. (Note that there is some confusion over the term
in nonlinear optics, since it is sometimes used to describe the
second-order polarizability, and occasionally for the molecular two-photon cross-section. More often however, it is used to describe the bulk 2-photon optical density of a sample. The letter
or
is more often used to denote the molecular two-photon cross-section.)
Two-photon excited fluorescence
Relation between the two-photon excited fluorescence and the total number of absorbed photons per unit time
is given by
:
where
and
are the
fluorescence quantum efficiency of the fluorophore and the fluorescence collection efficiency of the measurement system, respectively. In a particular measurement,
is a function of fluorophore concentration
, illuminated sample volume
, incident light intensity
, and two-photon absorption cross-section
:
:
Notice that the
is proportional to the square of the incident light as expected for TPA.
Units of cross-section
The molecular two-photon absorption cross-section is usually quoted in the units of Goeppert-Mayer (GM) (after its discoverer, Nobel laureate
Maria Goeppert-Mayer
Maria Goeppert Mayer (; June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus. She was the second woman to win a Nobel Pri ...
), where 1 GM is 10
−50 cm
4 s photon
−1. Considering the reason for these units, one can see that it results from the product of two areas (one for each photon, each in cm
2) and a time (within which the two photons must arrive to be able to act together). The large scaling factor is introduced in order that 2-photon absorption cross-sections of common dyes will have convenient values.
Development of the field and potential applications
Until the early 1980s, TPA was used as a
spectroscopic
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
tool. Scientists compared the OPA and TPA spectra of different organic molecules and obtained several fundamental structure property relationships. However, in late 1980s, applications started to be developed.
Peter Rentzepis suggested applications in
3D optical data storage. Watt Webb suggested microscopy and imaging. Other applications such as
3D microfabrication
Three-dimensional (3D) microfabrication refers to manufacturing techniques that involve the layering of materials to produce a three-dimensional structure at a microscopic scale. These structures are usually on the scale of micrometers and are pop ...
, optical logic, autocorrelation, pulse reshaping and optical power limiting were also demonstrated.
3D imaging of semiconductors
It was demonstrated that by using 2-photon absorption charge carriers can be generated spatially confined in a semiconductor device. This can be used to investigate the charge transport properties of such device.
Microfabrication and lithography
One of the most distinguishing features of TPA is that the rate of absorption of light by a molecule depends on the square of the light's intensity. This is different from OPA, where the rate of absorption is linear with respect to input intensity. As a result of this dependence, if material is cut with a high power
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
beam, the rate of material removal decreases very sharply from the center of the beam to its periphery. Because of this, the "pit" created is sharper and better resolved than if the same size pit were created using normal absorption.
3D photopolymerization
In
3D microfabrication
Three-dimensional (3D) microfabrication refers to manufacturing techniques that involve the layering of materials to produce a three-dimensional structure at a microscopic scale. These structures are usually on the scale of micrometers and are pop ...
, a block of gel containing monomers and a 2-photon active
photoinitiator
A photoinitiator is a molecule that creates reactive species ( free radicals, cations or anions) when exposed to radiation (UV or visible). Synthetic photoinitiators are key components in photopolymers (for example, photo-curable coatings, adhesiv ...
is prepared as a raw material. Application of a focused laser to the block results in polymerization only at the focal spot of the laser, where the intensity of the absorbed light is highest. The shape of an object can therefore be traced out by the laser, and then the excess gel can be washed away to leave the traced solid.
Imaging
The human body is not
transparent
Transparency, transparence or transparent most often refer to:
* Transparency (optics), the physical property of allowing the transmission of light through a material
They may also refer to:
Literal uses
* Transparency (photography), a still, ...
to
visible
Visibility, in meteorology, is a measure of the distance at which an object or light can be seen.
Visibility may also refer to:
* A measure of turbidity in water quality control
* Interferometric visibility, which quantifies interference contrast ...
wavelengths. Hence, one photon imaging using
fluorescent dye
A fluorophore (or fluorochrome, similarly to a chromophore) is a fluorescent chemical compound that can re-emit light upon light excitation. Fluorophores typically contain several combined aromatic groups, or planar or cyclic molecules with se ...
s is not very efficient. If the same dye had good two-photon absorption, then the corresponding excitation would occur at approximately two times the wavelength at which one-photon excitation would have occurred. As a result, it is possible to use excitation in the
far infrared
Far infrared (FIR) is a region in the infrared spectrum of electromagnetic radiation. Far infrared is often defined as any radiation with a wavelength of 15 micrometers (μm) to 1 mm (corresponding to a range of about 20 THz to ...
region where the human body shows good transparency.
