# Raman scattering

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Raman scattering or the Raman effect is the inelastic scattering of a photon by molecules which are excited to higher energy levels. The effect was discovered in 1928 by C. V. Raman and his student K. S. Krishnan in liquids, [1] and independently by Grigory Landsberg and Leonid Mandelstam in crystals. [2] The effect had been predicted theoretically by Adolf Smekal in 1923. [3]

In chemistry, nuclear physics, and particle physics, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved. In an inelastic scattering process, some of the energy of the incident particle is lost or increased. Although the term is historically related to the concept of inelastic collision in dynamics, the two concepts are quite distinct; inelastic collision in dynamics refers to processes in which the total macroscopic kinetic energy is not conserved. In general, scattering due to inelastic collisions will be inelastic, but, since elastic collisions often transfer kinetic energy between particles, scattering due to elastic collisions can also be inelastic, as in Compton scattering.

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and always moves at the speed of light within a vacuum.

Sir Chandrashekhara Venkata Raman was an Indian physicist born in the former Madras Province in India, who carried out ground-breaking work in the field of light scattering, which earned him the 1930 Nobel Prize for Physics. He discovered that when light traverses a transparent material, some of the deflected light changes wavelength and amplitude. This phenomenon, subsequently known as Raman scattering, results from the Raman effect. In 1954, the Indian government honoured him with India's highest civilian award, the Bharat Ratna.

## Contents

When photons are scattered by a material, most of them are elastically scattered (Rayleigh scattering), such that the scattered photons have the same energy (frequency and wavelength) as the incident photons but different direction. However, a small fraction of the scattered photons (approximately 1 in 10 million) are scattered inelastically, with the scattered photons having an energy different from, and usually lower than, those of the incident photons—these are Raman scattered photons. [4] Because of conservation of energy, the material either gains or loses energy in the process. Typically this is vibrational energy and the incident photons are of visible light, although rotational energy (if gas samples are used) and electronic energy levels (if an X-ray source is used) may also be probed. The Raman effect forms the basis for Raman spectroscopy which is used by chemists and physicists to gain information about materials.

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more paths due to localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections.

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified. Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process where the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped."

Rayleigh scattering, named after the British physicist Lord Rayleigh, is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. Rayleigh scattering does not change the state of material and is, hence, a parametric process. The particles may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, and is most prominently seen in gases. Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation we see as scattered light. This radiation is an integral part of the photon and no excitation or deexcitation occurs.

## History

The inelastic scattering of light was predicted by Adolf Smekal in 1923 [3] (and in German-language literature it may be referred to as the Smekal-Raman effect [5] ). In 1922, Indian physicist C. V. Raman published his work on the "Molecular Diffraction of Light," the first of a series of investigations with his collaborators that ultimately led to his discovery (on 28 February 1928) of the radiation effect that bears his name. The Raman effect was first reported by C. V. Raman and K. S. Krishnan, [1] and independently by Grigory Landsberg and Leonid Mandelstam, on 21 February 1928. In the former Soviet Union, Raman's contribution was always disputed; thus in Russian scientific literature this effect is usually referred to as "combination scattering" or "combinatory scattering". Raman received the Nobel Prize in 1930 for his work on the scattering of light. [6]

Adolf Gustav Stephan Smekal was an Austrian theoretical physicist, with interests in solid state physics, known for the prediction of the inelastic scattering of photons.

Sir Kariamanickam Srinivasa Krishnan, FRS, was an Indian physicist. He was a co-discoverer of Raman scattering, for which his mentor C. V. Raman was awarded the 1930 Nobel Prize in Physics.

Grigory Samuilovich Landsberg was a Soviet physicist who worked in the fields of optics and spectroscopy. Together with Leonid Mandelstam he co-discoverer inelastic combinatorial scattering of light, which is used now in Raman spectroscopy.

Although modern Raman spectroscopy nearly always involves the use of lasers, which were not available until more than three decades later, Raman and Krishnan used a mercury lamp and photographic plates to record spectra. [7]

A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term "laser" originated as an acronym for "Light Amplification by Stimulated Emission of Radiation". The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow.

