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800:. A molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy, which falls in the terahertz or infrared range. This forms the basis of infrared spectroscopy. Alternatively, the same vibrational excitation can be produced by an inelastic scattering process. This is called Stokes Raman scattering, by analogy with the
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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
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In the original description of the inverse Raman effect, 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
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which corresponds to the energy of the exciting laser photons. Absorption of a photon excites the molecule to the imaginary state and re-emission leads to Raman or
Rayleigh scattering. In all three cases the final state has the same electronic energy as the initial state but is higher in vibrational
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Light may be pulsed, so that beats do not appear. In
Impulsive Stimulated Raman Scattering (ISRS), the length of the pulses must be shorter than all relevant time constants. Interference of Raman and incident lights is too short to allow beats, so that it produces a frequency shift roughly, in best
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In contrast to IR spectroscopy, where there is a requirement for a change in dipole moment for vibrational excitation to take place, Raman scattering requires a change in polarizability. A Raman transition from one state to another is allowed only if the molecular polarizability of those states is
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the intensity of Raman scattering when the analyzer is aligned with the polarization of the incident laser. When polarized light interacts with a molecule, it distorts the molecule which induces an equal and opposite effect in the plane-wave, causing it to be rotated by the difference between the
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A classical physics based model is able to account for Raman scattering and predicts an increase in the intensity which scales with the fourth-power of the light frequency. Light scattering by a molecule is associated with oscillations of an induced electric dipole. The oscillating electric field
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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
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line. 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
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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,
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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
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The elastic light scattering phenomena called
Rayleigh scattering, in which light retains its energy, was described in the 19th century. The intensity of Rayleigh scattering is about 10 to 10 compared to the intensity of the exciting source. In 1908, another form of elastic scattering, called
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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 16 February 1928) of the radiation effect that bears his name. The Raman effect was first reported by Raman and his coworker
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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
257:, and therefore color) as the incident photons, but different direction. Rayleigh scattering usually has an intensity in the range 0.1% to 0.01% relative to that of a radiation source. An even smaller fraction of the scattered photons (about 1 in a million) can be scattered
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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
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on 21 February 1928 (5 days after Raman and
Krishnan). In the former Soviet Union, Raman's contribution was always disputed; thus in Russian scientific literature the effect is usually referred to as "combination scattering" or "combinatory scattering". Raman received the
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and Raman activity which may assist in assigning peaks in Raman spectra. Light polarized in a single direction only gives access to some Raman–active modes, but rotating the polarization gives access to other modes. Each mode is separated according to its symmetry.
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component of electromagnetic radiation may bring about an induced dipole in a molecule which follows the alternating electric field which is modulated by the molecular vibrations. Oscillations at the external field frequency are therefore observed along with
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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 that are already present, the faster more of them are added. Effectively, this
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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
502:, 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
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to record spectra. Early spectra took hours or even days to acquire due to weak light sources, poor sensitivity of the detectors and the weak Raman scattering cross-sections of most materials. The most common modern detectors are
1283:{\displaystyle {\frac {I_{\text{Stokes}}}{I_{\text{anti-Stokes}}}}={\frac {({\tilde {\nu }}_{0}-{\tilde {\nu }}_{M})^{4}}{({\tilde {\nu }}_{0}+{\tilde {\nu }}_{M})^{4}}}\exp \left({\frac {hc\,{\tilde {\nu }}_{M}}{k_{B}T}}\right)}
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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.
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is a quantum number. Since the selection rules for Raman and infrared absorption generally dictate that only fundamental vibrations are observed, infrared excitation or Stokes Raman excitation results in an energy change of
494:. This number arises from the ability of each atom in a molecule to move in three dimensions. When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3
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Kosloff, Ronnie; Hammerich, Audrey Dell; Tannor, David (1992). "Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control".
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energy in the case of Stokes Raman scattering, lower in the case of anti-Stokes Raman scattering or the same in the case of
Rayleigh scattering. Normally this is thought of in terms of wavenumbers, where
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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.
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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
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1824:. 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 ν
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2551:. 75th Birthday of Christian Colliex, 85th Birthday of Archie Howie, and 75th Birthday of Hannes Lichte / PICO 2019 - Fifth Conference on Frontiers of Aberration Corrected Electron Microscopy.
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1956:: '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').
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Itoh, Yuki; Hasegawa, Takeshi (2 May 2012). "Polarization
Dependence of Raman Scattering from a Thin Film Involving Optical Anisotropy Theorized for Molecular Orientation Analysis".
