# Optics and Spectroscopy (v.105, #2)

Interpretation of the electronic spectra of Fe and Co porphyrins based on quantum-chemical calculations by the density functional method by V. G. Maslov

*(163-170)*. Using the time-dependent formalism of the density functional theory (time-dependent density functional theory (TDDFT)), the energies and intensities of the electronic transitions of some Fe and Co porphyrins and their anionic forms with different electron localization are studied quantum chemically. It is shown that, in the majority of the considered cases, the calculations performed with the B3LYP functional with a comparatively narrow basis set (6-31G) are quite consistent with previous calculations of these objects by the ZINDO/S-CI semiempirical method taking into account double excitations. Furthermore, the level of agreement of the B3LYP calculations with experiment is the same as that obtained with the ZINDO/S-CI method.

**Keywords:**31.15.ee

Symmetry of a molecule in an external field by A. V. Burenin

*(171-175)*. It is stated that, although an external field distorts a rigid molecule, it does not destroy internal geometric symmetry of its dynamics, which is specified by a point group. As a consequence, degeneracies of stationary states connected with this group are preserved. This statement makes it possible to describe the spectrum of a molecule in an external field based only on symmetry principles, which is exemplified by the linear Zeeman effect.

**Keywords:**31.15.Hz

Numerical simulation of intramolecular dynamics during dual fluorescence by V. A. Morozov

*(176-182)*. The dynamics of transformation of a light pulse by a five-level model molecule whose secondary emission spectrum can contain two fluorescence bands is simulated. The system of equations that determine the time behavior of the matrix elements of the statistical operator of the molecule interacting with the light pulse is numerically solved. From this solution, the time dependences of the populations of the molecular states are determined for different values of the parameters of the irradiation pulse, which is described in terms of the classical theory, and of the parameters that characterize the rates of radiative and nonradiative spontaneous transitions of the molecule. Based on particular examples of the choice of these parameters, it is demonstrated that the mechanism by which dual fluorescence occurs in molecules with intramolecular hydrogen bonds can be efficiently established from the numerically simulated intramolecular dynamics.

**Keywords:**33.80.Rv; 34.30.+h; 42.65.Sf

Spurious states of the dirac equation in a finite basis set by I. I. Tupitsyn; V. M. Shabaev

*(183-188)*. The occurrence of spurious states for the Dirac equation in a finite basis set is considered. For a Coulomb central-field potential, the spectra of the radial Dirac operator in a finite basis set (without using the kinetic balance) are shown to coincide for two different values of the relativistic quantum number κ that differ in sign. For an attractive Coulomb potential, this means that, for any basis set, spurious states

*p*_{1/2},*d*_{3/2}, … (κ > 0) arise, whose energies exactly coincide with energies of the states 1*s*_{1/2}, 2*p*_{3/2}, … (κ < 0), respectively. In addition, the negative spectra of the Dirac operator in a finite basis set for κ > 0 and κ < 0 also coincide.**Keywords:**03.65.Pm; 03.65.Ge

Formation of lithium-like boron and nitrogen ions in the

^{4}*P*_{5/2}state in gaseous media by I. S. Dmitriev; Ya. A. Teplova; Yu. A. Fainberg*(189-193)*. We experimentally determined the fraction of α

_{v}of lithium-like boron B^{2+}and nitrogen N^{4+}ions in the^{4}*P*_{5/2}state having a velocity of 3.6 au that are formed upon capture of two (α_{2}) electrons by hydrogen-like B^{4+}and N^{6+}ions and upon capture of one (α_{1}) electron by helium-like (1*s*2*s*)^{1,3}*S*metastable B^{3+}and N^{5+}ions in gaseous media (H_{2}, He, N_{2}, Ar), as well as upon passage through a celluloid film. In light-element media (H_{2}, He), α_{2}increases proportional to the target thickness*T**g*_{ }and reaches a maximum at*T**g*_{ }≈ 10^{16}atom/cm^{2}(for B ions, α_{2}≈ 0.2 in H_{2}and α_{2}≈ 0.4 in He). For boron and nitrogen ions passing through thin layers of heavier gases (N_{2}, Ne), α_{2}depends considerably more weakly on*T**g*_{ }, and, in Ar, becomes practically constant. It is assumed that, since hydrogen and helium do not contain electrons with parallel spins, autoionizing lithium-like ions are formed as a result of successive (one by one) capture of electrons, whereas, in the heavier gases, simultaneous capture of two electrons predominates. At*T**g*_{ }∼ 10^{15}atom/cm^{2}, the fraction α_{1}of boron ions is the highest in He, ∼0.15, and the lowest in Ar, ∼0.07, being in qualitative agreement with calculations.**Keywords:**34.50.Fa; 34.50.Gb; 34.70.+e

