# Optics and Spectroscopy (v.106, #4)

Eigenvalue problem for bundle of operators and the sturm expansion method in quantum mechanics by S. I. Nikitin; A. I. Sherstyuk

*(467-470)*. Different variants of the generalized formulation of the eigenvalue problem related to a single-particle Schrödinger equation are considered. The nature of the spectrum of problems for a bundle of operators containing the Hamiltonian of the system is analyzed in relation to the form of the weighting operator. For rather general conditions, corresponding systems of eigenfunctions provide diagonal representations of the Green’s function and provide of a rather fast convergence of expansions over intermediate states. Cases of potentials with Coulomb asymptotics and short-range potentials are considered.

**Keywords:**03.65.-w; 31.15.-p

Analytical perturbations of wave functions and energy levels of vibrational states of molecules by S. P. Gavva

*(471-474)*. A method for investigating the excited vibrational states of molecules based on the analytical perturbation theory for linear operators is proposed. According to this theory, the similarity transformation of the total projector and the construction of the transforming function allow obtaining analytical representations of eigenvectors, and in the course of reduction, eigenvalues of the perturbed operator. Theoretical statements and formulas of contributions of analytical perturbations are applied to the investigation of vibrational-rotational interactions, determination of wave functions, and corresponding energy values of excited vibrational states of molecules.

**Keywords:**33.20.Ea

Calculation of higher-order approximations of the coefficients of the Herman-Wallis factor. Test for hydrogen halides by K. V. Kazakov; M. A. Gorbacheva

*(475-482)*. The higher-order approximations of the perturbation theory for the Herman-Wallis factor, which describes the effect of the vibrational-rotational interaction on the matrix elements of dipole moments of diatomic molecules, are calculated within the formalism of quantum number polynomials. An algorithm for taking into account higher orders of the perturbation theory for calculating random coefficients is found; the algorithm has a better convergence than previous theoretical methods. As applied to hydrogen halides, the results obtained agree well with current experimental data.

**Keywords:**31.15.Md; 33.15.Mt

Effect of vibronically induced spin-orbit coupling of electronic ππ* states on nonradiative intersystem crossing: Naphthalene by V. G. Klimenko; E. A. Gastilovich; S. A. Serov; R. N. Nurmukhametov

*(483-489)*. The effect of (I)

*S*_{1}(^{1}*B*2*u*_{ }) ⇝*T*_{1}(^{3}*B*1*u*_{ }) and (II)*S*_{1}⇝*T*_{2}(^{3}*B*3*g*_{ }) ⇝*T*_{1}transitions in naphthalene on the rate constant K_{ST}*s*^{ }of the*S*_{1}⇝*T*_{1}nonradiative transitions to all triplet sublevels*s*=*z, y, x*of the*T*_{1}state has been investigated in the approximation of vibronically induced spin-orbit couplings, taking into account all out-of-plane vibrational modes. The shapes of the vibrational modes that are most active in these transitions are determined. The calculated values*K*_{ST}= (0.33–0.75) × 10^{7}s^{−1}, obtained with allowance for the I and I + II transitions, are consistent with the experimental values (*K*_{ST})_{exp}found by different researchers. It is established in all calculation versions that*K*_{ST}> K_{ST}*z*^{ }> k_{ST}*x*^{ }. This relation is in qualitative agreement with the known magnetooptical data.**Keywords:**33.50.Hv

Time constants of radiative transitions from the 5

*d*[3/2]_{1}level of a xenon atom by I. A. Denezhkin; P. P. D’yachenko; V. P. Semenov*(490-494)*. Integral yields of spontaneous emission at wavelengths of 1.73, 2.03, and 2.65 μm have been measured upon excitation of pure xenon by a pulsed electron beam. These yields have been analyzed and experimental data have been obtained on time constants of radiative transitions 5

*d*[3/2]_{1}→ 6*p*[5/2]_{2}, 5*d*[3/2]_{1}→ 6*p*[3/2]_{1}, and 5*d*[3/2]_{1}→ 6*p*[1/2]_{0}of XeI, which appeared to be equal to (2300 ± 400) × 10^{−9}, (300 ± 40) × 10^{−9}, and (1300 ± 200) × 10^{−9}s, respectively. It is shown that the experimental data are in a qualitative agreement with the results of computational and theoretical investigations. The results of averaging the experimental and calculated data are proposed for use as recommended values of the corresponding constants.**Keywords:**32.70.Cs

Visual study of the microdrop component in sodium vapor-inert gas mixtures in a heat pipe by N. A. Gorbunov; A. N. Kopytov