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The energy range for vibrations is in the range of approximately 5 to 3500 cm. The fraction of molecules occupying a given vibrational mode at a given temperature follows a
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is the rotational state. This generally is only relevant to molecules in the gas phase where the Raman linewidths are small enough for rotational transitions to be resolved.
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Raman scattering generally gives information about vibrations within a molecule. In the case of gases, information about rotational energy can also be gleaned. For solids,
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to the incident photons, more commonly called a Raman shift. The locations of corresponding Stokes and anti-Stokes peaks form a symmetric pattern around the
Rayleigh
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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:
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Weiner, A. M.; Wiederrecht, Gary P.; Nelson, Keith A.; Leaird, D. E. (1991). "Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy".
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Krivanek, O. L.; Dellby, N.; Hachtel, J. A.; Idrobo, J. -C.; Hotz, M. T.; Plotkin-Swing, B.; Bacon, N. J.; Bleloch, A. L.; Corbin, G. J. (1 August 2019).
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as an exciting light source. Because lasers were not available until more than three decades after the discovery of the effect, Raman and
Krishnan used a
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including gases, liquids, and solids. Highly complex materials such as biological organisms and human tissue can also be analyzed by Raman spectroscopy.
1875:, in which 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
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261:, with the scattered photons having an energy different (usually lower) from those of the incident photons—these are Raman scattered photons. Because of
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Voehringer, Peter; Scherer, Norbert F. (1995). "Transient
Grating Optical Heterodyne Detected Impulsive Stimulated Raman Scattering in Simple Liquids".
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A selection rule relevant only to ordered solid materials states that only phonons with zero phase angle can be observed by IR and Raman, except when
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Iliev, M. N.; Abrashev, M. V.; Laverdiere, J.; Jandi, S.; et al. (16 February 2006). "Distortion-dependent Raman spectra and mode mixing in RMnO
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rather than light. An increase in photon energy which leaves the molecule in a lower vibrational energy state is called anti-Stokes scattering.
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The effect is exploited by chemists and physicists to gain information about materials for a variety of purposes by performing various forms of
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is the intensity of Raman scattering when the analyzer is rotated 90 degrees with respect to the incident light's polarization axis, and
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The following focuses on the theory of normal (non-resonant, spontaneous, vibrational) Raman scattering of light by discrete molecules.
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is given for anti-Stokes. When the exciting laser energy corresponds to an actual electronic excitation of the molecule then the
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in 1923 and in older German-language literature it has been referred to as the Smekal-Raman-Effekt. In 1922, Indian physicist
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is used in atmospheric physics to measure the atmospheric extinction coefficient and the water vapour vertical distribution.
1757:. Generally, as the exciting frequency is not equal to the scattered Raman frequency, the corresponding relative wavelengths
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816:(now known to correspond to lower energy) than the absorbed incident light. Conceptually similar effects can be caused by
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Jones, W. J.; Stoicheff, B. P. (30 November 1964). "Inverse Raman Spectra: Induced Absorption at Optical Frequencies".
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Dhar, Lisa; Rogers, John A.; Nelson, Keith A. (1994). "Time-resolved vibrational spectroscopy in the impulsive limit".
719:{\displaystyle E_{n}=h\left(n+{1 \over 2}\right)\nu =h\left(n+{1 \over 2}\right){1 \over {2\pi }}{\sqrt {k \over m}}\!}
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For high-intensity continuous wave (CW) lasers, stimulated Raman scattering can be used to produce a broad bandwidth
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Stimulated Raman transitions are also widely used for manipulating a trapped ion's energy levels, and thus basis
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Light has a certain probability of being scattered by a material. When photons are scattered, most of them are
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Lamb, G. L. (1971). "Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium".
1342:. In general, a normal mode is Raman active if it transforms with the same symmetry of the quadratic forms
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in recognition of its significance as a tool for analyzing the composition of liquids, gases, and solids.
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2356:"Raman Microspectroscopic Imaging of Binder Remnants in Historical Mortars Reveals Processing Conditions"
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Monitoring the polarization of the scattered photons is useful for understanding the connections between
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2985:"Live-Cell Bioorthogonal Chemical Imaging: Stimulated Raman Scattering Microscopy of Vibrational Probes"
1468:, which states that vibrational modes cannot be both IR and Raman active, applies to certain molecules.
