Raman scattering

Atomic force microscope with spectrometer, allowing to study Raman scattering

Raman scattering ( the Raman effect ) is inelastic scattering of optical radiation on substance molecules (solid, liquid or gaseous), accompanied by a noticeable change in the frequency of the radiation. In contrast to Rayleigh scattering , in the case of Raman scattering, spectral lines appear in the spectrum of the scattered radiation, which are not found in the spectrum of the primary (exciting) light. The number and location of the lines that appear are determined by the molecular structure of the substance.

Raman spectroscopy (or Raman spectroscopy) is an effective method of chemical analysis, studying the composition and structure of substances.

Entity Phenomenon

From the point of view of the classical theory

This view gives a somewhat simplified picture of the phenomenon. In the classical model, the electric field of light induces a variable dipole moment of the molecule, which oscillates with the frequency of the incident light, and changes in the dipole moment in turn lead to the emission of radiation by the molecule in all directions. In the classical model, it is assumed that a substance contains charges that can be separated, but held together by some forces acting along with Coulomb attraction . The formation of a wave at the interface with a substance causes an oscillating separation of these charges, that is, an oscillating electric dipole appears, which radiates at the oscillation frequency. This radiation is scattering. The expression for the radiation intensity is

I={\frac {16\pi ^{4}\nu ^{4}}{3c^{2}}}\left|{\vec {P}}\right|^{2}

{\ displaystyle I = {\ frac {16 \ pi ^ {4} \ nu ^ {4}} {3c ^ {2}}} \ left | {\ vec {P}} \ right | ^ {2}}

,

Where ${\vec {P}}$ ${\ displaystyle {\ vec {P}}}$ - induced dipole moment, defined as ${\vec {P}}=\alpha {\vec {E}}$ ${\ displaystyle {\ vec {P}} = \ alpha {\ vec {E}}}$ . Coefficient of proportionality $\alpha$ ${\ displaystyle \ alpha}$ this equation is called the polarizability of the molecule.

Consider a light wave as an electromagnetic field of intensity. $E$ ${\ displaystyle E}$ with oscillation frequency $\nu _{0}$ ${\ displaystyle \ nu _ {0}}$ :

{\vec {E}}={\vec {E}}_{0}\cos \left(2\pi \nu _{0}t\right)

{\ displaystyle {\ vec {E}} = {\ vec {E}} _ {0} \ cos \ left (2 \ pi \ nu _ {0} t \ right)}

,

Where $E_{0}$ ${\ displaystyle E_ {0}}$ - amplitude, a $t$ ${\ displaystyle t}$ - time. For a diatomic molecule placed in this field, the induced dipole moment ${\vec {P}}$ ${\ displaystyle {\ vec {P}}}$ recorded as

{\vec {P}}=\alpha {\vec {E}}_{0}\cos \left(2\pi \nu _{0}t\right)\quad (1)

{\ displaystyle {\ vec {P}} = \ alpha {\ vec {E}} _ {0} \ cos \ left (2 \ pi \ nu _ {0} t \ right) \ quad (1)}

In general, polarizability $\alpha$ ${\ displaystyle \ alpha}$ depends on the frequency of the field, so for a static field and electromagnetic radiation, it will be different. If the dipole radiates according to classical laws and the original radiation is polarized, then the scattering can also be polarized, since the particles are isotropic and the directions ${\vec {P}}$ ${\ displaystyle {\ vec {P}}}$ and ${\vec {E}}$ ${\ displaystyle {\ vec {E}}}$ match up. This is Rayleigh scattering, its intensity is proportional to the root-mean-square value ${\vec {P}}$ ${\ displaystyle {\ vec {P}}}$ . If the molecule oscillates with frequency $\nu _{1}$ ${\ displaystyle \ nu _ {1}}$ then the displacement of nuclei $q$ ${\ displaystyle q}$ (a certain generalized coordinate) can be written as

q=q_{0}\cos \left(2\pi \nu _{1}t\right)\quad (2)

{\ displaystyle q = q_ {0} \ cos \ left (2 \ pi \ nu _ {1} t \ right) \ quad (2)}

,

Where $q_{0}$ ${\ displaystyle q_ {0}}$ - oscillatory amplitude. With small fluctuations $\alpha$ ${\ displaystyle \ alpha}$ linearly dependent on $q$ ${\ displaystyle q}$ , therefore, decomposing $\alpha$ ${\ displaystyle \ alpha}$ in a taylor row in terms of nucleus displacement coordinates $q$ ${\ displaystyle q}$ near the equilibrium position, usually limited to the first member:

\alpha =\alpha _{0}+\left({\frac {\partial \alpha }{\partial q}}\right)_{0}\cdot q\quad (3)

{\ displaystyle \ alpha = \ alpha _ {0} + \ left ({\ frac {\ partial \ alpha} {\ partial q}} \ right) _ {0} \ cdot q \ quad (3)}

.