Photographic plates preceded photographic film as a capture medium in photography. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinner than common window glass, instead of a clear plastic film.

In 1998 the Raman effect was designated a National Historic Chemical Landmark by the American Chemical Society in recognition of its significance as a tool for analyzing the composition of liquids, gases, and solids. [8]

The National Historic Chemical Landmarks program was launched by the American Chemical Society in 1992 to recognize significant achievements in the history of chemistry and related professions. The program celebrates the centrality of chemistry. The designation of such generative achievements in the history of chemistry demonstrates how chemists have benefited society by fulfilling the ACS vision: Improving people's lives through the transforming power of chemistry. The program occasionally designates International Historic Chemical Landmarks to commemorate "chemists and chemistry from around the world that have had a major impact in the United States".

The American Chemical Society (ACS) is a scientific society based in the United States that supports scientific inquiry in the field of chemistry. Founded in 1876 at New York University, the ACS currently has nearly 157,000 members at all degree levels and in all fields of chemistry, chemical engineering, and related fields. It is the world's largest scientific society by membership. The ACS is a 501(c)(3) non-profit organization and holds a congressional charter under Title 36 of the United States Code. Its headquarters are located in Washington, D.C., and it has a large concentration of staff in Columbus, Ohio.

## Description

### Degrees of freedom

For any given chemical compound, there are a total of 3N degrees of freedom, where N is the number of atoms in the compound. This number arises from the ability of each atom in a molecule to move in three different directions (x, y, and z). [9] When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3N degrees of freedom are partitioned into molecular translational, rotational, and vibrational motion. Three of the degrees of freedom correspond to translational motion of the molecule as a whole (along each of the three spatial dimensions). Similarly, three degrees of freedom correspond to rotations of the molecule about the ${\displaystyle x}$, ${\displaystyle y}$, and ${\displaystyle z}$-axes. Linear molecules only have two rotations because rotations along the bond axis do not change the positions of the atoms in the molecule. The remaining degrees of freedom correspond to molecular vibrational modes. These modes include stretching and bending motions of the chemical bonds of the molecule. For a linear molecule, the number of vibrational modes is: [9]

In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and degrees of freedom of the system, are the dimensions of the phase space.

An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small; typical sizes are around 100 picometers.

In chemistry, the linear molecular geometry describes the geometry around a central atom bonded to two other atoms placed at a bond-angle of 180°. Linear organic molecules, such as acetylene (HC≡CH), are often described by invoking sp orbital hybridization for their carbon centers.

${\displaystyle 3N-3-2=3N-5}$

whereas for a non-linear molecule the number of vibrational modes are

${\displaystyle 3N-6}$

### Molecular vibrations and infrared radiation

The frequencies of molecular vibrations range from less than 1012 to approximately 1014 Hz. These frequencies correspond to radiation in the infrared (IR) region of the electromagnetic spectrum. At any given instant, each molecule in a sample has a certain amount of vibrational energy. However, the amount of vibrational energy that a molecule has continually changes due to collisions and other interactions with other molecules in the sample.

At room temperature, most of the molecules will be in the lowest energy state, which is known as the ground state. A few molecules will be in higher energy states, which are known as excited states. The fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution. Performing such a calculation shows that, for relatively low temperatures (such as those used for most routine spectroscopy), most of the molecules occupy the ground vibrational state. Such a molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy. This is the mechanism by which IR spectroscopy operates: infrared radiation is passed through the sample, and the intensity of the transmitted light is compared with that of the incident light. A reduction in intensity at a given wavelength of light indicates the absorption of energy by a vibrational transition. The energy, ${\displaystyle E}$, of a photon is

${\displaystyle E=h\nu }$,

where ${\displaystyle h}$ is Planck's constant and ${\displaystyle \nu }$ is the frequency of the radiation. Thus, the energy required for such a transition may be calculated if the frequency of the incident radiation is known.