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is conceptually similar but involves excitation of electronic, rather than vibrational, energy levels.
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regarding molecular vibrations apply to Raman scattering although the selection rules are different.
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Inaugural Address delivered to the South Indian Science Association on Friday, the 16th March, 1928
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is the wavenumber of the vibrational transition. Thus Stokes scattering gives a wavenumber of
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Wei, Lu; Hu, Fanghao; Chen, Zhixing; Shen, Yihui; Zhang, Luyuan; Min, Wei (16 August 2016).
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For solid materials, Raman scattering is used as a tool to detect high-frequency phonon and
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1053:. It shows the intensity of the scattered light as a function of its frequency difference
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when anharmonicity is important. The vibrational energy levels according to the QHO are
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Schematic of a dispersive Raman spectroscopy setup in a 180° backscattering arrangement.
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The inverse Raman effect is a form of Raman scattering first noted by W. J. Jones and
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of the molecule's point group. As with IR spectroscopy, only fundamental excitations (
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for his discovery of Raman scattering. The effect had been predicted theoretically by
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The Raman effect is also involved in producing the appearance of the blue sky (see
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Molecular vibrational energy is known to be quantized and can be modeled using the
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orientation of the molecule and the angle of polarization of the light wave. If
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The specific selection rules state that the allowed rotational transitions are
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Raman spectroscopy has been used to chemically image small molecules, such as
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K. S. Krishnan; Raman, C. V. (1928). "The Negative Absorption of Radiation".
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Suppose that the distance between two points A and B of an exciting beam is
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of the molecule. For a linear molecule, the number of vibrational modes is 3
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the Stokes light in the presence of the pump light, which is exploited in
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284:, in addition to other possibilities. More complex techniques involving
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Singh, R. (2002). "C. V. Raman and the Discovery of the Raman Effect".
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3050:. Graduate Texts in Physics (4 ed.). Springer. pp. 285–288.
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Everall, Neil J. (2002). "Raman Spectroscopy of the Condensed Phase".
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and photomultiplier tubes were common prior to the adoption of CCDs.
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conditions, inversely proportional to the cube of the pulse length.
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degrees of freedom are partitioned into molecular translational,
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Prof. R. W. Wood Demonstrating the New "Raman Effect" in Physics
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resulting from the external field and normal mode vibrations.
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Rotating-polarization coherent anti-Stokes Raman spectroscopy
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Explanation from Hyperphysics in Astronomy section of gsu.edu
295:, who discovered it in 1928 with assistance from his student
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of scattering between two electrons by emission of a virtual
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material is vibrational in origin and if the material is in
1335:{\displaystyle {\frac {\partial \alpha }{\partial Q}}\neq 0}
787:{\displaystyle E=h\nu ={h \over {2\pi }}{\sqrt {k \over m}}}
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Modern Raman spectroscopy nearly always involves the use of
265:, the material either gains or loses energy in the process.
2966:"Painless laser device could spot early signs of disease"
249:), such that the scattered photons have the same energy (
2112:
Smekal, A. (1923). "Zur Quantentheorie der Dispersion".
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Keresztury, Gábor (2002). "Raman Spectroscopy: Theory".
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The symmetry of a vibrational mode is deduced from the
960:{\displaystyle {\tilde {\nu }}_{0}-{\tilde {\nu }}_{M}}
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Scattering, absorption and radiative transfer (optics)
1840:; the application of the phenomenon is referred to as
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Several tricks may be used to get a larger amplitude:
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Weber, Alfons (2002). "Raman Spectroscopy of Gases".
1871:. This process can also be seen as a special case of
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The spectrum of the scattered photons is termed the
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A short description of spontaneous Raman scattering
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Stimulated Raman scattering and Raman amplification
335:The inelastic scattering of light was predicted by
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832:Raman scattering is conceptualized as involving a
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272:. Many other variants of Raman spectroscopy allow
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365:in 1930 for his work on the scattering of light.
291:The Raman effect is named after Indian scientist
2719:"What is polarised Raman spectroscopy? - HORIBA"
1927:Raman spectroscopy can be used to determine the
2647:perovskites (R=La,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Y)".
2545:"Progress in ultrahigh energy resolution EELS"
1963:, in biological systems by a vibrational tag.
479:For any given molecule, there are a total of 3
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2697:(4th ed.). McGraw–Hill. pp. 117–8.
2693:Banwell, Colin N.; McCash, Elaine M. (1994).
