# Optics and Spectroscopy (v.90, #3)

Calculation of the

*H*_{α}line profile in a high-temperature plasma by P. I. Mel’nikov; I. A. Ivanov*(303-314)*. A new method for calculating broadening of the

*H*_{α}line profile in a high-temperature plasma is proposed. Using the new program H-ALPHA, one can calculate the*H*_{α}line profile with an error smaller than 3% in a wide range of electron temperatures and densities (*T*_{e}=1–500 eV,*n*_{e}=10^{14}−10^{17}cm^{−3}). On the basis of these calculations, a method for the measurement of plasma temperature and density from the experimental*H*_{α}line profile is developed. The experimental tests of the method showed a good agreement with the diamagnetic measurements. Probabilities of electric dipole transitions in the spectra of ions of the erbium isoelectronic sequence by G. P. Anisimova; A. V. Loginov; V. I. Tuchkin

*(315-320)*. The probabilities of the 4

*f*^{13}6*p*→4*f*^{13}*ns*(*n*=6 and 7) electric dipole transitions are calculated for the spectra of YbIII, LuIV, and HfV ions of the erbium isoelectronic sequence. The wave functions of the intermediate coupling scheme, which are necessary for calculating the relative line strengths, are semiempirically obtained from experimentally measured energy intervals between the fine-structure levels. To pass to the absolute values, radial integrals of transitions are used, which are evaluated with the Hartree-Fock functions. Numerical simulation of a barrier discharge in Xe by G. N. Zvereva; G. N. Gerasimov

*(321-328)*. Components of plasma of a barrier discharge in xenon are calculated for various values of the parameter

*E/N.*Features of excimer population are analyzed. Efficiencies of the VUV emission yield are calculated, and basic channels of energy loss determining the efficiency are established. Kinetics of formation of the excited states of krypton atoms and ions upon electron-induced desorption from a solid surface by V. I. Yakovleva; A. B. Tsyganov; I. E. Kozlov

*(329-331)*. The kinetics of formation of the excited states of the atomic krypton ion is studied in pure krypton at a low pressure. The excited states are formed due to the dissociation of excited molecular ions desorbed from a solid surface by an electron beam. The lifetimes of these ions and their dissociation channels are determined.

Slow-electron excitation of

^{3}*S*,^{3}*P*, and^{3}*P*^{0}levels of the strontium atom by Yu. M. Smirnov*(332-338)*. The electron impact excitation of

^{3}*S*,^{3}*P*, and^{3}*P*^{0}levels of atomic strontium was investigated by the methods of extended crossed beams and optical spectroscopy. The results obtained are compared with the data of the previous experiment and the theoretical results. The behavior of excitation cross sections in spectral series of SrI is discussed. Resonances at slow electron collisions with zinc atoms and ions by E. É. Kontrosh; I. V. Chernyshova; L. Sovter; O. B. Shpenik

*(339-343)*. The optical excitation functions of four spectral lines corresponding to the transitions from the 4

^{1}*D*_{2}, 5^{3}*S*_{1}, 4^{3}*D*_{j}, and 6^{1}*S*_{0}levels of atomic Zn were investigated with an electron spectrometer of a new construction. For the first time, elastic scattering of slow electrons from the Zn ions at an angle close to 180° was studied. In the energy range under investigation (0–7 eV), both the optical excitation functions of atomic spectral lines and the differential cross section of elastic scattering manifested the resonant structure caused by the contribution of autoionization states of the atom. Study of traces of elements on a universal laser photoionization spectrometer by A. T. Khalmanov; Kh. S. Khamraev; A. T. Tursunov; O. Tukhlibaev

*(344-347)*. A new complex laser analytical spectrometer operating synchronously in the atomic beam regime and in the flame regime is developed. Analytical potentialities of the spectrometer are demonstrated by the example of determining sodium and calcium content in standard solutions and aluminum alloys. Processes of thermal atomization of Ca and Na in vacuum and the effect of the basis of a sample on the element determined are studied. Efficient excitation via Rydberg states is realized for these elements. The contents of Ca and Na in aluminum alloys are determined at levels of 10

^{−2}and 10^{−3}%, respectively. New equations for derivatives of vibrational frequencies by D. A. Knyazev

*(348-350)*. A new equation is presented that expresses first partial derivatives of eigenvalues of the secular equation in terms of first derivatives of coefficients of the secular equation and the eigenvalues themselves. The utility of this equation is demonstrated using the example of isotopic shifts in the vibrational frequencies of molecules with second-order submatrices. Simple expressions for second, third, and forth derivatives of the eigenvalues are derived for this case.

