# Optics and Spectroscopy (v.90, #2)

Microwave spectroscopy of the Zeeman effect in Rydberg atoms of sodium by I. I. Ryabtsev; D. B. Tret’yakov

*(145-148)*. Experimental results of studying the spectrum of the microwave 37

*P*-37*S*transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system. Radiative properties of Zeeman components of atomic multiplets: Magnetically induced decay of metastable

^{3}*P*_{2}and^{3}*P*_{0}states of inert gases by V. D. Ovsyannikov; E. V. Chaplygin*(149-156)*. It is shown that the magnetic field induces the radiative decay of metastable states of inert gases by mixing them with resonant sublevels of the lowest multiplet. The polarization and frequency structures of the “forbidden” lines induced by the magnetic field are determined, and the dependence of the intensity of π and σ components of these lines on the magnetic field is calculated. The effect is totally governed by the paramagnetic atom-field interaction, and the influence of the diamagnetic interaction is insignificant.

The influence of photoelectron-core correlations on the K-absorption spectrum of Ne by V. F. Demekhin; N. V. Demekhina

*(157-163)*. The inclusion of correlations of a photoelectron with core electrons in the intermediate state (1

*s*^{1}2*s*^{2}2*p*^{6}ε*p*) is shown to take into account the mutual influence of a photoelectron and core electrons as their radial parts are rearranged because of variations of the potential due to the appearance of an inner vacancy. As a consequence, the absorption probability increases (∼20%) in the region below the multiple ionization threshold. Isotopic shifts and the hyperfine structure of the samarium spectral lines at 672 and 686 nm by N. N. Kolachevskiĭ; A. A. Papchenko; N. A. Kiselev; V. N. Sorokin; A. V. Akimov; S. I. Kanorskii

*(164-170)*. Spectra of saturated absorption of Sm atomic vapor from the ground state

^{7}*F*_{0}and the first even metastable level^{7}*F*_{1}, ε′=292.58 cm^{−1}of the 4*f*^{6}6*s*^{2}configuration to the odd level 4_{f}^{6}(^{7}*F*)6*s*6*p*(^{3}*P*^{o})^{9}*F*_{1}^{o}, ε,=14863.85 cm^{−1}were recorded. The lines of the isotopic series were identified, and the hyperfine structure of lines in the spectra of isotopes with a nonzero nuclear spin was determined. The relative isotopic shifts and the hyperfine splitting of the even level 4*f*^{6}6*s*^{2}(^{7}*F*_{1}) were determined. Spectrum of the ethylene molecule with realization of its two isomeric forms: I. Stationary state classification by A. V. Burenin

*(171-177)*. It is shown that the use of dynamic noninvariant groups within the concept of the symmetry-group chain allows one to describe the spectrum of a molecular system when it is necessary to take into account the change of its isomeric form on changing the electronic state. The description is constructed for the example of the ethylene molecule whose equilibrium configuration for a particular electronic state realizes one of two isomeric forms. The first part of this work is devoted to the construction of the stationary-state classification.

Spectrum of the ethylene molecule with realization of its two isomeric forms: II. Operators of physical quantities by A. V. Burenin

*(178-182)*. It is shown that the use of dynamic noninvariant groups within the concept of the symmetry-group chain allows one to describe the spectrum of a molecular system when it is necessary to take into account changes in its isomeric form on changing the electronic state. A description is constructed for the example of the ethylene molecule, whose equilibrium configuration for a particular electronic state realizes one of two isomeric forms depending on the electronic state. The second part of this work is devoted to the construction of the effective operators of physical quantities.

Improvement of the parametric method of the theory of vibronic spectra of polyatomic molecules: Absorption spectra and the structure of butadiene, hexatriene, and octatetraene in the excited state by V. I. Baranov; A. N. Solov’ev

*(183-190)*. The structure of the excited states and absorption spectra of butadiene, hexatriene, and octatetraene are calculated by the parametric method of the theory of vibronic spectra using models of the first-and second-order approximations. It is shown that these molecular models adequately reflect the molecular structure and allow one to predict quantitatively the shape and fine vibrational structure of the absorption spectra. When passing to the second-order approximation, only two additional (angular) parameters are used. These parameters are transferable in the series of polyenes. Compared to the first-order approximation model, the second-order approximation model more accurately takes into account the angular deformations of polyenes upon their excitation and describes the intensity distribution in the vibrational spectrum, including weak lines. In addition, the calculations also quantitatively predict spectral variations in the molecular series. The parametric method is more efficient for modeling polyatomic molecules in the excited states and their vibrational spectra compared to other semiempirical and