276:to be examined, if gas samples are used, and
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8:
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1694:, then the vibrations at that frequency are
1599:{\displaystyle \rho ={\frac {I_{r}}{I_{u}}}}
1421:{\displaystyle (x^{2},y^{2},z^{2},xy,xz,yz)}
288:, multiple laser beams and so on are known.
234:are shifted to lower energy. This is called
2738:Journal of the Optical Society of America B
1935:for molecules that do not have an infrared
1784:A crossing of the beams may limit the path
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1698:; meaning they are not totally symmetric.
475:Degrees of freedom (physics and chemistry)
461:modes may also be observed. The basics of
368:In 1998 the Raman effect was designated a
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3102:Raman Effect: fingerprinting the universe
3082:Raman Spectroscopy – Tutorial at Kosi.com
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386:Raman spectroscopy § Instrumentation
16:Inelastic scattering of photons by matter
2433:Raman spectroscopy for chemical analysis
2200:Raman, C. V. (1928). "A new radiation".
1687:{\displaystyle \rho \geq {\frac {3}{4}}}
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314:
3152:Coherent anti-Stokes Raman spectroscopy
2393:
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1979:Coherent anti-Stokes Raman spectroscopy
23:
2695:Fundamentals of Molecular Spectroscopy
1895:Raman spectroscopy § Applications
7:
3329:
2494:Handbook of Vibrational Spectroscopy
2466:Handbook of Vibrational Spectroscopy
2089:Handbook of Vibrational Spectroscopy
1985:Coherent Raman Scattering Microscopy
3182:Surface-enhanced Raman spectroscopy
3172:Spatially offset Raman spectroscopy
2602:The Journal of Physical Chemistry A
2526:(Benjamin/Cummings 1982), pp.646-7
2435:. New York: John Wiley & Sons.
2354:Thomas Schmid; Petra Dariz (2019).
2038:Surface Enhanced Raman Spectroscopy
1765:are not equal. Thus, a phase-shift
902:{\displaystyle {\tilde {\nu }}_{M}}
873:is the wavenumber of the laser and
866:{\displaystyle {\tilde {\nu }}_{0}}
370:National Historic Chemical Landmark
230:as incident photons from a visible
3233:Stimulated Raman adiabatic passage
2496:. Vol. 1. Chichester: Wiley.
2468:. Vol. 1. Chichester: Wiley.
2091:. Vol. 1. Chichester: Wiley.
1478:
1439:
1317:
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14:
2862:The Journal of Physical Chemistry
1739:Stimulated Raman scattering is a
1457:{\displaystyle \Delta \nu =\pm 1}
1428:, which can be verified from the
3328:
3317:
3316:
2001:List of surface analysis methods
812:in 1852, with light emission at
398:published by Raman and Krishnan.
186:
31:
3192:Transmission Raman spectroscopy
3187:Tip-enhanced Raman spectroscopy
3072:Raman Effect - Classical Theory
2274:"C. V. Raman: The Raman Effect"
1747:Requirement for space-coherence
834:virtual electronic energy level
2562:10.1016/j.ultramic.2018.12.006
2402:. John Wiley & Sons, Ltd.
2059:Harris and Bertolucci (1989).
1496:{\displaystyle \Delta J=\pm 2}
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1116:
1106:
1062:depend on the temperature. In
1003:
981:
945:
923:
887:
851:
321:Molecular Diffraction of Light
236:normal Stokes-Raman scattering
1:
3296:Journal of Raman Spectroscopy
3177:Stimulated Raman spectroscopy
3044:Klingshirn, Claus F. (2012).
2989:Accounts of Chemical Research
2431:McCreery, Richard L. (2000).
1801:Optical parametric generation
1708:Stimulated Raman spectroscopy
299:. Raman was awarded the 1930
79:Light scattering by particles
3162:Resonance Raman spectroscopy
3001:10.1021/acs.accounts.6b00210
2027:Resonance Raman spectroscopy
1714:spontaneous Raman scattering
2831:10.1103/PhysRevLett.69.2172
2157:"A review of the 1931 book
2155:Nature (19 December 1931).