### Raman scattering

It is also possible to observe molecular vibrations by an inelastic scattering process. In inelastic (Raman) scattering, an absorbed photon is re-emitted with lower energy; the difference in energy between the incident photons and scattered photons corresponds to the energy required to excite a molecule to a higher vibrational mode.

Typically, in Raman spectroscopy high intensity laser radiation with wavelengths in either the visible or near-infrared regions of the spectrum is passed through a sample. Photons from the laser beam produce an oscillating polarization in the molecules, exciting them to a virtual energy state. The oscillating polarization of the molecule can couple with other possible polarizations of the molecule, including vibrational and electronic excitations.[ citation needed ] If the polarization in the molecule does not couple to these other possible polarizations, then it will not change the vibrational state that the molecule started in and the scattered photon will have the same energy as the original photon.[ citation needed ] This type of scattering is known as Rayleigh scattering.

When the polarization in the molecules couples to a vibrational state that is higher in energy than the state they started in, then the original photon and the scattered photon differ in energy by the amount required to vibrationally excite the molecule. In perturbation theory, the Raman effect corresponds to the absorption and subsequent emission of a photon via an intermediate quantum state of a material. The intermediate state can be either a "real", i.e. stationary state, or a virtual state.

### Stokes and anti-Stokes

The Raman interaction leads to two possible outcomes:

• the material absorbs energy and the emitted photon has a lower energy than the incident photon. This outcome is labeled Stokes Raman scattering in honor of George Stokes who showed in 1852 that fluorescence is due to light emission at longer wavelength (now known to correspond to lower energy) than the absorbed incident light.
• the material loses energy and the emitted photon has a higher energy than the absorbed photon. This outcome is labeled anti-Stokes Raman scattering.

The energy difference between the absorbed and emitted photon corresponds to the energy difference between two resonant states of the material and is independent of the absolute energy of the photon.

The spectrum of the scattered photons is termed the Raman spectrum. It shows the intensity of the scattered light as a function of its frequency difference Δν to the incident photons. The locations of corresponding Stokes and anti-Stokes peaks form a symmetric pattern around Δν=0. The frequency shifts are symmetric because they correspond to the energy difference between the same upper and lower resonant states. The intensities of the pairs of features will typically differ, though. They depend on the populations of the initial states of the material, which in turn depend on the temperature. In thermodynamic equilibrium, the lower state will be more populated than the upper state. Therefore, the rate of transitions from the more populated lower state to the upper state (Stokes transitions) will be higher than in the opposite direction (anti-Stokes transitions). Correspondingly, Stokes scattering peaks are stronger than anti-Stokes scattering peaks. Their ratio depends on the temperature, and can therefore be exploited to measure it.

### Distinction from fluorescence

The Raman effect differs from the process of fluorescence in that it is a scattering process. For fluorescence, the incident light is completely absorbed, transferring the system to an excited state. After a certain resonance lifetime, the system de-excites to lower energy states via emission of photons. The result of both processes is in essence the same: A photon with a frequency different from that of the incident photon is produced and the molecule is brought to a higher or lower energy level. But the major difference is that the Raman effect can take place for any frequency of incident light. In contrast to the fluorescence effect, the Raman effect is therefore not a resonant effect. In practice, this means that a fluorescence peak is anchored at a specific frequency, whereas a Raman peak maintains a constant separation from the excitation frequency.

### Selection rules

A Raman transition from one state to another is allowed only if the molecular polarizability of those states is different. For a vibration, this means that the derivative of the polarizability with respect to the normal coordinate associated to the vibration is non-zero: ${\displaystyle {\frac {\partial \alpha }{\partial Q}}\neq 0}$. In general, a normal mode is Raman active if it transforms with the same symmetry of the quadratic forms (${\displaystyle x^{2},y^{2},z^{2},xy,xz,yz}$), which can be verified from the character table of the molecule's symmetry group.

The specific selection rules state that the allowed rotational transitions are ${\displaystyle \Delta J=\pm 2}$, where ${\displaystyle J}$ is the rotational state.