Excitation of quintet levels of the ytterbium atom by slow electrons by Yu. M. Smirnov

*(194-201)*. The excitation of transitions from upper quintet levels of the ytterbium atom is studied by the method of extended crossing beams. Seventy-five cross sections are measured at the excitation electron energy of 50 eV. Twelve optical excitation functions are recorded in the electron energy range from 0 to 200 eV.

**Keywords:**34.50.Fa

Diagnostics of an O

_{2}(^{1}Δ) generator using multichannel recording of oxygen emission spectra by M. V. Zagidullin; V. D. Nikolaev; M. I. Svistun; N. A. Khvatov; E. V. Fomin*(202-207)*. The concentrations of water vapor and O

_{2}(^{1}Δ), as well as the temperature in the gas flow at the exit of a singlet oxygen generator, are determined using multichannel recording of the singlet oxygen emission spectrum in the bands at 634, 703, 762, and 1268 nm. The water vapor concentration is found from the intensity ratio of the 762-nm band, which corresponds to the^{1}Σ →^{3}Σ transition of the oxygen molecule, and the dimole emission band at 634 nm. From the ratio of the integrated intensities of the bands at 634 and 1268 nm, the O_{2}(^{1}Δ) concentration is determined and it is shown that the yield of O_{2}(^{1}Δ) at the exit from the gas generator is about 52%. The temperature of the gas flow, determined by the rotational structure of the oxygen emission spectrum in the band at 762 nm, is about 300 K under the nominal conditions of the gas generator operation. The ratio of the photon fluxes in the 703 and 634nm bands of the O_{2}(^{1}Δ) dimole emission is 1.06. The temperature dependence of the dimole emission bandwidths is determined, which can be used for estimating the gas temperature at the exit of the O_{2}(^{1}Δ) generator.**Keywords:**33.20.-t; 33.70.-w

Effect of the vibrational pattern of out-of-plane vibrational modes on vibronically induced spin-orbit coupling between ππ* states involved in nonradiative intersystem crossing transitions by E. A. Gastilovich; N. V. Korol’kova; S. A. Serov; V. G. Klimenko; R. N. Nurmukhametov

*(208-216)*. To describe nonradiative intersystem crossing between excited ππ* states, the matrix elements of the operator of spin-orbit interaction are calculated. Adiabatic electronic functions that depend on out-of-plane normal vibrational coordinates are used as a zero approximation. Using dibenzofuran and tetrachloro-substituted dioxin as examples and taking into account all the out-of-plane vibrational modes, the effects of the vibrational patterns of these modes on the matrix elements under consideration, as well as of the spin-orbit coupling in carbon, oxygen, and chlorine atoms of individual atomic groups of the molecule, are discussed.

**Keywords:**33.50.-j

Dynamic fluorescence quenching and the highest excited states of molecules by V. I. Tomin

*(217-222)*. The dynamic fluorescence quenching in organic molecules, or quenching of the second kind according to Vavilov’s classification, is an efficient method of investigating excited states in solutions and is widely used in various fields. The effect of quenching on the intensity of the fluorescence from the first and higher singlet states of organic molecules is studied. The results may serve as a basis for determining the nature of the short-wavelength luminescence and can be used to distinguish the

*S**n*_{ }fluorescence from the comparably intense luminescence of impurities, which is a very important problem when investigating such emissions. A method for obtaining dynamic quenching by specially chosen quenchers is proposed. The method is based on an experimentally found strong increase in the constants of bimolecular collisions of luminophore and quencher molecules when the luminophore is excited through the highest singlet states.**Keywords:**33.50.Dq

Determination of the stern-volmer constant in quantum systems with dual fluorescence by V. I. Tomin