1721:stimulated Raman scattering
595:quantum harmonic oscillator
589:Quantum harmonic oscillator
394:An early Raman spectrum of
3390:
3374:Fiber-optic communications
2944:10.1103/PhysRevLett.13.657
2669:10.1103/physrevb.73.064302
1892:
1705:
1537:
586:
472:
450:
383:
282:if an X-ray source is used
3312:
2889:Reviews of Modern Physics
2278:American Chemical Society
2202:Indian Journal of Physics
2061:Symmetry and Spectroscopy
1863:Supercontinuum generation
1534:Symmetry and polarization
1064:thermodynamic equilibrium
597:(QHO) approximation or a
374:American Chemical Society
3303:Vibrational Spectroscopy
3274:Rule of mutual exclusion
2909:10.1103/RevModPhys.43.99
1466:rule of mutual exclusion
441:X-ray Raman spectroscopy
278:electronic energy levels
2924:Physical Review Letters
2811:Physical Review Letters
2398:Long, Derek A. (2002).
2373:10.3390/heritage2020102
2159:Der Smekal-Raman-Effekt
348:, and independently by
3157:Raman optical activity
2768:10.1364/JOSAB.8.001264
2232:Physics in Perspective
2063:. Dover Publications.
1849:inverse Raman spectrum
1771:(1/λ − 1/λ')
1688:
1654:
1627:
1600:
1517:
1497:
1458:
1422:
1336:
1284:
1046:
1019:
961:
903:
867:
798:Boltzmann distribution
788:
720:
556:
536:
516:
425:charge-coupled devices
407:
399:
324:
301:Nobel Prize in Physics
263:conservation of energy
2252:10.1007/s000160200002
1689:
1655:
1653:{\displaystyle I_{u}}
1628:
1626:{\displaystyle I_{r}}
1601:
1518:
1498:
1459:
1423:
1337:
1285:
1043:
1020:
962:
904:
868:
789:
721:
557:
537:
517:
405:
393:
318:
243:elastically scattered
134:X-ray crystallography
3249:Depolarization ratio
3091:Scientific American,
3047:Semiconductor Optics
2972:. 27 September 2010.
2522:and John H. Meiser,
2006:National Science Day
1991:Depolarization ratio
1974:Brillouin scattering
1838:inverse Raman effect
1816:Inverse Raman effect
1665:
1637:
1610:
1563:
1554:depolarization ratio
1540:Depolarization ratio
1507:
1475:
1436:
1346:
1303:
1073:
971:
913:
877:
841:
739:
608:
546:
526:
506:
447:Molecular vibrations
212:inelastic scattering
3269:Rayleigh scattering
3208:Raman amplification
2936:1964PhRvL..13..657J
2901:1971RvMP...43...99L
2874:10.1021/j100009a027
2823:1992PhRvL..69.2172K
2795:10.1021/cr00025a006
2750:1991JOSAB...8.1264W
2661:2006PhRvB..73f4302I
2614:2012JPCA..116.5560I
2317:1928Natur.122...12R
2244:2002PhP.....4..399S
2126:1923NW.....11..873S
2114:Naturwissenschaften
1954:Rayleigh Scattering
1943:Raman amplification
1937:absorption spectrum
1857:thermal equilibrium
1799:be large. It is an
1719:On the other hand,
463:infrared absorption
453:Molecular vibration
420:photographic plates
247:Rayleigh scattering
3138:Raman spectroscopy
2524:Physical Chemistry
2408:10.1002/0470845767
2284:on 12 January 2013
2134:10.1007/BF01576902
2022:Raman spectroscopy
1947:optical amplifiers
1900:Raman spectroscopy
1844:Raman spectroscopy
1822:Boris P. Stoicheff
1684:
1650:
1623:
1596:
1546:molecular symmetry
1528:phonon confinement
1513:
1493:
1454:
1418:
1332:
1280:
1047:
1015:
957:
899:
863:
784:
716:
583:Vibrational energy
552:
532:
512:
484:degrees of freedom
469:Degrees of freedom
408:
400:
325:
270:Raman spectroscopy
226:being gained by a
224:vibrational energy
94:Powder diffraction
3351:
3350:
2817:(15): 2172–2175.
2704:978-0-07-707976-5
2649:Physical Review B
2622:10.1021/jp301070a
2608:(23): 5560–5570.