*ab initio*methods. Elementary sequential spectral line and statistical properties of the thermal reservoir of free polyatomic molecules by Yu. S. Demchuk

*(191-198)*. The formation of vibronic spectra of free polyatomic molecules is studied by taking the concept of sequences as constituent elements of vibronic bands. Statistical properties of the thermal reservoir of oscillators, which randomly perturbs optically active transitions in a polyatomic molecule, are considered. The spectral shape, position, and width of the elementary sequential lines (ESL) are determined. It is shown that the ESLs have a Lorentzian shape if the perturbations are short-term and the pulse shape is symmetric about its origin. The position of the ESLs depends on the total vibrational energy of the thermal reservoir of oscillators in the initial electronic state of a molecule. The analysis of the statistical properties of the thermal reservoir of polyatomic molecules shows that one should distinguish between the ESL linewidth of individual molecules and the ESL linewidth averaged over the entire thermal ensemble. It is shown that individual molecules of the thermal ensemble that have different total vibrational energies are characterized by different widths of the ESLs. Consequently, the exchange and redistribution dynamics of the vibrational energy stored in the initial electronic state should manifest itself in the difference between the single-molecule ESL widths measured at different instants in time.

Modeling of the time-resolved vibronic spectra of polyatomic molecules: The formulation of the problem and analysis of kinetic equations by S. A. Astakhov; V. I. Baranov

*(199-206)*. A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculations of the spectra can be found by the methods developed. The time dependences of the populations of a great number (>10

^{3}) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling three-dimensional spectra of polyatomic molecules containing several tens of atoms. Photophysics of the triple state of metal complexes of 9-anthracenecarboxylic acid by T. A. Shakhverdov; R. Érgashev

*(207-211)*. The triplet-triplet (T-T) absorption spectra and the T-T absorption decay kinetics are measured for solutions of 9-anthracenecarboxylic acid (ACA) and its complexes with metal ions (Cd

^{3+}and Ln^{3+}=Y^{3+}, La^{3+}, Ce^{3+}, Eu^{3+}, Gd^{3+}, and Tb^{3+}) in dimethylsulfoxide (DMSO) by the methods of flashlamp and laser pulse photolysis. The rate constants*k*_{T}of intracomplex quenching of the triplet state are measured for ACA complexes with ions Gd^{3+}, Ce^{3+}, Tb^{3+}, and Eu^{3+}. Larger values of*k*_{T}in complexes of ACA with paramagnetic ions Ce^{3+}, Tb^{3+}, and Eu^{3+}, which have low-lying energy levels, compared to the values of*k*_{T}for complexes with other ligands (pyrene-3-sulfonate, pyrene-1,3,6,8-tetrasulfonate, and benzo[ghi]perylene-1,2-dicarboxylate) were explained by the lower energy of the triplet state of ACA (14400 cm^{−1}). For a complex with a paramagnetic ion Gd^{3+}, which has no low-lying energy levels, the value of*k*_{T}is close to that measured by us earlier for the inner-sphere complex of pyrene-1,3,6,8-tetrasulfonate with the same ion. These results confirm our earlier assumption about the inner-sphere complexing of ACA with Ln^{3+}ions in DMSO. Probabilities of rovibronic transitions in the

*I*^{1}Π_{g}^{−},*J*^{1}Δ_{g}^{−}→*C*^{1}Π_{±}^{u}systems of bands of the deuterium molecule by S. A. Astashkevich; B. P. Lavrov*(212-221)*. Probabilities of spontaneous rovibronic transitions

*I*^{1}Π_{g}^{−},*v*′*J*′,*J*^{1}Δ_{g}^{−},*v*′,*J*′→*C*^{1}Π_{u}^{±},*v*″,*J*″ of the D_{2}molecule (for vibrational and rotational quantum numbers*v*′=*v*″=0–3 and*J*′=1–9,*J*″=*J*′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical*b initio*data on electronic transition dipole moments of the 3*d*π^{1}Π_{g}→2*p*π^{1}Π_{u}and 3*d*πδ^{1}Δ_{g}→2*p*π^{1}Π_{u}transitions. The dependences of the transition probabilities on*J*′ for the same bands of both hydrogen isotopomers H_{2}and D_{2}were found to be identical. They represent monotone functions for*R*and*P*branches and functions with a maximum (minimum) for*Q*branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse. Lattice effects in the waveguide propagation of a magnetic