It is sometimes said, incorrectly, that Rayleigh scattering is relevant to imaging techniques such as two-photon. According to
Rayleigh's scattering law, the amount of scattering is proportional to
, where
is the wavelength. As a result, if the wavelength is increased by a factor of 2, the Rayleigh scattering is reduced by a factor of 16. However, Rayleigh scattering only takes place when scattering particles are much smaller than the wavelength of light (the sky is blue because air molecules scatter blue light much more than red light). When particles are larger, scattering increases approximately linearly with wavelength: hence clouds are white since they contain water droplets. This form of scatter is known as
Mie scattering
The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the ...
and is what occurs in biological tissues. So, although longer wavelengths do scatter less in biological tissues, the difference is not as dramatic as Rayleigh's law would predict.
Optical power limiting
Another area of research is ''optical power limiting''. In a material with a strong nonlinear effect, the absorption of light increases with intensity such that beyond a certain input intensity the output intensity approaches a constant value. Such a material can be used to limit the amount of optical power entering a system. This can be used to protect expensive or sensitive equipment such as
sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
s, can be used in protective goggles, or can be used to control noise in laser beams.
Photodynamic therapy
Photodynamic therapy
Photodynamic therapy (PDT) is a form of phototherapy involving light and a photosensitizing chemical substance, used in conjunction with molecular oxygen to elicit cell death (phototoxicity).
PDT is popularly used in treating acne. It is used cl ...
(PDT) is a method for treating
cancer
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal b ...
. In this technique, an organic molecule with a good triplet quantum yield is excited so that the
triplet state
In quantum mechanics, a triplet is a quantum state of a system with a spin of quantum number =1, such that there are three allowed values of the spin component, = −1, 0, and +1.
Spin, in the context of quantum mechanics, is not a mechanical ...
of this molecule interacts with
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
. The ground state of oxygen has triplet character. This leads to triplet-triplet annihilation, which gives rise to singlet oxygen, which in turn attacks cancerous cells. However, using TPA materials, the window for excitation can be extended into the
infrared
Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
region, thereby making the process more viable to be used on the human body.
Two-photon pharmacology
Photoisomerization
In chemistry, photoisomerization is a form of isomerization induced by photoexcitation. Both reversible and irreversible photoisomerizations are known for photoswitchable compounds. The term "photoisomerization" usually, however, refers to a re ...
of
azobenzene
Azobenzene is a photoswitchable chemical compound composed of two phenyl rings linked by a N=N double bond. It is the simplest example of an aryl azo compound. The term 'azobenzene' or simply 'azo' is often used to refer to a wide class of simi ...
-based pharmacological ligands by 2-photon absorption has been described for use in
photopharmacology
Photopharmacology, an emerging approach in medicine, involves activating and deactivating photoswitchable molecules with light for target drug delivery. Clinicians use the energy of light to change the shape and chemical properties of a drug, res ...
. It allows controlling the activity of endogenous proteins in intact tissue with pharmacological selectivity in three dimensions. It can be used to study
neural circuits
A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks.
Biological neural networks have inspired th ...
and to develop drug-based non invasive phototherapies.
Optical data storage
The ability of two-photon excitation to address molecules deep within a sample without affecting other areas makes it possible to store and retrieve information in the volume of a substance rather than only on a surface as is done on the
DVD
The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any kind ...
. Therefore,
3D optical data storage has the possibility to provide media that contain
terabyte
The byte is a units of information, unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character (computing), character of text in a computer and for this ...
-level data capacities on a single disc.
Compounds
To some extent, linear and 2-photon absorption strengths are linked. Therefore, the first compounds to be studied (and many that are still studied and used in e.g. 2-photon microscopy) were standard dyes. In particular, laser dyes were used, since these have good photostability characteristics. However, these dyes tend to have 2-photon cross-sections of the order of 0.1–10 GM, much less than is required to allow simple experiments.
It was not until the 1990s that rational design principles for the construction of two-photon-absorbing molecules began to be developed, in response to a need from imaging and data storage technologies, and aided by the rapid increases in computer power that allowed quantum calculations to be made. The accurate quantum mechanical analysis of two-photon absorbance is orders of magnitude more computationally intensive than that of one-photon absorbance, requiring highly correlated calculations at very high levels of theory.