*(495-498)*. The parameters (size, density, and velocity) of the microdrop component in the cooling zone of a heat pipe in Na + He and Na + Kr mixtures have been determined by visualization. It is found that particles in helium have an average size of 14 μm and concentration of 1.6 × 10

^{4}cm^{−3}, while the corresponding values for krypton are 42 μm and 3 × 10^{3}cm^{−3}. The effect of microdrops as causes of nonequilibrium enhanced concentration of sodium trimers is analyzed. Such a concentration of trimers can explain the high IR absorption coefficients (above 0.9 μm), which were previously observed in heat pipes.**Keywords:**36.40.Vz; 36.40.Mr

Emission characteristics and parameters of gas-discharge plasma in mixtures of heavy inert gases with chlorine by A. K. Shuaibov; A. N. Malinin

*(499-504)*. The ultraviolet (UV) radiation from longitudinal glow-discharge plasma in three- and four-component mixtures of argon, krypton, and xenon with chlorine has been investigated. The total radiation of Ar, Kr, and Xe monochlorides and chlorine molecules in the spectral range 170–310 nm has been optimized with respect to the composition and the pressure of gas mixtures, as well as the discharge current. The mean output power, the electric power of discharge, and the efficiency of a broadband low-pressure exciplex halogen lamp have been determined. Parameters of the glow discharge in Ar-Kr-Cl

_{2}and Kr-Xe-Cl_{2}mixtures have been simulated numerically. The electron energy distribution functions have been determined through the solution of the Boltzmann kinetic equation. These functions have been used to calculate the plasma parameters, namely, electron transfer characteristics, specific losses of discharge power for electronic processes, and ionization and attachment coefficients.**Keywords:**52.25.-b

Effect of oxygen and iodine on the optical and magnetic properties of fullerite C

_{60}by I. V. Bagrov; I. M. Belousova; A. V. Ermakov; V. M. Kiselev; I. M. Kislyakov; E. N. Sosnov*(505-513)*. The effect of oxygen and iodine on the optical and magnetic properties of fullerite C

_{60}is studied by luminescence and EPR spectroscopy within widely varied experimental conditions (temperature of the medium, oxygen or buffer gas pressure, concentration of iodine vapor). It is demonstrated that the efficiency of the singlet oxygen formation when a fullerene sample is irradiated by a neodymium laser at a wavelength of 532 nm and the amplitude of the EPR signal emitted from the unirradiated sample are strongly affected by the concentrations of both oxygen and iodine vapor sorbed by the fullerene sample, as well as by its surface temperature. The spin-spin and spin-lattice relaxation times of paramagnetic centers in fullerite samples studied in the presence of molecular oxygen are determined by the method of microwave radiation absorption saturation.**Keywords:**42.55.-f; 76.30.-v; 78.66.Tr

Reabsorption of laser-induced fluorescence in a plant canopy: Stochastic model by G. M. Krekov; M. M. Krekova; A. A. Lisenko; G. G. Matvienko

*(514-519)*. This paper continues the series of publications on the statistical simulation of transspectral processes. A system of interrelated radiative transfer equations is proposed. This system gives a formal basis for a numerical analysis of a wider range of spectroscopic effects that accompanies the propagation of laser radiation in the environment, such as the reabsorption of fluorescence in dense disperse media containing two and more fluorophores. As applied to the problem of lidar monitoring of the state of a plant canopy, an optical model is developed in which a leaf is not treated as an individual scattering element, but rather as a local volume of a multiphase medium with a complex polydisperse structure. The Monte Carlo algorithms have been modified so that they have achieved the simulation of fluorescence and reabsorption processes. Test calculations have demonstrated the adequacy of the proposed approach.

**Keywords:**42.68.Wt; 42.62.Fi; 42.62.Be

Luminescence quenching of cyclometalated Pt(II) complexes by halogenide ions by M. S. Khakhalina; O. A. Rodionova; M. V. Puzyk; K. P. Balashev

*(520-522)*. The luminescence quenching of [Pt(CΛN)En]ClO

_{4}complexes ((CΛN)^{−}= ppy^{−}, tpy^{−}, and bt^{−}are deprotonated forms of 2-phenylpyridine, 2(2′-thienyl(pyridine), and 2-phenylbenzothiazole, respectively; En is ethylenediamine) by halogenide ions (Hal^{−}= Cl^{−}, Br^{−}, I^{−}) in ethanol solutions is studied. It is shown that the quenching has a dynamic character and its bimolecular rate constants are consistent with the enhancement of nonradiative deactivation of the excited state of {[Pt(CΛN)En]*...Hal} collision complexes with increasing spin-orbit interaction constant of the halogen.**Keywords:**33.50.Dq