*EH*polariton along a macroscopically thin magnetoelectric film by S. V. Tarasenko*(222-230)*. It is shown that the lattice effect is able to induce previously unknown anomalies in the spectrum of the bulk magnetic

*EH*polariton travelling along a macroscopically thin magnetoelectric film even in the presence of total coherent matching of this film to a nonmagnetic coating. The character of these anomalies substantially depends on the relationship between the Néel and Debye temperatures of a magnetic crystal. Magnetooptical properties of a ferromagnetic superlattice by A. F. Bukhan’ko; A. L. Sukstanskii

*(231-239)*. Transmission and reflection of a normally incident wave from a magnetic superlattice consisting of 2

*N*ferromagnetic layers with alternating orientation of the magnetization vector are considered. The characteristic matrix of a superlattice relating wave amplitudes at the entrance to the system and at the exit from it is calculated in the closed form and Jones matrices determining all the basic magnetooptical characteristics of the structure (transmission and reflection coefficients, the degree of polarization of transmitted and reflected waves, and so on) are constructed. A significant dependence of these characteristics on the number of layers is demonstrated. Study of the structure of aqueous solutions of ionic macromolecules by low-frequency Raman spectroscopy by A. Z. Bol’shagina; A. M. Saletskii; A. V. Chervyakov

*(240-243)*. Using low-frequency Raman spectroscopy, the structure of aqueous solutions of polyacrylic acid as a function of polyelectrolyte concentration and chain length was studied. The fractal dimension of structures in aqueous solutions of polyacrylic acid with different acid concentrations and polyion chain lengths was determined. The size of fractal regions in systems with different structures was estimated.

Modeling of blood vessel heating by laser radiation by L. G. Astaf’eva; G. I. Zheltov; A. S. Rubanov

*(244-249)*. A model for the calculation of heating of a blood vessel, which is modeled by an infinite circular cylinder and located in the hypodermic layer, under the action of laser radiation is proposed. Heating of such a vessel under the action of radiation with wavelengths most often used for laser therapy is calculated within the framework of the model proposed. The heating process is compared with the case of skin heating by laser radiation in the multilayer model of the skin.

Optimization of parameters and the ultimate sensitivity of interferometric detectors of gravitational waves by Yu. V. Troitskiĭ

*(250-255)*. The signal-to-shot-noise ratio is calculated for three types of laser interferometers used in gravitational wave detectors: for two types of Fabry-Perot interferometers (with direct reading of the output signal and with the modulation technique used for outcoupling the signal) and for the Michelson interferometer with Fabry-Perot arms. It is shown that the signal-to-noise ratio can be substantially increased by using “supermirrors” with losses of the order of 10

^{−6}. It is very important, in this case, to properly choose the mirror transmittance, because, otherwise, the sensitivity inevitably decreases by orders of magnitude and the requirements of lasers become more stringent. The efforts to increase the signal-to-noise ratio by increasing the power are limited either by an insufficient laser power or by the overheating of interferometer mirrors. Our estimates show that the present-day technical level with laser power of about 1 W provides sufficient sensitivity for detecting gravitational waves. Sensitivity of interferometers under conditions of intense illumination, field mismatch, and light scattering in the mirrors by Yu. V. Troitskiĭ

*(256-260)*. The problem of ultimate sensitivity of the Fabry-Perot reflection interferometer (RI), which is used for measuring ultrasmall displacements, is considered. The sensitivity depends on the shot noise and is restricted, with the available light power margin, by the power that can be released inside the RI due to the light absorption in the mirrors. In addition, the sensitivity is affected by a mismatch between the RI and light source fields (leading to an excess shot noise) and by the light scattering in the mirrors (a favorable factor reducing the RI heating for specified total losses). An expression for the sensitivity is derived that takes into account the above factors and involves the power

*P*_{int}released inside the interferometer. This makes it possible to optimize the RI parameters by minimizing*P*_{int}and maximizing the sensitivity. Interaction of solitons in a medium with relaxation of gain and saturable absorption by N. N. Rozanov; S. V. Fedorov; A. N. Shatsev

*(261-265)*. Results of numerical simulation of soliton interaction in a laser with relaxation of gain and saturable saturation are presented. Interactions of co-and counterpropagating fast and slow solitons are analyzed. Typical scenarios of collisions and new resulting soliton-like structures are found.

