# Raman scattering

"Raman Effect" redirects here. For the 2008 film, see Raman Effect (film).

Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by C. V. Raman and K. S. Krishnan in liquids,[1] and by G. Landsberg and L. I. Mandelstam in crystals.[2] The effect had been predicted theoretically by Adolf Smekal in 1923.[3]

When photons are scattered from an atom or molecule, most photons are elastically scattered (Rayleigh scattering), such that the scattered photons have the same energy (frequency and wavelength) as the incident photons. A small fraction of the scattered photons (approximately 1 in 10 million) are scattered by an excitation, with the scattered photons having a frequency different from, and usually lower than, that of the incident photons.[4] In a gas, Raman scattering can occur with a change in energy of a molecule due to a transition (see energy level). Chemists are primarily concerned with the transitional Raman effect.

## 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 (that is why in the former Soviet Union the priority of Raman 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]

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.[7]

## 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). 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 $x$, $y$, and $z$-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:

$3N-3-2 = 3N-5$

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

$3N-6$

### 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 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, $E$, of a photon is

$E=h \nu$,

where $h$ is Planck’s constant and $\nu$ 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

Other investigations carried out by Raman were: his experimental and theoretical studies on the diffraction of light by acoustic waves of ultrasonic and hypersonic frequencies (published 1934-1942), and those on the effects produced by X-rays on infrared vibrations in crystals exposed to ordinary light. In 1948 Raman, through studying the spectroscopic behaviour of crystals, approached in a new manner fundamental problems of crystal dynamics. His laboratory had been dealing with the structure and properties of diamond, the structure and optical behaviour of numerous iridescent substances (labradorite, pearly felspar, agate, opal, and pearls).

It is also possible to observe molecular vibrations by an inelastic scattering process. In inelastic scattering, an absorbed photon is re-emitted with lower energy. In Raman scattering, the difference in energy between the excitation 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. If the polarization in the molecule does not couple to these other possible polarization, 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. 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 scattering

The different possibilities of light scattering: Rayleigh scattering (no exchange of energy: incident and scattered photons have the same energy), Stokes Raman scattering (atom or molecule absorbs energy: scattered photon has less energy than the incident photon) and anti-Stokes Raman scattering (atom or molecule loses energy: scattered photon has more energy than the incident photon)

The Raman interaction leads to two possible outcomes:

• the material absorbs energy and the emitted photon has a lower energy than the absorbed photon. This outcome is labeled Stokes Raman scattering.
• 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 upper state will be less populated than the lower state. Therefore, the rate of transitions from the lower 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 (which can practically be exploited for the measurement of temperature).

### Distinction from fluorescence

The Raman effect differs from the process of fluorescence. For the latter, the incident light is completely absorbed and the system is transferred to an excited state from which it can go to various lower states only after a certain resonance lifetime. 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

[clarification needed] The distortion of a molecule in an electric field, and therefore the vibrational Raman cross section, is determined by its polarizability. A Raman transition from one state to another, and therefore a Raman shift, can be activated optically only in the presence of non-zero polarizability derivative with respect to the normal coordinate (that is, the vibration or rotation): $\partial \alpha / \partial Q \ne 0$. Stokes and Anti-Stokes lines only arise if the polarizability changes during the vibration, i.e. $\partial \alpha / \partial Q \ne 0$. Raman-active vibrations/rotations can be identified by using almost any textbook that treats quantum mechanics or group theory for chemistry. Then, Raman-active modes can be found for molecules or crystals that show symmetry by using the appropriate character table for that symmetry group.

## 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, e.g., using a third-order nonlinear susceptibility $\chi^{(3)}$.

### Need of 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.

Several tricks may be used to get a large amplitude:

- Conveniently used optically anisotropic crystals may have an equal relative wavelength

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

- Light may be pulsed, so that beats do not appear.

It is the "Impulsive Stimulated Raman Scattering (ISRS), in which the length of the pulses must be shorter than all relevant time constants. The interference of the Raman and incident light is too short to allow beats, so that it produces a frequency shift. 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 ordinary incoherent light. However, it appears in space, in excited atomic hydrogen, producing Hubble's redshift.

## 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[8] 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.

### 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.