In this expression $\alpha _{0}$ ${\ displaystyle \ alpha _ {0}}$ - polarizability of the molecule in an equilibrium configuration, a $\left({\frac {\partial \alpha }{\partial q}}\right)_{0}$ ${\ displaystyle \ left ({\ frac {\ partial \ alpha} {\ partial q}} \ right) _ {0}}$ - derivative of polarizability $\alpha$ ${\ displaystyle \ alpha}$ by offset $q$ ${\ displaystyle q}$ at the equilibrium point. Substituting expressions (2) and (3) into equation (1), we obtain the following expression for the induced dipole moment:

{\begin{aligned}{\vec {P}}&=\alpha {\vec {E_{0}}}\cos \left(2\pi \nu _{0}t\right)=\\&=\alpha _{0}{\vec {E_{0}}}\cos \left(2\pi \nu _{0}t\right)+\left({\frac {\partial \alpha }{\partial q}}\right)_{0}q_{0}{\vec {E_{0}}}\cos \left(2\pi \nu _{0}t\right)\cos \left(2\pi \nu _{1}t\right)=\\&=\alpha _{0}{\vec {E_{0}}}\cos \left(2\pi \nu _{0}t\right)+{\frac {1}{2}}\left({\frac {\partial \alpha }{\partial q}}\right)_{0}q_{0}{\vec {E_{0}}}{\Big \{}\cos {\big [}2\pi \left(\nu _{0}+\nu _{1}\right)t{\big ]}+\cos {\big [}2\pi \left(\nu _{0}-\nu _{1}\right)t{\big ]}{\Big \}}\\\end{aligned}}

{\ displaystyle {\ begin {aligned} {\ vec {P}} & = \ alpha {\ vec {E_ {0}}} \ cos \ left (2 \ pi \ nu _ {0} t \ right) = \ \ & = \ alpha _ {0} {\ vec {E_ {0}}} \ cos \ left (2 \ pi \ nu _ {0} t \ right) + \ left ({\ frac {\ partial \ alpha} {\ partial q}} \ right) _ {0} q_ {0} {\ vec {E_ {0}}} \ cos \ left (2 \ pi \ nu _ {0} t \ right) \ cos \ left ( 2 \ pi \ nu _ {1} t \ right) = \\ & = \ alpha _ {0} {\ vec {E_ {0}}} \ cos \ left (2 \ pi \ nu _ {0} t \ right) + {\ frac {1} {2}} \ left ({\ frac {\ partial \ alpha} {\ partial q}} \ right) _ {0} q_ {0} {\ vec {E_ {0} }} {\ Big \ {} \ cos {\ big [} 2 \ pi \ left (\ nu _ {0} + \ nu _ {1} \ right) t {\ big]} + \ cos {\ big [ } 2 \ pi \ left (\ nu _ {0} - \ nu _ {1} \ right) t {\ big]} {\ Big \}} \\\ end {aligned}}}

.

The first term describes an oscillating dipole, the frequency of which is $\nu _{0}$ ${\ displaystyle \ nu _ {0}}$ (Rayleigh scattering), the second term refers to Raman scattering with frequencies $\nu _{0}+\nu _{1}$ ${\ displaystyle \ nu _ {0} + \ nu _ {1}}$ (anti-Stokes) and $\nu _{0}-\nu _{1}$ ${\ displaystyle \ nu _ {0} - \ nu _ {1}}$ (Stokes) Thus, when a molecule is irradiated with monochromatic light at a frequency $\nu _{0}$ ${\ displaystyle \ nu _ {0}}$ , as a result of induced electron polarization, it scatters radiation as with a frequency $\nu _{0}$ ${\ displaystyle \ nu _ {0}}$ and with frequencies $\nu _{0}\pm \nu _{1}$ ${\ displaystyle \ nu _ {0} \ pm \ nu _ {1}}$ (Raman scattering), where $\nu _{1}$ ${\ displaystyle \ nu _ {1}}$ - frequency of oscillation. ^[one]