2178:10.1038/1281026c0
2070:978-0-486-66144-5
1741:nonlinear optical
1682:
1594:
1516:{\displaystyle J}
1324:
1274:
1249:
1217:
1197:
1175:
1141:
1119:
1098:
1095:
1085:
1006:
984:
948:
926:
890:
854:
814:longer wavelength
782:
781:
770:
713:
712:
701:
681:
646:
555:{\displaystyle z}
535:{\displaystyle y}
515:{\displaystyle x}
490:is the number of
429:Photodiode arrays
354:Leonid Mandelstam
350:Grigory Landsberg
274:rotational energy
170:
169:
54:Bragg diffraction
3381:
3364:Raman scattering
3332:
3331:
3320:
3319:
3264:Raman scattering
3259:Nonlinear optics
3254:Four-wave mixing
3223:Raman microscope
3131:
3124:
3117:
3108:
3061:
3031:
3030:
3020:
2995:(8): 1494–1502.
2980:
2974:
2973:
2962:
2956:
2955:
2919:
2913:
2912:
2884:
2878:
2877:
2868:(9): 2684–2695.
2857:
2851:
2850:
2805:
2799:
2798:
2783:Chemical Reviews
2778:
2772:
2771:
2761:
2733:
2727:
2726:
2715:
2709:
2708:
2690:
2681:
2680:
2640:
2634:
2633:
2597:
2591:
2590:
2564:
2540:
2534:
2520:Keith J. Laidler
2517:
2508:
2507:
2489:
2480:
2479:
2461:
2455:
2454:
2428:
2422:
2421:
2400:The Raman Effect
2395:
2386:
2385:
2375:
2366:(2): 1662–1683.
2351:
2345:
2344:
2325:10.1038/122012b0
2300:
2294:
2293:
2291:
2289:
2280:. Archived from
2270:
2264:
2263:
2227:
2221:
2220:
2197:
2191:
2190:
2180:
2152:
2146:
2145:
2109:
2103:
2102:
2084:
2075:
2074:
2056:
2012:Nonlinear optics
1873:four-wave mixing
1789:
1779:
1772:
1767:Θ = 2π
1764:
1760:
1756:
1730:Raman amplifiers
1693:
1691:
1690:
1685:
1683:
1675:
1659:
1657:
1656:
1651:
1649:
1648:
1632:
1630:
1629:
1624:
1622:
1621:
1605:
1603:
1602:
1597:
1595:
1593:
1592:
1583:
1582:
1573:
1558:
1522:
1520:
1519:
1514:
1502:
1500:
1499:
1494:
1463:
1461:
1460:
1455:
1427:
1425:
1424:
1419:
1387:
1386:
1374:
1373:
1361:
1360:
1341:
1339:
1338:
1333:
1325:
1323:
1315:
1307:
1289:
1287:
1286:
1281:
1279:
1275:
1273:
1269:
1268:
1258:
1257:
1256:
1251:
1250:
1242:
1230:
1218:
1216:
1215:
1214:
1205:
1204:
1199:
1198:
1190:
1183:
1182:
1177:
1176:
1168:
1160:
1159:
1158:
1149:
1148:
1143:
1142:
1134:
1127:
1126:
1121:
1120:
1112:
1104:
1099:
1097:
1096:
1093:
1087:
1086:
1083:
1077:
1035:beat frequencies
1024:
1022:
1021:
1016:
1014:
1013:
1008:
1007:
999:
992:
991:
986:
985:
977:
966:
964:
963:
958:
956:
955:
950:
949:
941:
934:
933:
928:
927:
919:
908:
906:
905:
900:
898:
897:
892:
891:
883:
872:
870:
869:
864:
862:
861:
856:
855:
847:
828:Raman scattering
793:
791:
790:
785:
783:
774:
773:
771:
769:
758:
725:
723:
722:
717:
714:
705:
704:
702:
700:
689:
687:
683:
682:
674:
652:
648:
647:
639:
620:
619:
599:Dunham expansion
578:
574:
564:Linear molecules
561:
559:
558:
553:
541:
539:
538:
533:
521:
519:
518:
513:
497:
489:
482:
332:was discovered.
280:may be examined
209:
208:
205:
204:
201:
198:
195:
192:
178:Raman scattering
162:
155:
148:
35:
21:
3389:
3388:
3384:
3383:
3382:
3380:
3379:
3378:
3354:
3353:
3352:
3347:
3308:
3283:
3237:
3196:
3140:
3135:
3068:
3058:
3057:978-364228362-8
3043:
3040:
3038:Further reading
3035:
3034:
2982:
2981:
2977:
2964:
2963:
2959:
2930:(22): 657–659.
