# Optics and Spectroscopy (v.105, #4)

Calculation of the interruption function in the fourth order of the perturbation theory by A. E. Protasevich

*(481-488)*. General expressions for fourth-order terms for calculating the interruption function

*S*(*b*) in terms of the perturbation theory are derived for molecules with different symmetry properties and arbitrary trajectories of the relative motion of colliding molecules. An expression for a quadruple integral over time appearing in the definition of new resonance functions is written in terms of the Fourier transform of the coefficients of the intermolecular interaction potential.**Keywords:**82.20.Fd

Effect of a heavy atom in the

*S*_{1}(ππ*) ↝*T*_{1}(ππ*) nonradiative transition. 9,10-Dichloroanthracene by E. A. Gastilovich; V. G. Klimenko; N. V. Korol’kova; R. N. Nurmukhametov*(489-495)*. The rate constant

*K*_{ST}for the nonradiative intersystem crossing transition*S*_{1}(^{1}*B*1*u*_{ }) ↝*T*_{1}(^{3}*B*1*u*_{ }) (I) in 9,10-dichloroanthracene (DClA) is calculated in terms of the model of vibronic-induced spin-orbit (VISO) interactions. The magnitude fluorescence quantum yield ϕ_{fl}is estimated. Comparison of*K*_{ST}(I) and ϕ_{fl}for DClA with the corresponding values obtained earlier for anthracene (AC), where*K*_{ST}is governed by the conversion channels (I) and*S*_{1}(^{1}*B*1*u*_{ }) ↝*T*_{2}(^{3}*B*3*g*_{ }) (II), shows that the theoretical estimates reflect the anomalous heavyatom effect in these molecules in accordance with the experimental (literature) data. The cause for this effect is revealed. The influence of different factors on the*K*_{ST}(I) constant and on the ratio of its components*K*_{ST}*s*^{ }(where*s*denotes the*z*and*y*spin-sublevels) is established for DClA. These factors are the magnitude of the spin-orbit coupling parameter in a chlorine atom, the change, as compared to AC (in the same conversion channel (I)) of the distribution of electrons in the carbon core of the DClA molecule, and the change in the form of out-of-plane vibrational modes involved in VISO interactions.**Keywords:**33.50.Hv

Studying reactions that proceed from highest excited states of molecules using fluorescence quenching by V. I. Tomin

*(496-510)*. The steady-state monochromatic excitation of a luminophore that has fluorescing products is considered. The effect of dynamic quenching of highest excited states on the fluorescence of singlet states under its excitation via singlet

*S*_{1}and*S**n*_{ }(*n*≥ 2) states is discussed. It is shown that the use of the method of fluorescence dynamic quenching by foreign impurities opens new possibilities for studying photoreactions that proceed via*S**n*_{ }singlet states. A large number of primary photoprocesses are considered which include the electron density redistribution (the internal electron transfer) in the excited state, protolytic reactions, intramolecular proton transfer (phototautomerization), hydrogen bonding, and formation of excimers and exciplexes. It is shown that, upon dynamic quenching, the bimolecular quenching constant of an excited level depends on the amount of thermal energy released in the luminophore before the occurrence of the light emission event. Based on the experimental measurements of the fluorescence spectra at different quencher contents, the calculation of the Stern-Volmer constant for reaction products is considered in detail. It is shown that this constant can be most reliably determined from the dependence of the fluorescence intensity ratio of the initial reagents and the quencher product rather than from the dependence of the fluorescence intensity of the products on the concentration of the quencher. The relations determined are used in analysis of the experimental fluorescence spectra of solutions of 3-hydroxyflavone excited by radiation with different wavelengths lying in the range of the*S*_{1}and*S*_{2}absorption bands. The temperature behavior of the Stern-Volmer constant for different fluorescence bands of 3-hydroxyflavone is considered. It is shown that, if these constants for the normal and tautomeric forms are correctly determined, their temperature dependences are similar.**Keywords:**33.50.Dq

Investigation of the mechanisms of exciton coherence relaxation in single GaAs/AlGaAs quantum wells by the methods of excitonic induction by S. V. Poltavtsev; V. V. Ovsyankin; B. V. Stroganov; Yu. K. Dolgikh; S. A. Eliseev; Yu. P. Efimov; V. V. Petrov

*(511-516)*. The mechanisms of exciton coherence relaxation in GaAs quantum wells in the linear mode have been experimentally investigated. An experimental technique has been developed for measuring the total phase relaxation rate, rates of reversible and temperature-irreversible excitonic phase relaxation, and the radiative decay rate Γ

*R*_{ }of excitonic polarization. The experimental values of Γ*R*_{ }for a quantum well of specified thickness, obtained for a series of samples, have a spread not larger than 15%. This accuracy made it possible to estimate the shape of the dependence of Γ*R*_{ }on the well thickness*L**Z*_{ }. It is experimentally found that Γ*R*_{ }is temperature-independent up to 80 K.**Keywords:**73.21.-b; 68.65.Fg; 73.63.Hs; 78.67.De

Structure and luminescence properties of antimony(III) complex compounds by T. V. Sedakova; A. G. Mirochnik; V. E. Karasev

*(517-523)*. The influence of the structure of the anion sublattice on the spectral luminescence properties is investigated using the example of antimony(III) complex compounds with outer-sphere organic cations. It is established that the factors favorable for the enhancement of the luminescence of antimony(III) ions are the island structure of the anion sublattice with minimum distortions of the antimony(III) coordination polyhedron and closely spaced energy levels of the outer-sphere organic cation and the antimony(III) ion.