From the point of view of quantum theory

Illustration

The origin of this effect is most conveniently explained in the framework of the quantum theory of radiation. According to it, the radiation of frequency ν is considered as a stream of photons with energy h ν , where h is the Planck constant . When colliding with molecules, photons are scattered. In the case of elastic dispersion, they will deviate from the direction of their movement without changing their energy ( Rayleigh scattering ). But it may be that in a collision an energy exchange between the photon and the molecule will occur. In this case, a molecule can both acquire and lose a part of its energy in accordance with the rules of quantization — its energy can change by an amount ΔE corresponding to the difference in energy between its two allowed states. In other words, the value of Δ E must be equal to the change in the vibrational and / or rotational energy of the molecule. If a molecule acquires energy Δ E , then after scattering the photon will have energy h ν - Δ E and, accordingly, the radiation frequency ν - Δ E / h . And if the molecule loses energy Δ E , the frequency of radiation scattering will be ν + Δ E / h . Radiation scattered with a frequency less than that of the incident light is called Stokes radiation, and radiation with a higher frequency is called anti-Stokes. ^[2] At not very high temperatures, the population of the first vibrational level is small, at room temperature at a vibrational frequency of 1000 cm ^−1, only 0.7% of molecules are on the first vibrational level, therefore the intensity of anti-Stokes scattering is small. With increasing temperature, the population of the excited vibrational level increases and the intensity of anti-Stokes scattering increases. ^[one]

Empirical laws of Raman scattering

Spectral satellite lines accompany each line of primary light.
The frequency shift of the satellites relative to the primary line characterizes the scattering substance and is equal to the natural frequencies of molecular vibrations.
Satellites are two groups of lines located symmetrically relative to the exciting line. The satellites shifted to the red (long-wave) side relative to the original line are called “red” (or Stokes, by analogy with luminescence), and those shifted to purple (short-wave) - “purple” (anti-Stokes). The intensity of the red satellites is much higher.
With increasing temperature, the intensity of anti-Stokes satellites is rapidly increasing.

Opening History

Several well-known physicists theoretically predicted the possibility of Raman scattering even before its experimental detection. Adolphe Smekal was the first to predict Raman scattering (in 1923), followed by the theoretical work of Kramers , Heisenberg , Dirac , Schrödinger and others.

Discovery of Raman Scattering at Moscow State University (Moscow)

In 1918, L.I. Mandelstam predicted the splitting of the Rayleigh scattering line due to the scattering of light by thermal acoustic waves. Starting in 1926, Mandelstam and Landsberg launched an experimental study of molecular scattering of light in crystals at Moscow State University (MGU) , aiming to detect the fine structure in the scattering spectrum caused by the modulation of scattered light by elastic thermal waves whose frequencies lie in the acoustic range (continued studies of the phenomenon, now called Mandel'shtam-Brillouin scattering ). As a result of these studies, on February 21, 1928, Landsberg and Mandelstam discovered the effect of Raman scattering (they registered new lines of the spectrum resulting from the modulation of scattered light by vibrations of atoms in the crystal lattice in the optical frequency range). They reported on their discovery at a colloquium of April 27, 1928 and published relevant scientific results in Soviet and two German journals ^[3] ^[4] ^[5] .

Studies in Calcutta

In 1921, at the University of Calcutta, Indian physicists Raman and Seshagiri Rao discovered features in the polarization of light scattered with distilled water in the presence of light filters in the detection channel. In 1923, Raman showed that the features of polarization are associated with the presence in the medium of some additional luminescence with a wavelength that differs markedly from the wavelength of the incident radiation ^[6] . As a possible explanation hypothesis, fluorescence could be advanced, however, chemical cleaning of the solution did not lead to the disappearance of the effect. The latter led Raman to the idea that the observed phenomenon is a fundamentally new phenomenon, and since 1923 Raman has begun a program to study the “new world” in liquids and vapors. In the period from 1923 to 1928, his group shows the presence of scattering with a change in frequency in more than 100 transparent liquids, gases and solids. The main research method, however, was the use of additional light filters and polarizers, which did not allow an adequate interpretation of the observed phenomenon. But in 1928, Raman suggested that the observed effect is supposedly some analogue of the Compton effect in optics, suggesting that the photon can be “partially absorbed”, and the parts cannot be arbitrary and should correspond to the infrared absorption spectra of light. Indian scientists C.V. Raman and K.S. Krishnan ( Krishnan ) undertake experimental verification of this hypothesis and find a line spectrum in the radiation they studied for many years ^[7] . Experimental material accumulated over many years allowed them to immediately publish an article in which they declared the discovery of a new kind of glow inherent in a wide class of substances.