*(223-227)*. The mathematical relations describing the properties of the steady-state spontaneous emission of quantum systems with dual fluorescence under conditions of dynamic quenching of excited states by foreign impurities are analyzed. The direct dependence of the intensity and yield of the photoproduct fluorescence on the quencher concentration is not simple and cannot serve as a convenient base for determining the Stern-Volmer constant. It is shown that, in the case of a kinetic character of product formation, the fluorescence intensity ratio of the initial dye and its photoproduct linearly increases with the quencher concentration. The relation obtained can be used to determine the constant of bimolecular quenching of the excited states of reaction products. This conclusion is based on the analysis of the experimental fluorescence spectra of 3-hydroxyflavone, obtained upon excitation in the region of the

*S*_{1}absorption band under conditions of dynamic quenching by potassium iodide. This analysis can be applied to a wide range of luminophores with photoreactions accompanied by dual fluorescence (charge transfer, proton transfer, phosphorescence, complexation, etc.).**Keywords:**33.50.Dq

Spectroscopic study of thulium-activated double sodium yttrium fluoride Na

_{0.4}Y_{0.6}F_{2.2}:Tm^{3+}crystals: I. Intensity of spectra and luminescence kinetics by S. E. Ivanova; A. M. Tkachuk; A. Mirzaeva; F. Pellé*(228-241)*. Na

_{0.4}Y_{0.6}F_{2.2}:Tm^{3+}crystals with a thulium content from 1 to 100 at % have been grown by the Stockbarger-Bridgman method. The optical spectra of Na_{0.4}Y_{0.6}F_{2.2}:Tm^{3+}crystals were investigated in detail at room and low (10 K) temperatures, and the luminescence kinetics was analyzed using different excitation methods. The structure of the Stark splitting of thulium levels as “quasi-centers,” characterized by inhomogeneous broadening of the Stark components, is determined from analysis of the absorption spectrum at 10 K. The oscillator strengths of the transitions from the ground state to excited multiplets are determined from the absorption cross-section spectra at 300 K for ten transitions in the range 5000–38 500 cm^{−1}and seven transitions in the range 5000–28 500 cm^{−1}. The transition intensity parameters Ω*t*_{ }, obtained by the Judd-Ofelt method from the spectra due to the transitions to ten and seven excited levels, were found to be, respectively, (i) Ω_{2}= 1.89 × 10^{−20}, Ω_{4}= 2.16 × 10^{−20}, and Ω_{6}= 1.40 × 10^{−20}cm^{2}and (ii) Ω_{2}= 2.04 × 10^{−20}, Ω_{4}= 2.01 × 10^{−20}, and Ω_{6}= 1.44 × 10^{−20}cm^{2}. These values of the intensity parameters were used to calculate the radiative transition probabilities and branching ratios and to estimate the multiphonon nonradiative transition probabilities for NYF:Tm. The luminescence decay kinetics from thulium radiative levels upon their selective excitation by nanosecond laser pulses has been studied and the lifetimes of thulium radiative levels in NYF crystals have been found.**Keywords:**78.55.-m

The vibrational spectrum of the OCS molecule based on the data on spectra of liquid and cryosolutions by V. N. Bocharov; A. P. Burtsev; O. S. Gulidova; T. D. Kolomiĭtsova; D. N. Shchepkin

*(242-250)*. The IR absorption spectra of liquid OCS (

*T*= 135(1) K) and of the following solutions—OCS + Ar (*T*= 90 K), OCS + N_{2}(*T*= 90 K), OCS + Kr (*T*= 130 K), and OCS + Xe (*T*= 163 K)—are measured in the range 800–7000 cm^{−1}. From 16 to 40 bands corresponding to transitions to vibrational states up to the third order inclusive are interpreted for basic isotope modification and for the isotopically substituted molecules^{18}O^{12}C^{32}S,^{16}O^{13}C^{32}S, and^{16}O^{12}C^{34}S. In the spectra of the liquids, the spectral moments*M*(1) and*M*(2) of all the observed bands are determined. The harmonic frequencies ω*i*_{ }and the anharmonicity constants*x**ik*_{ }are calculated for all the systems, including the liquid. The anharmonicity is found to be constant within the experimental error. A large shift Δω_{3}is primarily determined by the dipole-induced dipole interaction.**Keywords:**33.20.Ea

Concentration quenching and migration of excitations in a bulk Cd

_{0.5}Mn_{0.5}Te crystal by N. N. Vasil’ev*(251-256)*. The curves of intracenter luminescence decay for Mn