The allowed vibrational transitions are ${\displaystyle \Delta \nu =\pm 1}$, where ${\displaystyle \nu }$ is the vibrational state.

## Stimulated Raman scattering and Raman amplification

The Raman-scattering process as described above takes place spontaneously; i.e., in random time intervals, one of the many incoming photons is scattered by the material. This process is thus called spontaneous Raman scattering.

On the other hand, stimulated Raman scattering can take place when some Stokes photons have previously been generated by spontaneous Raman scattering (and somehow forced to remain in the material), or when deliberately injecting Stokes photons ("signal light") together with the original light ("pump light"). In that case, the total Raman-scattering rate is increased beyond that of spontaneous Raman scattering: pump photons are converted more rapidly into additional Stokes photons. The more Stokes photons are already present, the faster more of them are added. Effectively, this amplifies the Stokes light in the presence of the pump light, which is exploited in Raman amplifiers and Raman lasers.

Stimulated Raman scattering is a nonlinear-optical effect. It can be described using a third-order nonlinear susceptibility ${\displaystyle \chi ^{(3)}}$.

### Requirement for space-coherence

Suppose that the distance between two points A and B of an exciting beam is x. Generally, as the exciting frequency is not equal to the scattered Raman frequency, the corresponding relative wavelengths λ and λ' are not equal. Thus, a phase-shift Θ = 2πx(1/λ − 1/λ') appears. For Θ = π, the scattered amplitudes are opposite, so that the Raman scattered beam remains weak.

• A crossing of the beams may limit the path x.

Several tricks may be used to get a larger amplitude:

• In an optically anisotropic crystal, a light ray may have two modes of propagation with different polarizations and different indices of refraction. If energy may be transferred between these modes by a quadrupolar (Raman) resonance, phases remain coherent along the whole path, transfer of energy may be large. It is an Optical parametric generation.
• Light may be pulsed, so that beats do not appear. In Impulsive Stimulated Raman Scattering (ISRS), [10] [11] [12] [13] the length of the pulses must be shorter than all relevant time constants. [14] Interference of Raman and incident lights is too short to allow beats, so that it produces a frequency shift roughly, in best conditions, inversely proportional to cube of length of pulses.

In labs, femtosecond laser pulses must be used because the ISRS becomes very weak if the pulses are too long. Thus ISRS cannot be observed using nanosecond pulses making ordinary time-incoherent light.

## Inverse Raman effect

The inverse Raman effect in optics (the branch of physics which deals with the properties and behavior of light) is a form of Raman scattering. It was first noted by W.J.Jones and B.P. Stoicheff.

If a material is simultaneously irradiated by intense monochromatic light of frequency νL (typically a laser beam) and light of a continuum of higher frequencies, among the possibilities for light scattering are:

• from the monochromatic beam at νL to the continuum at νLM (anti-Stokes Raman scattering)
• from the continuum at νLM to the monochromatic beam at νL (Stokes Raman scattering)

where νM is a Raman frequency of the material. The strength of these two scatterings depends (among other things) on the energy levels of the material, their occupancy, and the intensity of the continuum. In some circumstances Stokes scattering can exceed anti-Stokes scattering; in these cases the continuum (on leaving the material) is observed to have an absorption line (a dip in intensity) at νLM. This phenomenon is referred to as the inverse Raman effect; the application of the phenomenon is referred to as inverse Raman spectroscopy , and a record of the continuum is referred to as an inverse Raman spectrum.

In the original description of the inverse Raman effect, [15] the authors discuss both absorption from a continuum of higher frequencies and absorption from a continuum of lower frequencies. They note that absorption from a continuum of lower frequencies will not be observed if the Raman frequency of the material is vibrational in origin and if the material is in thermal equilibrium.

## Applications

Raman spectroscopy employs the Raman effect for substances analysis. The spectrum of the Raman-scattered light depends on the molecular constituents present and their state, allowing the spectrum to be used for material identification and analysis. Raman spectroscopy is used to analyze a wide range of materials, including gases, liquids, and solids. Highly complex materials such as biological organisms and human tissue [16] can also be analyzed by Raman spectroscopy.