Effect of a polar environment on the resonant generation of higher optical harmonics by dipole molecules by V. A. Kovarskiĭ; O. B. Prepelitsa

*(351-355)*. An analysis is made of the effect of fluctuations of a polar environment on the resonant generation of higher optical harmonics by dipole molecules in a strong electromagnetic field. The cases of slow and strong fluctuations of the environment are considered. It is shown that the electric fields produced by fluctuating dipole moments of the medium lead to anomalous temperature dependences of the scattered-radiation intensity. In the case of slow fluctuations and some additional conditions, the harmonic intensity exponentially increases with temperature. In contrast, in the case of rapid fluctuations under exact resonant conditions, the harmonic intensity decreases with increasing temperature. Under nonresonant excitation of molecules, a polar medium has no effect on the generation of higher harmonics.

Calculation of vibrations of the H-bonds and electrooptical parameters of the F(HF)

_{2}]^{−}complex by V. P. Bulychev; G. S. Denisov; H. -H. Limbach; R. M. Shukailov*(356-361)*. The problem of calculating the vibrations of the F(HF)

_{2}]^{−}complex with hydrogen bonds is considered with allowance for the anharmonicity and interaction of motions in different degrees of freedom. A systematic solution of this problem is proposed which consists in separating the total vibrational system into subsystems, obtaining sufficiently exact vibrational wave functions of subsystems, and expanding the vibrational wave functions of the total system in basis functions constructed from the wave functions of subsystems. At the first stage of our study, the stretching and bending modes of two F...HF hydrogen bonds are considered with the use of an exact kinetic energy operator and a nonempirical three-dimensional potential energy surface. It is shown that these vibrational modes of the complex are characterized by significant mechanical and electric anharmonicities. The calculated values of frequencies of the symmetric and antisymmetric vibrations of hydrogen bonds are in good agreement with the experimental findings. Fractal properties of the vibrational-rotational absorption bands of water vapor by Yu. V. Kistenev; Yu. N. Ponomarev

*(362-366)*. The vibrational-rotational bands in the absorption spectra of atmospheric water vapor are interpreted using multifractal analysis. The fractal properties of the frequency distribution of absorption lines are considered, as well as “the absorption density”—the total absorption within a small frequency interval normalized to the total absorption in the region of the vibrational-rotational band. It is shown that the vibrational-rotational absorption bands of atmospheric water vapor exhibit specific multifractal characteristics.

Electronic structure and fluorescence spectrum of the HeO

^{+}cation by A. N. Petrov; A. I. Panin*(367-370)*. Quantum-mechanical calculations of the potential curves of the HeO

^{+}ion are preformed which correlate with four lower dissociation limits and indicate the excimer type of the ion. The transition dipole moments of the 2^{2}Σ^{−}→1^{2}Σ^{−}and 2^{4}Σ^{−}→1^{4}Σ^{−}transitions are calculated. The energies and radiative lifetimes of vibrational levels are determined and structural and spectroscopic constants of the states 1^{2}Σ^{−}, 2^{2}Σ^{−}, 1^{4}Σ^{−}, and 2^{4}Σ^{−}are calculated. The fluorescence spectrum corresponding to the 2^{2}Σ^{−}→1^{2}Σ^{−}and 2^{4}Σ^{−}→1^{4}Σ^{−}transitions is also calculated. The possibility of lasing at these transitions is discussed. Efficiency of the use of two-photon absorption in impurity liquid crystals as a mechanism of optical limitation by V. V. Danilov; E. N. Sosnov; O. V. Chistyakova; T. A. Shakhverdov; T. Brunier

*(371-374)*. An analysis is made of the advantages of impurity liquid-crystal systems that are associated with the existence of the excitonic mechanism of electronic excitation energy transfer in them. Using the two-photon absorption in such systems, one can substantially expand the dynamic range of optical limitation.