^{2+}ions in the Cd_{0.5}Mn_{0.5}Te semiconductor solid solution, obtained in a low-temperature experiment, have been simulated by the Monte Carlo method. The features of the kinetics of the 2-eV band in the time interval where significant nonexponentiality of relaxation at different points of the emission band profile manifests itself, as well the integral kinetics and energy relaxation, have been considered. Migration of ion excitations and concentration quenching (which was previously disregarded) are considered to be the main mechanisms determining the kinetic curve formation. It was established that excitation by 2.34-eV photons leads to both selective (intracenter) and band excitation of Mn^{2+}ions. Comparison of the results of numerical simulation and experiment showed that the characteristic values of the migration and quenching rates (*W**m*_{ }and*W**q*_{ }, respectively) are close in magnitude and*W**q, m*_{ }≈ 0.1/τ, where τ is the lifetime at the long-wavelength band wing with the exponential kinetics. The estimated quantum yield (0.56) indicates significant influence of the concentration quenching on the 2-eV luminescence quantum yield in Cd1 −*x*_{ }Mn*x*_{ }Te and Zn1 −*x*_{ }Mn*x*_{ }S crystals with a high concentration of Mn^{2+}ions.**Keywords:**78.55.Et

Polarization modulation spectroscopy of surface plasmon resonance by L. J. Berezhinsky; L. S. Maksimenko; I. E. Matyash; S. P. Rudenko; B. K. Serdega

*(257-264)*. The features of surface plasmon resonance in gold nanofilms deposited on the surface of a total-internal-reflection prism have been investigated theoretically, using the Fresnel equation, and experimentally, with application of the polarization modulation technique. The angular characteristics of the polarization difference of the reflection coefficients for

*s*-and*p*-polarized light, Δρ =*R**s*_{ }^{2}−*R**p*_{ }^{2}, were measured in the wave-length range λ = 0.4–2.0 μm. It is shown that the characteristics of Δρ, in contrast to the results of standard measurements by the surface plasmon resonance method, have a resonance peak. Due to this, the characteristics of the polarization difference contain nonresonant components whose magnitudes are determined by the internal reflection coefficients for the metal and insulator; these parameters depend on the film thickness. The calculated and experimental data coincide when the model assumes exponential dependence of the refractive indices and extinction coefficients on the thickness of the metal film. It is established that the characteristic parameter of the exponential is a metal film thickness of 11.0 ± 0.5 nm, at which the film optical parameters correspond to the bulk characteristics.**Keywords:**73.20.Mf

Complexes of moving transversely one-dimensional laser solitons by N. N. Rozanov; S. V. Fedorov; A. N. Shatsev

*(265-267)*. Complexes of weakly coupled moving solitons are found by numerical solution of the generalized Ginzburg-Landau equation for the transversely one-dimensional scheme of a wide-aperture

*A*-class laser with saturable absorption. As distinct from the case of complexes of motionless solitons, the phase difference between the neighboring moving solitons is close to 7π/2.**Keywords:**42.65.Tg

The doppler frequency shift caused by the inhomogeneities of a medium induced by pulses of intense laser radiation by N. N. Rozanov; Al. S. Kiselev; An. S. Kiselev

*(268-269)*. Self-reflection of pulses of intense laser radiation from an inhomogeneity induced by them in a medium with fast optical nonlinearity is analyzed. The reflected radiation is characterized by a considerable Doppler shift and by a signal magnitude that is sufficient for experimental detection.

**Keywords:**42.65.Tg; 03.50.De

Optimization of self-frequency doubling in periodically and quasi-periodically poled nonlinear crystals by D. V. Kovalevsky; V. M. Detkova; A. V. Kurochkin

*(270-279)*. The theory of self-frequency doubling in a periodically poled nonlinear crystal is generalized to the case of varied domain thickness (quasi-periodically poled crystals). A particular statistical model of quasi-periodicity is considered. The effect of quasi-periodicity on the output emission intensity is calculated. The degree of quasi-periodicity allowable for practical applications is estimated, and the advantages of quasi-periodically poled crystals are discussed. The problem of maximization of the output emission intensity for periodically and quasi-periodically poled crystals is considered. The dependence of the output emission intensity on the crystal length is investigated, and an upper estimate for the maximum intensity is obtained. A formula for the optimal reflection coefficient of the output mirror as a function of the crystal length is derived.