2921:
2920:
2916:
2886:
2885:
2881:
2859:
2858:
2854:
2807:
2806:
2802:
2780:
2779:
2775:
2759:10.1.1.474.7172
2735:
2734:
2730:
2717:
2716:
2712:
2705:
2692:
2691:
2684:
2646:
2642:
2641:
2637:
2599:
2598:
2594:
2549:Ultramicroscopy
2542:
2541:
2537:
2518:
2511:
2504:
2491:
2490:
2483:
2476:
2463:
2462:
2458:
2443:
2430:
2429:
2425:
2418:
2397:
2396:
2389:
2353:
2352:
2348:
2311:(3062): 12–13.
2302:
2301:
2297:
2287:
2285:
2272:
2271:
2267:
2229:
2228:
2224:
2199:
2198:
2194:
2154:
2153:
2149:
2120:(43): 873–875.
2111:
2110:
2106:
2099:
2086:
2085:
2078:
2071:
2058:
2057:
2053:
2048:
2043:
1996:Fiber amplifier
1969:
1897:
1891:
1865:
1835:
1829:
1818:
1785:
1774:
1766:
1762:
1758:
1752:
1749:
1710:
1704:
1663:
1662:
1640:
1635:
1634:
1613:
1608:
1607:
1584:
1574:
1561:
1560:
1556:
1542:
1536:
1505:
1504:
1473:
1472:
1434:
1433:
1430:character table
1378:
1365:
1352:
1344:
1343:
1316:
1308:
1301:
1300:
1296:
1294:Selection rules
1260:
1259:
1239:
1231:
1225:
1206:
1187:
1165:
1161:
1150:
1131:
1109:
1105:
1088:
1078:
1071:
1070:
1029:effect occurs.
1027:resonance Raman
996:
974:
969:
968:
938:
916:
911:
910:
880:
875:
874:
844:
839:
838:
830:
737:
736:
666:
662:
631:
627:
611:
606:
605:
591:
585:
576:
572:
544:
543:
524:
523:
504:
503:
495:
487:
480:
477:
471:
455:
449:
437:
388:
382:
380:Instrumentation
313:
189:
185:
166:
46:
45:
39:Feynman diagram
17:
12:
11:
5:
3387:
3385:
3377:
3376:
3371:
3366:
3356:
3355:
3349:
3348:
3346:
3345:
3338:
3326:
3313:
3310:
3309:
3307:
3306:
3299:
3291:
3289:
3285:
3284:
3282:
3281:
3276:
3271:
3266:
3261:
3256:
3251:
3245:
3243:
3239:
3238:
3236:
3235:
3230:
3225:
3220:
3215:
3210:
3204:
3202:
3198:
3197:
3195:
3194:
3189:
3184:
3179:
3174:
3169:
3164:
3159:
3154:
3148:
3146:
3142:
3141:
3136:
3134:
3133:
3126:
3119:
3111:
3105:
3104:
3099:
3094:
3093:December 1930)
3084:
3079:
3074:
3067:
3066:External links
3064:
3063:
3062:
3056:
3039:
3036:
3033:
3032:
2975:
2957:
2914:
2879:
2852:
2800:
2789:(1): 157–193.
2773:
2728:
2723:www.horiba.com
2710:
2703:
2682:
2644:
2635:
2592:
2535:
2509:
2502:
2481:
2474:
2456:
2441:
2423:
2417:978-0471490289
2416:
2387:
2346:
2295:
2265:
2238:(4): 399–420.
2222:
2192:
2171:(3242): 1026.