For solid materials, Raman scattering is used as a tool to detect high-frequency phonon and magnon excitations.

Raman lidar is used in atmospheric physics to measure the atmospheric extinction coefficient and the water vapour vertical distribution.

Stimulated Raman transitions are also widely used for manipulating a trapped ion's energy levels, and thus basis qubit states.

Raman spectroscopy can be used to determine the force constant and bond length for molecules that do not have an infrared absorption spectrum.

Raman amplification is used in optical amplifiers.

The Raman effect is also involved in producing the appearance of the blue sky (see Rayleigh Effect: 'Rayleigh scattering of molecular nitrogen and oxygen in the atmosphere includes elastic scattering as well as the inelastic contribution from rotational Raman scattering in air').

### Supercontinuum generation

For high-intensity continuous wave (CW) lasers, SRS can be used to produce broad bandwidth spectra. This process can also be seen as a special case of four-wave mixing, wherein the frequencies of the two incident photons are equal and the emitted spectra are found in two bands separated from the incident light by the phonon energies. The initial Raman spectrum is built up with spontaneous emission and is amplified later on. At high pumping levels in long fibers, higher-order Raman spectra can be generated by using the Raman spectrum as a new starting point, thereby building a chain of new spectra with decreasing amplitude. The disadvantage of intrinsic noise due to the initial spontaneous process can be overcome by seeding a spectrum at the beginning, or even using a feedback loop as in a resonator to stabilize the process. Since this technology easily fits into the fast evolving fiber laser field and there is demand for transversal coherent high-intensity light sources (i.e., broadband telecommunication, imaging applications), Raman amplification and spectrum generation might be widely used in the near-future.

## Related Research Articles

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of LIGO and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency.

In physics, attenuation or, in some contexts, extinction is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates.

Raman spectroscopy ; named after Indian physicist Sir C. V. Raman) is a spectroscopic technique used to observe vibrational, rotational, and other low-frequency modes in a system. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified.

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify the elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

Fluorescence spectroscopy is a type of electromagnetic spectroscopy that analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electrons in molecules of certain compounds and causes them to emit light; typically, but not necessarily, visible light. A complementary technique is absorption spectroscopy. In the special case of single molecule fluorescence spectroscopy, intensity fluctuations from the emitted light are measured from either single fluorophores, or pairs of fluorophores.

In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied after the illumination of a material occurs, but in principle, the technique can be applied to any process that leads to a change in properties of a material. With the help of pulsed lasers, it is possible to study processes that occur on time scales as short as 10−16 seconds.

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy where rotational, vibrational and electronic energy changes occur simultaneously.

Brillouin scattering, named after Léon Brillouin, refers to the interaction of light and material waves within a medium. It is mediated by the refractive index dependence on the material properties of the medium; as described in optics, the index of refraction of a transparent material changes under deformation.

Resonance Raman spectroscopy is a Raman spectroscopy technique in which the incident photon energy is close in energy to an electronic transition of a compound or material under examination. The frequency coincidence can lead to greatly enhanced intensity of the Raman scattering, which facilitates the study of chemical compounds present at low concentrations.

High resolution electron energy loss spectroscopy (HREELS) is a tool used in surface science. The inelastic scattering of electrons from surfaces is utilized to study electronic excitations or vibrational modes of the surface or of molecules adsorbed to a surface. Hence in contrast to other electron energy loss spectroscopies (EELS) HREELS deals with small energy losses in the range of 10−3 eV to 1 eV. It plays an important role in the investigation of surface structure, catalysis, dispersion of surface phonons and the monitoring of epitaxial growth.