The most important features of strongly TPA molecules were found to be a long conjugation system (analogous to a large antenna) and substitution by strong donor and acceptor groups (which can be thought of as inducing nonlinearity in the system and increasing the potential for charge-transfer). Therefore, many
push-pull olefins exhibit high TPA transitions, up to several thousand GM. It is also found that compounds with a real intermediate energy level close to the "virtual" energy level can have large 2-photon cross-sections as a result of resonance enhancement. There are several databases of two-photon absorption spectra available online.
Compounds with interesting TPA properties also include various
porphyrin
Porphyrins ( ) are a group of heterocyclic macrocycle organic compounds, composed of four modified pyrrole subunits interconnected at their α carbon atoms via methine bridges (=CH−). The parent of porphyrin is porphine, a rare chemical com ...
derivatives, conjugated
polymers
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic an ...
and even
dendrimers
Dendrimers are highly ordered, branched polymeric molecules. Synonymous terms for dendrimer include arborols and cascade molecules. Typically, dendrimers are symmetric about the core, and often adopt a spherical three-dimensional morphology. The ...
. In one study a
diradical
In chemistry, a diradical is a molecular species with two electrons occupying molecular orbitals (MOs) which are degenerate. The term "diradical" is mainly used to describe organic compounds, where most diradicals are extremely reactive and i ...
resonance contribution for the compound depicted below was also linked to efficient TPA. The TPA wavelength for this compound is 1425 nanometer with observed TPA cross section of 424 GM.
:
Coefficients
The two-photon absorption coefficient is defined by the relation
so that
Where
is the two-photon absorption coefficient,
is the absorption coefficient,
is the transition rate for TPA per unit volume,
is the
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
, is the
reduced Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
,
is the photon frequency and the thickness of the slice is
.
is the number density of molecules per cm
3,
is the
photon energy
Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, ...
(J),
is the two-photon absorption cross section (cm
4s/molecule).
The SI units of the beta coefficient are m/W. If
(m/W) is multiplied by 10
−9 it can be converted to the CGS system (cal/cm s/erg).
Due to different laser pulses the TPA coefficients reported has differed as much as a factor 3. With the transition towards shorter laser pulses, from
picosecond to subpicosecond durations, noticeably reduced TPA coefficient have been obtained.
In water
Laser induced TPA in water was discovered in 1980.
Water absorbs UV radiation near 125 nm exiting the 3a1
orbital leading to
dissociation
Dissociation, in the wide sense of the word, is an act of disuniting or separating a complex object into parts. Dissociation may also refer to:
* Dissociation (chemistry), general process in which molecules or ionic compounds (complexes, or salts ...
into OH
− and H
+. Through TPA this dissociation can be achieved by two photons near 266 nm. Since water and heavy water have different vibration frequencies and inertia they also need different photon energies to achieve dissociation and have different absorption coefficients for a given photon wavelength.
A study from Jan 2002 used a femtosecond laser tuned to 0.22 Picoseconds found the coefficient of D
2O to be 42±5 10
−11(cm/W) whereas H
2O was 49±5 10
−11(cm/W).
Two-photon emission
The opposite process of TPA is two-photon emission (TPE), which is a single electron transition accompanied by the emission of a photon pair. The energy of each individual photon of the pair is not determined, while the pair as a whole conserves the transition energy. The spectrum of TPE is therefore very broad and continuous. TPE is important for applications in astrophysics, contributing to the continuum radiation from planetary
nebulae
A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming region ...
(theoretically predicted for them in and observed in ). TPE in condensed matter and specifically in semiconductors was only first observed in 2008,
with emission rates nearly 5 orders of magnitude weaker than one-photon spontaneous emission, with potential applications in
quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
.
See also
*
Two-photon circular dichroism
*
Two-photon excitation microscopy
Two-photon excitation microscopy (TPEF or 2PEF) is a fluorescence imaging technique that allows imaging of living tissue up to about one millimeter in thickness, with 0.64 μm lateral and 3.35 μm axial spatial resolution. Unlike traditional fl ...
*
Virtual particle
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...
s are in virtual state where the
probability amplitude
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density.
Probability amplitudes provide a relationship between the quan ...
is not conserved.
References
{{reflist
External links
Web-based calculator for the rate of 2-photon absorption
Nonlinear optics