Low-dimensional transport of the triplet excitation of chrysene in porous matrices by S. A. Bagnich

*(375-380)*. The transport kinetics of the triplet state of solid chrysene embedded in the channels of various porous matrices is studied by observing its delayed luminescence. As matrices, a porous glass was used, which was obtained by leaching a sodium borosilicate glass and natural chrysotile-asbestos minerals. It is shown that the annihilation kinetics of the triplet states for all the samples studied is inhomogeneous, with the rate described by a power dependence on time. The value of the exponent depends on the system topology. Its values obtained from the analysis of the decay kinetics of delayed luminescence suggest that the geometry of the porous network of a sodium borosilicate glass is close to that of a three-dimensional percolation cluster.

Calculation of the probability of nonradiative electronic transitions from deep centers in GaAs in the one-coordinate approximation by S. V. Bulyarskiĭ; N. S. Grushko; A. V. Zhukov

*(381-386)*. A study was made of the experimental optical bands of radiative V

_{Ga}S_{As}and V_{Ga}Sn_{Ga}complexes in GaAs in a wide temperature range. Parameters of the one-coordinate model of the centers were determined. The configuration-coordinate diagram of the V_{Ga}S_{As}complex was constructed. Using parameters of the one-coordinate model of the V_{Ga}S_{As}complex as the base, the field dependences of emission rates were calculated. The calculation results were compared with the experimental data. A conclusion was made that the one-coordinate model can be used for the description of the field dependence of the rate of hole emission from the V_{Ga}S_{As}center. Inverse optical magnus effect in the Majorana representation by N. R. Sadykov

*(387-389)*. An equation describing the effect of additional bending during photon motion along a twisted path is obtained from Maxwell’s equations in the Majorana representation. The generalized Rytov law in an arbitrary curvilinear system of coordinates forms the basis for the effect. The effect considered is inverse to the optical Magnus effect.

Dynamics of ultimately short pulses in partially absorbing media by S. V. Sazonov; A. F. Sobolevskii

*(390-395)*. Propagation of broad-band ultimately short light pulses in a partially absorbing medium is analyzed in the framework of the three-level model. Nonlinear wave equations are obtained describing propagation of light pulses in media with quadratic (all three transitions are allowed) or cubic (one of the transitions is forbidden) nonlinearity in the range of optical transparency or with the sine-Gordon-type nonlinearity in the region of absorption. Using the averaged variational principle, the approximate solutions of equations in the form of unipolar soliton-like signals are found and conditions of their transverse stability are determined. A stable propagation of a broad-band pulse is shown to be possible under conditions when monochromatic signals exhibit self-focusing.

Surface waves at the boundary of a chiral medium by V. V. Fisanov

*(396-397)*. The exact analytical solution of the dispersion relation for the propagation constant of the surface waves existing at the plane interface between chiral and magnetodielectric media is given and studied. An enhancement of the chirality effect due to matching of the permittivities of the media is noted.

Diffraction of an ultrashort pulse by an aperture by M. K. Lebedev; Yu. A. Tolmachev

*(398-404)*. The scalar problem of diffraction of an infinitely short pulse by a plane screen is solved within Kirchhoff’s approximation. The response of an infinitely small aperture is calculated, and the explicit solution is found for the case of a circular aperture.

Acoustooptical interaction of light beams under conditions of internal conical refraction by G. V. Kulak

*(405-407)*. The collinear acoustooptical (AO) interaction of light beams under conditions of internal conical refraction is considered. The dependences of the diffraction efficiency on the ratio of radii of light and ultrasonic beams, the AO coupling length, and the ultrasound intensity are found. An analytical expression is obtained describing the diffraction efficiency of collinear AO conversion of annular beams of internal conical refraction.

Orientational averaging of integrated cross sections in the discrete dipole method by N. G. Khlebtsov

*(408-415)*. Using the discrete dipole method, exact and approximate analytical solutions for orientation-averaged cross sections for extinction, absorption, and scattering of light are obtained. The analytical solutions can be applied to the calculation of integrated cross sections of fractal clusters formed by primary particles with different optical properties (soot in air and aqueous suspensions of aggregates of polystyrene, gold, and silver nanoparticles). It is shown that two models of aggregates that differ only in trajectories (ballistic or Brownian) of primary particles and intermediate clusters and in average fractal dimensions give close values of averaged extinction cross sections.