According to Raman: “The lines of the spectrum of the new radiation were first detected on February 28, 1928,” that is, a week later than Landsberg and Mandelstam at Moscow State University . On the other hand, Indian physicists published 16 papers on the behavior of light in liquids and vapors ^[8] at the time of publication of Landsberg and Mandelstam’s paper on Raman Scattering in Crystals. Despite the fact that Soviet physicists carried out their research on light scattering since 1918 and absolutely independently of Raman, the Nobel Prize in Physics in 1930 was awarded only to Raman “for his work on light scattering and for the discovery of the effect named after him” ^{[ 9]} . (Based on statistics, in the early stages of their work, the Nobel Committee extremely reluctantly gave the prize to more than one person.) Since then, the Raman scattering of light in foreign literature has been called the Raman effect .

In 1957, Raman was also awarded the International Lenin Prize for Strengthening Peace among Nations.

Research in Paris

In 1925, the French physicists Rocard , Cabanne, and Dorre searched for Raman scattering of gases in gases, but did not find it. They then failed to register light of low intensity.

About title

In general, physicists did not immediately realize that the Raman scattering of light in crystals discovered by Landsberg and Mandelstam is the same phenomenon as the effect discovered in Raman and Ramp in liquids and vapor ^[10] . Moreover, Raman published his results before the publication of the works of Landsberg and Mandelstam. Therefore, in the English-language literature, the phenomenon under consideration is called the “Raman effect” ( eng. Raman effect ) or “Raman scattering” ( Raman scattering ).

In the Russian-language scientific literature, following the classics of molecular light scattering by Landsberg, Mandelstam, Fabelinsky, and many other Soviet scientists, this phenomenon is traditionally called "Raman scattering of light." And despite the fact that the term "Raman scattering" is used only by Russian-speaking scientists and in Russian-language textbooks, this situation is unlikely to change, since the resistance to the unjust decision of the Nobel Committee from 1930 is still very large. ^[10] ^[11] ^[12]

Stimulated Raman Scattering (WRC)

With an increase in the intensity of the pump wave, the intensity of the scattered Stokes radiation becomes more and more. In such conditions, it is necessary to consider the interaction of molecules of the medium simultaneously with two electromagnetic waves: a laser pump wave at a frequency $\omega _{0}$ ${\ displaystyle \ omega _ {0}}$ and the Stokes wave on the frequency $\omega _{c}=\omega _{0}-\Omega$ ${\ displaystyle \ omega _ {c} = \ omega _ {0} - \ Omega}$ . The cause of the reverse effect of light waves on molecular vibrations is the dependence $\alpha (q)$ ${\ displaystyle \ alpha (q)}$ polarization from the generalized coordinate. The energy of interaction of a molecule with a light wave is expressed as

H=-PE=-\alpha (q)E^{2},

{\ displaystyle H = -PE = - \ alpha (q) E ^ {2},}

and therefore when $\partial {\alpha }/\partial {q}\neq 0$ ${\ displaystyle \ partial {\ alpha} / \ partial {q} \ neq 0}$ force arises in the light field

F=-{\frac {\partial {H}}{\partial {q}}}={\frac {\partial {\alpha }}{\partial {q}}}E^{2},

{\ displaystyle F = - {\ frac {\ partial {H}} {\ partial {q}}} = {\ frac {\ partial {\ alpha}} {\ partial {q}}} E ^ {2}, }