2147:
2104:
2097:
2076:
2069:
2050:
2049:
2047:
2044:
2042:
2041:
2035:
2030:
2024:
2019:
2014:
2009:
2003:
1998:
1993:
1988:
1982:
1976:
1970:
1968:
1965:
1929:force constant
1893:Main article:
1890:
1887:
1869:supercontinuum
1864:
1861:
1831:
1825:
1817:
1814:
1809:
1808:
1804:
1792:
1791:
1748:
1745:
1706:Main article:
1703:
1700:
1681:
1678:
1673:
1670:
1647:
1643:
1620:
1616:
1591:
1587:
1581:
1577:
1571:
1568:
1538:Main article:
1535:
1532:
1512:
1492:
1489:
1486:
1483:
1480:
1453:
1450:
1447:
1444:
1441:
1417:
1414:
1411:
1408:
1405:
1402:
1399:
1396:
1393:
1390:
1385:
1381:
1377:
1372:
1368:
1364:
1359:
1355:
1351:
1331:
1328:
1322:
1319:
1314:
1311:
1295:
1292:
1291:
1290:
1278:
1272:
1267:
1263:
1255:
1248:
1245:
1237:
1234:
1228:
1224:
1221:
1213:
1209:
1203:
1196:
1193:
1186:
1181:
1174:
1171:
1164:
1157:
1153:
1147:
1140:
1137:
1130:
1125:
1118:
1115:
1108:
1102:
1091:
1081:
1051:Raman spectrum
1012:
1005:
1002:
995:
990:
983:
980:
954:
947:
944:
937:
932:
925:
922:
896:
889:
886:
860:
853:
850:
829:
826:
808:discovered by
780:
777:
768:
765:
761:
756:
753:
750:
747:
744:
728:
727:
711:
708:
699:
696:
692:
686:
680:
677:
672:
669:
665:
661:
658:
655:
651:
645:
642:
637:
634:
630:
626:
623:
618:
614:
587:Main article:
584:
581:
569:chemical bonds
551:
531:
511:
473:Main article:
470:
467:
451:Main article:
448:
445:
436:
433:
384:Main article:
381:
378:
346:K. S. Krishnan
330:Mie scattering
319:First page of
312:
309:
297:K. S. Krishnan
168:
167:
165:
164:
157:
150:
142:
139:
138:
137:
136:
131:
126:
121:
116:
111:
106:
101:
96:
91:
86:
81:
76:
71:
66:
61:
56:
48:
47:
37:
36:
28:
27:
15:
13:
10:
9:
6:
4:
3:
2:
3386:
3375:
3372:
3370:
3367:
3365:
3362:
3361:
3359:
3344:
3343:
3339:
3337:
3336:
3327:
3325:
3324:
3315:
3314:
3311:
3305:
3304:
3300:
3298:
3297:
3293:
3292:
3290:
3286:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3246:
3244:
3240:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3213:Raman cooling
3211:
3209:
3206:
3205:
3203:
3199:
3193:
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3158:
3155:
3153:
3150:
3149:
3147:
3143:
3139:
3132:
3127:
3125:
3120:
3118:
3113:
3112:
3109:
3103:
3100:
3098:
3095:
3092:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3069:
3065:
3059:
3053:
3049:
3048:
3042:
3041:
3037:
3028:
3024:
3019:
3014:
3010:
3006:
3002:
2998:
2994:
2990:
2986:
2979:
2976:
2971:
2967:
2961:
2958:
2953:
2949:
2945:
2941:
2937:
2933:
2929:
2925:
2918:
2915:
2910:
2906:
2902:
2898:
2895:(2): 99–124.
2894:
2890:
2883:
2880:
2875:
2871:
2867:
2863:
2856:
2853:
2848:
2844:
2840:
2836:
2832:
2828:
2824:
2820:
2816:
2812:
2804:
2801:
2796:
2792:
2788:
2784:
2777:
2774:
2769:
2765:
2760:
2755:
2751:
2747:
2743:
2739:
2732:
2729:
2724:
2720:
2714:
2711:
2706:
2700:
2696:
2689:
2687:
2683:
2678:
2674:
2670:
2666:
2662:
2658:
2655:(6): 064302.
2654:
2650:
2639:
2636:
2631:
2627:
2623:
2619:
2615:
2611:
2607:
2603:
2596:
2593:
2588:
2584:
2580:
2576:
2572:
2568:
2563:
2558:
2554:
2550:
2546:
2539:
2536:
2533:
2532:0-8053-5682-7
2529:
2525:
2521:
2516:
2514:
2510:
2505:
2499:
2495:
2488:
2486:
2482:
2477:
2471:
2467:
2460:
2457:
2452:
2448:
2444:
2438:
2434:
2427:
2424:
2419:
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3263:
3201:Applications
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1945:is used in
1933:bond length
1882:fiber laser
1696:depolarized
1094:anti-Stokes
363:Nobel Prize
341:C. V. Raman
293:C. V. Raman
129:Wolf effect
114:Small-angle
3358:Categories
3145:Techniques
2503:0471988472
2475:0471988472
2442:0471231878
2098:0471988472
2046:References
2033:Scattering
500:rotational
255:wavelength
109:Rutherford
25:Scattering
3009:0001-4842
2952:0031-9007
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2754:CiteSeerX
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3288:Journals
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2970:BBC News
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2240:Bibcode
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2008:(India)
1763:λ'
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396:benzene
372:by the
311:History
216:photons
180:or the
174:physics
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119:Tyndall
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