Diagram method for exact solution of the problem of scanning near-field microscopy by S. I. Bozhevolnyi; V. Z. Lozovski; Yu. V. Nazarok

*(416-425)*. A method is presented for calculating near-field images of nanoobjects from the intensity distributions measured using the scanning near-field optical microscopy technique. The method is based on a formally exact solution of the self-consistent local-field equation, which was derived using the diagram technique for summation of infinite series. It is shown that the self-consistent fields calculated with and without considering the dielectric substrate differ significantly. Near-field images of simple geometric objects—parallelepipeds with various side ratios—are calculated.

Speckle interferometry of phase-modulated beams by N. M. Kozhevnikov; A. E. Korolev; M. Yu. Lipovskaya

*(426-428)*. It is shown experimentally that a scatterer placed in the interference field of the signal and the reference beams can be used for detecting phase-modulated optical signals. The signal observed in this case is formed by the space-time modulation of the speckle structure of the beams. The influence of the geometry of the interferometer and the amplitude of phase modulation on the parameters of the output signal is considered.

Diffusion-controlled photoprocesses on chemically modified porous silica by V. V. Bryukhanov

*(429-434)*. Photoprocesses involving organic luminophores adsorbed on the surface of wide-porous silica chemically modified with

*n*-alkyl hydrocarbons with different chain lengths are studied upon cw and pulsed laser excitation. The results of the study are interpreted within the framework of a diffusion model of acceleration of the exchange-resonance processes of triplet-triplet energy transfer and triplet-triplet homo-and hetero-annihilation of the interacting molecules. Specific features of the resonance interaction of a coherent wave with an ensemble of impurity atoms of a photonic crystal by A. M. Basharov

*(435-438)*. Two-quantum relaxation transitions in an impurity atom that are activated by its resonance interaction with a monochromatic wave lead to hole burning in the distribution of atoms populating the lower energy level over detunings from the resonance. In this case, the levels of an impurity atom lying within the gap or the pseudogap in the density of photon states of a photonic crystal act as a trap. The impurity atoms change to these levels in the process of interaction of a monochromatic wave with the atomic transition that is not influenced by specific spectral features of a photonic crystal.

Inelastic interaction of ultrashort pulses of polarized light with an ensemble of isolated quantum dots by S. O. Elyutin; E. V. Kazantseva; A. I. Maimistov

*(439-445)*. A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.

Optical anisotropy of phthalocyanine films by B. M. Ayupov; S. A. Prokhorova

*(446-451)*. Using vacuum deposition, phthalocyanine films at constant and variable angles of vapor incidence on a substrate were produced. In some experiments, substrates were placed in a magnetic field, which was oriented along the surface. Hydrogen phthalocyanine films were processed with iodine and methyl iodide vapors. The anisotropy of samples was studied by the zero single-wave ellipsometry. In the experiments, the analyzer axis was oriented in the plane of incidence or in the plane of a sample, and a search for the polarizer and analyzer angles of suppression as functions of the polar angle of a sample was carried out. It is shown that the experimental data can be classified on the basis of three models proposed for the structure of phthalocyanine films. An expression for the description of anisotropy of films described by the three models is presented, and a method for finding parameters of a model is described. It is anticipated that reverse problems in the study of anisotropic media by ellipsometry can be solved without determining elements of the reflection matrix.

On algebraic foundations of Fourier holography by A. V. Pavlov

*(452-457)*. Fourier holography is considered as the physical basis of an algebraic model. A constructive interpretation of the formal axiomatics is presented. It is shown that the scheme of Fourier holography corresponds to an additive semigroup with convolution serving as abstract summation. The correlation operation plays the role of subtraction, and a diffraction-limited point source becomes an additive neutral element. The Fourier holography scheme sequentially constructs model elements in accordance with the Peano axioms. It realizes the axis of model elements correctly with respect to the summation and subtraction operations within the limits of angular invariance.

Polarization-correlation analysis of anisotropic structures in bone tissue for the diagnostics of pathological changes by O. V. Angel’skiĭ; A. G. Ushenko; D. N. Burkovets; Yu. A. Ushenko

*(458-462)*. A method for the correlation analysis of polarization-filtered laser images of bone tissue is considered. Its ability to visualize the bone-tissue multifractal network in its normal and pathological states is analyzed. A set of criteria for the optical diagnostics of osteoporosis is determined.