acting on molecular vibrations. This force can lead to their resonant “buildup” if the electromagnetic field contains components with frequencies $\omega _{1}$ ${\ displaystyle \ omega _ {1}}$ and $\omega _{2}$ ${\ displaystyle \ omega _ {2}}$ whose difference is close to the natural frequency of molecular vibrations $\Omega$ ${\ displaystyle \ Omega}$ : $\omega _{1}-\omega _{2}\thickapprox \Omega$ ${\ displaystyle \ omega _ {1} - \ omega _ {2} \ thickapprox \ Omega}$ . Under these conditions, phasing of molecular vibrations takes place: chaotic intramolecular motion, having a fluctuating character, is superimposed with regular forced vibrations, the phases of which in different molecules are determined by the phases of the components of the light field. This leads to the instability of an intense monochromatic wave in a Raman-active medium. In case its intensity exceeds the threshold value $I_{0}\geqslant I_{thr}$ ${\ displaystyle I_ {0} \ geqslant I_ {thr}}$ , Stokes wave with frequency $\omega _{c}=\omega _{0}-\Omega$ ${\ displaystyle \ omega _ {c} = \ omega _ {0} - \ Omega}$ increases exponentially as it spreads in the environment . With $I_{c}\ll I_{0}$ ${\ displaystyle I_ {c} \ ll I_ {0}}$ (in the approximation of a given pump field)

I_{c}=I_{c0}e^{gI_{0}z},

{\ displaystyle I_ {c} = I_ {c0} e ^ {gI_ {0} z},}

and the gain

g={\frac {8\pi ^{2}c^{2}}{\hbar \omega _{c}^{3}n^{2}\Gamma }}N{\frac {d\sigma }{do}}g'(\omega _{0}-\omega _{c})

{\ displaystyle g = {\ frac {8 \ pi ^ {2} c ^ {2}} {\ hbar \ omega _ {c} ^ {3} n ^ {2} \ Gamma} N {\ frac {d \ sigma} {do}} g '(\ omega _ {0} - \ omega _ {c})}

directly expressed through the parameters of the spontaneous scattering line: $d\sigma /do$ ${\ displaystyle d \ sigma / do}$ - scattering cross section, $2\Gamma$ ${\ displaystyle 2 \ Gamma}$ - line width, $N$ ${\ displaystyle N}$ - density of molecules $g'(\omega _{0}-\omega _{c})$ ${\ displaystyle g '(\ omega _ {0} - \ omega _ {c})}$ - line form factor. With $gI_{0}z\gg 1$ ${\ displaystyle gI_ {0} z \ gg 1}$ source wave frequency $\omega _{0}$ ${\ displaystyle \ omega _ {0}}$ depleted, there is an effective energy exchange between the waves. With a sufficiently strong excitation, the difference in populations between the excited vibrational levels also changes. Alignment of populations leads to the suppression of WRC, a theoretical description in this case requires a quantum approach.

Forced Raman scattering was first observed by Woodbury and Ng in 1962 when building a Q-switched ruby laser. ^[13] As a Q-modulator, they used a Kerr cell filled with liquid nitrobenzene. As a result, in the generated laser pulse, together with the main radiation of a ruby laser at a wavelength of 694.3 nm, radiation was detected at a wavelength of 767 nm, whose power reached $1/5$ ${\ displaystyle 1/5}$ from the power of the main radiation. As it turned out, the difference in the observed wavelengths corresponded to the strongest Raman scattering line in nitrobenzene (1345 cm ^{– 1} ), and the phenomenon was soon interpreted.

In contrast to spontaneous Raman scattering, the result of which is incoherent radiation with an intensity several orders of magnitude less than the pumping intensity, when stimulated Raman scattering the Stokes wave is coherent and its intensity is comparable in magnitude with the intensity of the exciting light. ^[12]

Raman Spectroscopy (RS) Techniques

Scientific journals on Raman scattering

Raman scattering initiated a whole direction in spectroscopy of molecules and crystals - Raman spectroscopy. This method today is one of the most powerful methods for studying molecular structures, so it is not surprising that there are a number of scientific journals devoted entirely to the problem of Raman scattering.

Journal of Raman Spectroscopy (Journal of Raman Spectroscopy) (inaccessible link) .
Surface Enhanced Raman Scattering Physics and Applications (Physics and applications of surface-enhanced Raman spectroscopy).

In addition to these journals, many articles on Raman spectroscopy are published in other general and specialized journals.

Literature

Akhmanov S. A. , Koroteev N. I. Methods of nonlinear optics in light scattering spectroscopy. - Moscow: Science, 1981. - (Modern problems of physics).
Shen I.R. Principles of nonlinear optics = Shen Y. R. The principles of nonlinear optics. - Moscow: Science, 1989. - ISBN 5-02-014043-0 .
Demtröder V. Laser Spectroscopy: Basic Principles and Experimental Technique = Demtröder W. Laser spectroscopy: basic principles and technology. - Moscow: Science, 1985.