Mixed-ligand complexes of Pt(II) and Pd(II) with 2-phenylbenzothiazole by O. A. Rodionova; M. V. Puzyk; K. P. Balashev

*(523-528)*. The mixed-ligand cyclometalated [M(Bt)(μ-Cl)]

_{2}and [(M(N∧N))(Bt)]^{+}complexes (M = Pd(II), Pt(II); Bt^{−}is the deprotonated form of 2-phenylbenzothiazole; and ( N∧N) is ethylenediamine (En) and orthophenanthroline (Phen)) are studied and described by^{1}H NMR spectroscopy, electronic absorption and emission spectroscopy, and voltammetry. The one-electron reduction of complexes is attributed to the electron transfer to the π * orbitals of both diimine and cyclometalated ligands. The long-wavelength absorption bands and vibrationally structured luminescence bands are assigned to optical transitions that are localized mainly on the M(Bt) metal-complex fragment.**Keywords:**33.50.Dq

Luminescence quenching of cyclometalated Pt(II) complexes in acetonitrile and methanol by molecular oxygen by M. S. Khakhalina; O. A. Rodionova; M. V. Puzyk

*(529-531)*. A method is developed for quenching the luminescence of methanol and acetonitrile solutions of cyclometalated Pt(II) complexes with molecular oxygen. A mechanism of luminescence quenching is suggested and bimolecular quenching rate constants are calculated.

**Keywords:**33.50. Dq

Correlation analysis of the shifts of the electronic spectra of anthracene, phenanthrene, and fluorene as functions of the temperature in the gas phase and of the refractive index in

*n*-paraffin solvents by I. A. Ar’ev; N. I. Lebovka*(532-536)*. The temperature-induced shifts of the maxima of the longest-wavelength bands of the

*S*_{1}←*S*_{0}and*S*_{2}←*S*_{0}transitions in phenanthrene and the*S*_{1}←*S*_{0}transition in fluorene in the gas phase are measured. A correlation analysis of these data and similar data on the*S*_{1}←*S*_{0}and*S*_{1}→*S*_{0}transitions in anthracene is fulfilled. The positions of the maxima of analogous bands of the*S*_{1}←*S*_{0}transition in anthracene,*S*_{1}←*S*_{0}and*S*_{2}←*S*_{0}transitions in phenanthrene, and*S*_{1}←*S*_{0}transition in fluorene dissolved in liquid*n*-paraffins are also measured and analyzed as functions of (*n*^{2}− 1)/(*n*^{2}+ 2), where*n*is the refractive index of the solvent. The results confirm the conclusion of the Mirumyantz-Demchuk theory about the linear temperature dependence of the wave number of a band maximum but contradict the prediction that, upon extrapolation to*T*= 0 K, the positions of the maxima correspond to the electronic transitions in the molecule unperturbed by out-of-plane vibrations of the aromatic core.**Keywords:**33.20.-t

Energy characteristics of photothermal vibrational instability at stimulated Raman and Mandelstam-Brillouin scattering in aerosol droplets by M. V. Zhuravlev

*(537-544)*. The threshold intensity and the combination frequencies for photothermal vibrational instability in high-

*Q*aqueous aerosol droplets in the two-mode regime have been calculated. The selection rules for coupling electromagnetic and temperature modes in a droplet are obtained. A comparative analysis of the threshold excitation intensities of photothermal vibrational instability, stimulated Mandelstam-Brillouin scattering, and stimulated Raman scattering in droplets is performed. It is shown that photothermal vibrational instability in the two-mode regime can be developed at a pump intensity of about 10^{4}W/cm^{2}for droplets with radii of 2–20 μm for a pump wavelength of 0.532 μm. A method of remote measurement of the microphysical droplet parameters from the additional periodic temperature shift of droplet eigenfrequencies in the spectrum of stimulated Raman scattering and lasing is proposed.**Keywords:**78.35.+c

Optical method for determining the shape anisotropy of sodium nanoparticles in an island film by T. A. Vartanyan; A. E. Logunov; V. V. Khromov

*(545-548)*. The optical anisotropy of nanoparticle ensembles on transparent dielectric substrates is studied by fluctuation-polarization microscopy. The method is based on measuring fluctuations in the optical characteristics of small areas of a film. The hypothesis that the resonance absorption peaks correspond to the plasma oscillation modes in different directions of sodium particles, which are simulated by three-axial ellipsoids, is confirmed by the frequency dispersion of the polarization signal.