Diffraction phenomena in a dichroic medium by N. N. Rozanov

*(266-268)*. Diffraction phenomena accompanying the propagation of narrow directed beams of coherent radiation in a medium with anisotropy of absorption and gain are theoretically analyzed. A quasi-optical equation is obtained, which differs from the traditional equation by the complexity of the diffraction coefficient, and this leads to effective diffusion of radiation in anisotropically absorbing media. Because of this, the intensity of minima observed in the far-field region in the case of diffraction of coherent radiation by a slit does not vanish, but has a finite value. The solution for Gaussian beams is constructed. It is shown that the beam width increases as the square root of the path length in an anisotropic medium, whereas the angular divergence varies in inverse proportion to the square root of the path length.

Effect of the initiating-pulse area on induced superradiance by A. A. Bogdanov; A. I. Zaitsev

*(269-274)*. The formation of reflected and transmitted waves in induced superradiance is studied. It is shown that the relationship between reflected and transmitted waves periodically varies with increasing initiating-pulse area. The effect is attributed to the periodic cooperative exchange between forward and backward waves in a sample and its termination at the moment corresponding to the pulse delay time.

Optical holography of diatomic small nanostructure objects and the near-field effect: Dimensional resonances at normal incidence of external optical radiation on a small object by O. N. Gadomskiĭ; A. S. Kunitsyn

*(275-281)*. The interaction of an atomic group occupying a volume with linear dimensions which are considerably smaller than the length of an external light wave is considered. On the basis of the joint set of equations for the electric field strength of the light wave and the optical equations for linear dipole oscillators, the self-consistent problem of determination of the field at the points of location of the atoms, as well as at different points of observation outside the atomic group (a small object) in the wave and near-field zones, is solved. An optical plane hologram of a small object is obtained by way of interference of the coherent field of dipoles of the object and a reference coherent wave in a certain plane of observation points far from the object in the wave zone. It is shown with the help of numerical experiments that a small object forms interference fringes with a good contrast, which allows one to use optical quasi-resonant emission for the development of a nondestructive method of investigation of small objects.

Verifiable post-Maxwellian effect of the nonlinear electrodynamics in vacuum by V. I. Denisov; I. P. Denisova

*(282-287)*. The lasing frequencies of a ring laser with counterpropagating electromagnetic waves are calculated for the case when a part of the laser circuit is subjected to a constant electromagnetic field. It is demonstrated that, according to equations of the parametrized post-Maxwellian electrodynamics of vacuum, two waves with different planes of polarization and frequencies should propagate in each direction of the ring laser. The analysis has shown that, with the help of advanced ring lasers and external electromagnetic fields attainable in the laboratory, the post-Maxwellian parameters can be measured with a precision that would be sufficient to verify the most popular theoretical models of the nonlinear electrodynamics of vacuum.

Nonlinear distortion of laser beams by optical glasses by E. L. Bubis; A. K. Potemkin; S. V. Shubin

*(288-291)*. The critical energy of thermal self-action in a number of optical glasses made in Russia is measured. It is emphasized that one should take into account the effect of thermoelastic stress when calculating this energy.

Role of light-induced scattering in the optical limitation of laser radiation on the basis of fullerene-containing media by I. M. Belousova; V. A. Grigor’ev; O. B. Danilov; A. G. Kalintsev; A. V. Kris’ko; N. G. Mironova; M. S. Yur’ev

*(292-301)*. A theoretical and experimental study of the contribution of light-induced scattering to nonlinear optical limitation is made. It is shown that light-induced scattering makes a considerable contribution to the optical limitation of radiation by fullerene-containing solutions. Radiation is scattered by small-scale (1–10 μm) inhomogeneities of density, and the corresponding increments are rather large. Because of this, scattering can be initiated by small-scale inhomogeneities of the input beam. Numerical simulation of nonlinear scattering is made, and the angular distribution and limitation of radiation in optical limiters are calculated. The calculation results are compared with the experiment.