**Keywords:**42.65.Ky

A nonlinear optical model of an air medium in the problem of filamentation of femtosecond laser pulses of different wavelengths by V. Yu. Fedorov; V. P. Kandidov

*(280-287)*. A frequency-dependent model of nonlinear optical response of atmospheric air upon propagation of a femtosecond laser pulse is constructed. The model is derived on the basis of generalized experimental and theoretical data on the cubic susceptibility and photoionization of gaseous components of air. The model was proved by solving the problems of filamentation of a femtosecond laser pulse with a wavelength lying in the range 0.24 to 1.2 μm.

**Keywords:**52.38.Hb

Two-level atoms moving in strong biharmonic and monochromatic counterpropagating fields by S. A. Pulkin; T. H. Yoon; A. I. Kuz’min; S. V. Uvarova

*(288-291)*. The polarization and power spectra of radiation of two-level atoms moving in a field of biharmonic and monochromatic counterpropagating waves are computer simulated. It is shown that, as the frequencies of the counterpropagating waves are scanned with respect to the central frequency of the Doppler contour in the intensity distribution of groups of atoms moving at velocities that satisfy the resonance conditions for multiphoton transitions between quasi-energy levels, apart from well-known sub-Doppler resonances, narrow peaks appear. Such resonances should also occur for the stimulated light pressure force.

**Keywords:**42.50.Hz

Light scattering by multilayered axisymmetric particles: Solution of the problem by the separation of variables method by V. G. Farafonov; A. A. Vinokurov

*(292-305)*. A new solution to the problem of light scattering by multilayered particles possessing axial symmetry is obtained. Two methods are applied for this purpose. One is the separation of variables method with expansion of fields in terms of spherical wave functions, and the other is a novel approach based on the separation of fields into axisymmetric and nonaxisymmetric parts and on the choice of specific scalar potentials for each of them. A specific feature of the new solution is that the dimension of truncated linear algebraic systems used for determining unknown expansion coefficients of fields does not increase with an increasing number of layers. Using double-and three-layer spheroidal and Chebyshev particles of different shape and size as examples, the domain of applicability of the solution presented is compared with that of the solution previously obtained by the extended boundary conditions method. Except for nearly spherical particles, the solution presented is shown to be more favorable than the previously obtained solution.

**Keywords:**42.68.Mj

Fluorescence of semiconductor nanorods in liquid-crystal composites by V. V. Danilov; M. V. Artem’ev; A. V. Baranov; G. M. Ermolaeva; N. A. Utkina; A. I. Khrebtov

*(306-309)*. The fluorescence of CdSe/ZnS nanorods in liquid-crystal and anisotropic polymer composites is studied. A high degree of the fluorescence anisotropy is shown. It is found that a solubilizer strongly affects the CdSe/ZnS orientation, which opens new possibilities for creating electrically controlled liquid-crystal composites.

**Keywords:**78.67.Bf

Nonlinear model of sequential recording of superimposed holographic gratings in photopolymer composites with allowance for the self-diffraction from spatial harmonics by E. A. Dovol’nov; S. N. Sharangovich

*(310-319)*. The problems of sequential recording of superimposed holographic diffraction structures of transmission and reflection types in photopolymer composites have been investigated taking into account an arbitrary degree of photopolymerization nonlinearity and the interference pattern contrast at an arbitrary ratio of the photopolymerization and diffusion mechanisms of recording and self-diffraction processes. A theoretical model for

*N*superimposed phase diffraction structures has been constructed by solving interrelated kinetic equations of photopolymerization for*H*+ 1 spatial harmonics of each diffraction structure. This approach makes it possible to investigate the temporal dynamics of the harmonic amplitudes, spatial profile, diffraction efficiency, and angular selectivity of recorded gratings. The model proposed takes into account the diffraction of recording beams from the first harmonic of the*i*th grating during formation of the (*i*+ 1)th grating.**Keywords:**42.40.-i

Methods of ellipsometric analysis of polarization optical properties of inhomogeneous surface layers of optoelectronics elements by V. S. Zemlyanskiĭ; I. A. Khramtsovskiĭ; A. N. Gorlyak; A. A. Stepanchuk

*(320-325)*. The basic regularities of changes in the main ellipsometric parameters of a light beam reflected from inhomogeneous surface layers of silicate glasses have been described on the basis of the Drude-Born theories of polarized light reflection. A method of physicomathematical modeling of the refractive index profile in an inhomogeneous surface layer of silicate glasses is reported, which makes it possible to determine, with the lowest second-kind error probability, a model of an inhomogeneous reflecting system that is adequate to the object of study.

**Keywords:**78.20.Ci