**Keywords:**42.25.Bs; 78.20.-e; 42.87.-d

Spectral properties of Nd

^{3+}ions in samples of transparent Y_{2}O_{3}ceramics by S. N. Ushakov; M. A. Uslamina; E. V. Zharikov*(549-555)*. The spectral and luminescent characteristics of samples of Y

_{2}O_{3}:Nd^{3+}ceramics obtained from different precursors under different preparation conditions (the concentration of an HfO_{2}compacting additive, the temperature and time of synthesis) are studied at 300 and 77 K. It is shown that the spectral positions of absorption and luminescence lines of ceramics correspond to those of a Y_{2}O_{3}:Nd^{3+}single crystal. At the same time, the absorption and luminescence spectra show an inhomogeneous broadening, characteristic of disordered crystals and glass. The energies of the^{4}*I*_{9/2}and^{4}*F*_{3/2}Stark states of the Nd^{3+}ion are calculated. The calculation results nearly coincide with the data from the literature for the Y_{2}O_{3}:Nd^{3+}single crystal and transparent ceramics. Samples containing the compacting additive show additional lines, whose intensities correlate with its concentration and the method of preparation of Y_{2}O_{3}:Nd^{3+}ultradispersed powders. It is assumed that these lines are related to the fact that either Nd^{3+}ions enter the composition of the HfO_{2}compacting additive or Hf^{4+}ions are present in the nearest environment of Nd^{3+}ions at the boundaries of granules enriched with HfO_{2}.**Keywords:**78.40.-q; 78.55.-m

Luminescence peculiarities and optical properties of MgMoO

_{4}and MgMoO_{4}:Yb crystals by D. A. Spasskii; V. N. Kolobanov; V. V. Mikhaĭlin; L. Yu. Berezovskaya; L. I. Ivleva; I. S. Voronina*(556-563)*. Magnesium molybdate is considered as a promising material for cryogenic scintillation bolometers. The luminescence properties of MgMoO

^{4}have been investigated on single crystals grown from melts of stoichiometric and nonstoichiometric compositions and on crystals doped with Yb^{3+}ions. Their optical properties are interpreted taking into account the anisotropy of the MgMoO^{4}crystal structure.**Keywords:**78.55.-m; 78.40.-q

Dissipative solitons in quantum dot lasers by S. V. Fedorov

*(564-569)*. The spatiotemporal dynamics of radiation in wide-aperture semiconductor quantum-dot lasers is studied analytically and numerically. It was found that the choice of relatively rapid amplifying layers with quantum dots of a small size and slow absorbing layers with a maximal rate of exciton capture from wetting layers is optimal for the stability of spatial dissipative solitons in a single-longitudinal-mode laser. A large relaxation time of the slow absorber was found to result in a substantial decrease in the sensitivity of solitons to the tilt of the mirrors, which increases their stability and gives real chances of the experimental revealing of laser solitons.

**Keywords:**42.65.Tg

Quantum fluctuations of spatial dissipative solitons in a nonlinear interferometer by L. A. Nesterov; Al. S. Kiselev; An. S. Kiselev; N. N. Rosanov

*(570-588)*. A quantum Langevin equation is derived that makes it possible to study the radiation field in a large-aperture nonlinear interferometer excited by external classical radiation. This equation is linearized in the vicinity of the solution for a stationary soliton. A mathematical formalism for obtaining a spectral representation of the solution to the linearized problem is constructed. It is shown that, in general, the excitation spectrum of a soliton consists of three branches, two of which belong to a continuous spectrum, while the third branch is discrete. The spectral representation obtained makes it possible to rigorously define the operator of soliton coordinate fluctuations, since, as is shown in the study, the traditional definition of this operator leads to a divergence in the vicinity of the solution. A new type of dissipative soliton is found, which is a natural generalization of a stationary soliton and takes into account its motion. A relation is found between this soliton and the contribution to the solution for field fluctuations from the discrete spectrum expansion. The mean squares of fluctuations of the soliton coordinate and momentum are calculated. A range of parameters is determined where the momentum of the soliton can always be measured with a spread smaller than the standard quantum limit. This possibility is related to the occurrence of states squeezed with respect to the soliton momentum. A scheme is proposed for the experimental observation of these states.

**Keywords:**42.65.Tg

Determination of the parameters of rotational and translational diffusion of a resonant medium by nonlinear polarization spectroscopy by N. D. Milovskiĭ; V. M. Gelikonov; G. B. Malykin

*(589-599)*. A complete theoretical interpretation of the experimental data on the transformation of the polarization state of a weak wave in a layer of resonant medium (methane) depending on the intensity of high-power counterpropagating wave is presented in terms of the vector theory of radiation-matter interaction. A method for the experimental determination of the coefficients of rotational and translational gas diffusion is developed based on the theoretical calculation of two types of dichroism and birefringence and the use of experimental data on the change in the probe wave polarization at saturation of the resonant transition by the intensity of a counterpropagating wave with two different (linear and circular) field polarizations. This method also takes into account low backscattering of the strong wave field from optical path inhomogeneities.