Coherent anti-Stokes Raman spectroscopy, also called Coherent anti-Stokes Raman scattering spectroscopy (CARS), is a form of spectroscopy used primarily in chemistry, physics and related fields. It is sensitive to the same vibrational signatures of molecules as seen in Raman spectroscopy, typically the nuclear vibrations of chemical bonds. Unlike Raman spectroscopy, CARS employs multiple photons to address the molecular vibrations, and produces a coherent signal. As a result, CARS is orders of magnitude stronger than spontaneous Raman emission. CARS is a third-order nonlinear optical process involving three laser beams: a pump beam of frequency ωp, a Stokes beam of frequency ωS and a probe beam at frequency ωpr. These beams interact with the sample and generate a coherent optical signal at the anti-Stokes frequency (ωprpS). The latter is resonantly enhanced when the frequency difference between the pump and the Stokes beams (ωpS) coincides with the frequency of a Raman resonance, which is the basis of the technique's intrinsic vibrational contrast mechanism.

Ultrafast laser spectroscopy is a spectroscopic technique that uses ultrashort pulse lasers for the study of dynamics on extremely short time scales. Different methods are used to examine dynamics of charge carriers, atoms and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges; some common methods are listed below.

Two-photon absorption (TPA) is the absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy, most commonly an excited electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, typically several orders of magnitude weaker than linear absorption at low light intensities. It differs from linear absorption in that the optical transition rate due to TPA depends on the square of the light intensity, thus it is a nonlinear optical process, and can dominate over linear absorption at high intensities.

X-ray Raman scattering (XRS) is non-resonant inelastic scattering of x-rays from core electrons. It is analogous to vibrational Raman scattering, which is a widely used tool in optical spectroscopy, with the difference being that the wavelengths of the exciting photons fall in the x-ray regime and the corresponding excitations are from deep core electrons.

Spatially offset Raman spectroscopy (SORS) is a variant of Raman spectroscopy that allows highly accurate chemical analysis of objects beneath obscuring surfaces, such as tissue, coatings and bottles. Examples of uses include analysis of: bone beneath skin, tablets inside plastic bottles, explosives inside containers and counterfeit tablets inside blister packs. There have also been advancements in the development of deep non-invasive medical diagnosis using SORS with the hopes of being able to detect breast tumors.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

Resonant inelastic X-ray scattering (RIXS) is an X-ray spectroscopy technique used to investigate the electronic structure of molecules and materials.

Rotating-polarization coherent anti-Stokes Raman spectroscopy, (RP-CARS) is a particular implementation of the coherent anti-Stokes Raman spectroscopy microscopy (CARS). RP-CARS takes advantage of polarization-dependent selection rules in order to gain information about molecule orientation anisotropy and direction within the optical point spread function.

Brillouin spectroscopy is an empirical spectroscopy technique which allows for the determination of elastic moduli for a given material. The technique uses inelastic scattering of light when it encounters acoustic phonons in a crystal, a process known as Brillouin scattering, to determine phonon energies and therefore interatomic potentials of a material. The scattering occurs when an electromagnetic wave interacts with a density wave, photon-phonon scattering.

Stimulated Raman spectroscopy, also referred to as stimulated raman scattering (SRS) is a form of spectroscopy employed in physics, chemistry, biology, and other fields. The basic mechanism resembles that of spontaneous Raman spectroscopy: a pump photon, of the angular frequency , which is absorbed by a molecule has some small probability of inducing some vibrational transition, as opposed to inducing a simple Rayleigh transition. This will then result in the molecule's emission of a photon at a shifted frequency. However, SRS, as opposed to spontaneous Raman spectroscopy, is a third-order non-linear phenomenon involving a second photon—the Stokes photon of angular frequency —which stimulates a specific transition. When the difference in frequency between both photons resembles that of a specific vibrational transition the occurrence of this transition is resonantly enhanced. In SRS, the signal is equivalent to changes in the intensity of the pump and Stokes beams. Employing a pump laser beam of a constant frequency and a Stokes laser beam of a scanned frequency allows for the unraveling of the spectral fingerprint of the molecule. This spectral fingerprint differs from those obtained by other spectroscopy methods such as Rayleigh scattering as the Raman transitions confer to different exclusion rules than those which apply for Rayleigh transitions.

## References

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