Notes

↑ ¹ ² Pentin Yu. A. Basics of molecular spectroscopy / Pentin Yu. A., Kuramshina G. M., - M .: Mir; BINOMIAL. Laboratory of Knowledge, 2008. P98. ISBN 978-5-94774-765-2 (BINOM. LZ), ISBN 978-5-03-003846-9 (World)
↑ Benwell K. Basics of molecular spectroscopy: Trans. from English - M .: Mir, 1985. - 384 p.
↑ Landsberg G., Mandelstam L. Eine neue Erscheinung bei der Lichtzertreuung // Naturwissenschaften. 1928. V. 16. S. 557.
↑ Landsberg G. S., Mandelstam L. I. New phenomenon in the scattering of light (preliminary report) // Journal of Russian physical and chemical. about-va. 1928. T. 60. p. 335.
↑ Landsherg GS, Mandelstam LI Uber die Lichtzerstrenung in Kristallen // Zeitschrift fur Physik. 1928. V. 50. S. 769.
↑ [KR Ramanathan, Proc. Indian Assoc. Cultiv. Sci. (1923) VIII, p. 190]
↑ Ind. J. Phys . 1928. V. 2 . P. 387.
↑ [Nature 123 50 1929]
↑ Information about Raman from the website of the Nobel Committee (Eng.)
↑ ¹ ² V.L. Ginzburg, I.L. Fabelinskii, “On the history of the discovery of Raman scattering”
↑ Fabelinsky, IL, On the 50th Anniversary of the Discovery of Raman Scattering, Uspekhi Fiz. - 1978. - V. 126, no. 1. - p. 123-152.
↑ ¹ ² Fabelinsky, I. L. Combinational Light Scattering - 70 years (From the history of physics) // Uspekhi Fiz. - 1998. - V. 168, No. 12. - P. 1342-1360
↑ Woodbury, EJ; Ng, WK Ruby laser operation in the near IR (Eng.) // Proceedings of the Institute of Radio Engineers : journal. - 1962. - November ( vol. 50 , no. 11 ). - P. 2367 . - DOI : 10.1109 / JRPROC.1962.287964 .

[autogenerated1-1] ¹ ² Pentin Yu. A. Basics of molecular spectroscopy / Pentin Yu. A., Kuramshina G. M., - M .: Mir; BINOMIAL. Laboratory of Knowledge, 2008. P98. ISBN 978-5-94774-765-2 (BINOM. LZ), ISBN 978-5-03-003846-9 (World)

[2] Benwell K. Basics of molecular spectroscopy: Trans. from English - M .: Mir, 1985. - 384 p.

[3] Landsberg G., Mandelstam L. Eine neue Erscheinung bei der Lichtzertreuung // Naturwissenschaften. 1928. V. 16. S. 557.

[4] Landsberg G. S., Mandelstam L. I. New phenomenon in the scattering of light (preliminary report) // Journal of Russian physical and chemical. about-va. 1928. T. 60. p. 335.

[5] Landsherg GS, Mandelstam LI Uber die Lichtzerstrenung in Kristallen // Zeitschrift fur Physik. 1928. V. 50. S. 769.

[6] [KR Ramanathan, Proc. Indian Assoc. Cultiv. Sci. (1923) VIII, p. 190]

[7] Ind. J. Phys . 1928. V. 2 . P. 387.

[8] [Nature 123 50 1929]

[9] Information about Raman from the website of the Nobel Committee (Eng.)

[vivovoco.astronet.ru-10] ¹ ² V.L. Ginzburg, I.L. Fabelinskii, “On the history of the discovery of Raman scattering”

[11] Fabelinsky, IL, On the 50th Anniversary of the Discovery of Raman Scattering, Uspekhi Fiz. - 1978. - V. 126, no. 1. - p. 123-152.

[multiple-12] ¹ ² Fabelinsky, I. L. Combinational Light Scattering - 70 years (From the history of physics) // Uspekhi Fiz. - 1998. - V. 168, No. 12. - P. 1342-1360

[13] Woodbury, EJ; Ng, WK Ruby laser operation in the near IR (Eng.) // Proceedings of the Institute of Radio Engineers : journal. - 1962. - November ( vol. 50 , no. 11 ). - P. 2367 . - DOI : 10.1109 / JRPROC.1962.287964 .