**Keywords:**42.62.Fi

Anti-stokes self-shift and broadening of the femtosecond laser emission spectrum in a strongly absorbing medium by V. G. Bespalov; V. M. Kiselev; I. M. Kislyakov; S. A. Kozlov; V. N. Krylov; G. V. Lukomskiĭ; L. A. Nesterov; S. E. Putilin; N. V. Vysotina; N. N. Rosanov; V. E. Semenov; V. A. Smirnov

*(600-608)*. We have experimentally found a self-shift of the emission spectrum center of gravity for 35-fs output pulses of a Ti:sapphire laser system (

*λ*_{c}= 800 nm) by 75 nm towards shorter wavelengths (more than two half-widths of the initial spectrum) upon focusing the pulses into a strongly absorbing an SZS-23 optical color filter (*K**λ*_{ = 800 nm}= 0.98 mm^{−1}) for the power density in the focal spot ∼10^{13}W/cm^{2}. The effect was accompanied by a simultaneous homogeneous broadening of the spectrum up to 190 nm (FWHM) without the deep dips typical of a spectral supercontinuum, which shows that the phase self-modulation is smooth. The absence of phase distortions over the cross section of the beam with the broadened spectrum was confirmed by the beam divergence, which was close to that of the initial laser beam. These characteristics allow one to hope for the possibility of obtaining the time compression of the beam down to 8–10 fs in duration with the energy conversion factor of ∼10^{−4}. Numerical simulation allowed us to explain the observed effect by nonlinear pulse reshaping and selective absorption in the medium.**Keywords:**42.65.Tg

Reflection of radiation from moving inhomogeneities of a medium: Inhomogeneous wave regimes and the ambiguity problem of doppler frequency shifts by N. N. Rosanov

*(609-613)*. For the problem of the reflection and transmission of monochromatic radiation incident on a moving inhomogeneity of medium characteristics, the regimes for transforming a real frequency into a complex one are discovered. This makes it possible to develop spectroscopy of complex frequencies for absorbing media or near the regime of total internal reflection. It is also shown that, taking into account the complex frequencies, Doppler frequency shifts are found unambiguously if initial conditions for radiation and medium are specified.

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

Temperature and baric changes in the refractive indices of LiKSO

_{4}crystals by V. I. Stadnyk; O. S. Kushnir; R. S. Brezvin; V. M. Gaba*(614-620)*. The effect of uniaxial pressures (up to 200 bar) along the main crystallophysical axes on the spectral (300–750 nm) and temperature (77–300 K) dependences of the refractive indices

*n**i*_{ }(λ,*T*) of LiKSO_{4}crystals has been investigated. A baric increase in*n**i*_{ }(λ,*T*) is revealed, which is caused by the increase in the electronic polarizability α*i*_{ }, bond refraction, and the change in the oscillator parameters due to the variation in the band gap*E**g*_{ }. It is shown that uniaxial pressure shifts phase-transition points both to high and low temperatures by affecting the crystal structure. A ternary point is found in which the incommensurate phase disappears and a paraelectric-to-commensurate phase transition occurs under pressure.**Keywords:**78.20.Fm; 78.30.Am

Suppression of the spectral selectivity of two-layer phase-relief diffraction structures by G. I. Greisukh; E. A. Bezus; D. A. Bykov; E. G. Ezhov; S. A. Stepanov

*(621-626)*. The method and results of studying the effect of relief depth on the attainable degree of reducing the spectral selectivity of two-layer diffraction structures based on plastics and glass. The possibilities of suppressing the spectral selectivity of double- and single-relief structures are compared.

**Keywords:**42.40.Lx

Propagation of light in a quasi-two-dimensional Si/SiO

_{2}superlattice with variable strip thickness by V. V. Rumyantsev; S. A. Fedorov*(627-631)*. The propagation of an electromagnetic excitation localized in a nonideal quasi-two-dimensional Si/SiO

_{2}system that constitutes a topologically ordered set of strips with a random number of defect strips is numerically simulated within the virtual crystal approximation. The defect strips differ from the basic strips (for an ideal periodic structure) in both the composition and the thickness. The concentration dependence of the lowest photonic bandgap of the nonideal striped Si/SiO_{2}film is studied. It is found that the presence of foreign layers in this nonideal superlattice causes a considerable renormalization of its polariton spectrum.**Keywords:**78.20.-e