**Keywords:**78.55.-m

Luminescence of pure yttria by V. V. Osipov; A. V. Rasuleva; V. I. Solomonov

*(524-530)*. Pulsed cathodoluminescence of samples of nominally pure yttria—commercially available powder, nanopowder prepared from it, and ceramics sintered from this nanopowder—is studied in the range 380–850 nm. The luminescence spectra at room temperature exhibit broad bands at λ ≈ 437 and 487 nm and series of narrow bands that are located in the blue (435–510 nm), orange (515–640 nm), red (645–700 nm), and infrared (785–840 nm) spectral ranges. These series are most pronounced in the spectra of commercially available powders. It is assumed that these series are emitted by bound radicals , which are a part of the surface structure of yttria crystals.

**Keywords:**78.55.-m; 78.60.-b

Pulsed cathodoluminescence of irradiated LiF-O and LiF(U)-O crystals by L. A. Lisitsyna; V. I. Oleshko; S. N. Putintseva; V. M. Lisitsyn

*(531-537)*. The spectral kinetic characteristics of the luminescence excited in previously irradiated (≤10

^{6}Gy) LiF-O and LiF(U)-O crystals have been investigated in the spectral range 4–1.8 eV by pulsed spectrometry with nanosecond time resolution. The luminescence of the crystals was excited by nanosecond nitrogen-laser or electron-beam pulses at 300 K. The inertial character of uranium luminescence enhancement and the dependence of the number of enhancement stages on the excitation technique are revealed. A difference in the character of the dependences of the intensities of the pulse photo-and cathodoluminescence of uranium on the irradiation dose is found.**Keywords:**78.55.Fv; 78.60.Hk

Growth and spectroscopic studies of NaLa(MoO

_{4})_{2}:Tm^{3+}crystals: A new promising laser material by Yu. K. Voron’ko; E. V. Zharikov; D. A. Lis; A. V. Popov; V. A. Smirnov; K. A. Subbotin; M. N. Khromov; V. V. Voronov*(538-546)*. Single crystals of scheelite-like disordered double molybdate NaLa(MoO

_{4})_{2}doped with thulium ions with dopant concentrations of 3.0 × 10^{19}and 1.2 × 10^{20}cm^{−3}are grown by the Czochralski method. Spectral and luminescent studies of crystals grown are performed in wavelength ranges of 800 nm (the transitions^{3}*H*_{6}↔^{3}*H*_{4}) and 2 μm (the transitions^{3}*H*_{6}↔^{3}*F*_{4}), including the measurements of the polarized absorption and luminescence spectra of these crystals and the decay kinetics of their excited states. A model that satisfactorily describes the decay kinetics of the luminescence from the^{3}*H*_{4}level taking into account cross-relaxation interactions is proposed. The prospects for the use of these crystals as active media in two-micrometer solid-state lasers are discussed.**Keywords:**78.20.-e; 78.55.-m

Dissipative discrete spatial optical solitons in a system of coupled optical fibers with the Kerr and resonance nonlinearities by Al. S. Kiselev; An. S. Kiselev; N. N. Rozanov

*(547-556)*. The propagation of monochromatic radiation in a system of weakly coupled single-mode optical fibers with saturable amplification and absorption and Kerr nonlinearity of the refractive index is analyzed. Conditions of stability and bistability of plane-wave regimes are determined. Discrete dissipative optical solitons are found and their stability is studied. The hysteresis dependences of the peak intensity of the discrete solitons on the value of the Kerr nonlinearity and the input beam intensity are demonstrated. The numerical estimates of the parameters of the spatial dissipative discrete solitons are presented.

**Keywords:**42.81.Dp

Superradiant reflection and scattering of light from a Bose-Einstein condensate of a dilute gas by Yu. A. Avetisyan; E. D. Trifonov

*(557-565)*. A semiclassical theory of scattering and reflection of light from a Bose-Einstein condensate of a dilute gas is developed without using the mean-field approximation and with taking into account multiple scattering by each atom.

**Keywords:**42.50.Gy

A model of nonstationary backward stimulated Raman scattering in an extended system: Interaction of forward and backward Stokes waves by N. I. Shamrov

*(566-575)*. A semiclassical model of nonstationary stimulated Raman scattering with account of forward and backward waves of different frequencies is proposed. Equations for the elements of a collective density matrix and electric-field amplitudes are obtained applying the averaging method. It is shown that forward waves are generated by a united polarization component, whereas each of the backward waves is formed by its own component. The description is based on the approximation of small scattering angles and assumes that the quantities considered do not depend on transverse coordinates. The emission dynamics of forward-backward Stokes pulses is investigated both for the linear case and under the strong depletion of pumping and level populations. The domain of applicability of the model of nonstationary forward stimulated Raman scattering is determined.

**Keywords:**42.25.Fx; 42.50.Fx

Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothly-irregular integrated structures by L. A. Sevast’yanov; A. A. Egorov

*(576-584)*. The waveguide propagation of a monochromatic electromagnetic wave in a multilayer smoothly-irregular integrated dielectric structure has been studied under natural physical and mathematical assumptions. Approximate solution of the vector electrodynamic problem satisfying the condition of smoothly varying shape of the structure is found using the Kantorovich method of the partial separation of variables, since the conventional method of separating variables, which is usually employed for regular waveguides, in the given case is inapplicable. Using the obtained solution, it is possible to describe analytically the fields of smoothly deforming modes of a dielectric waveguide, their interrelation, and the dispersion relations between the distribution of the phase slowing coefficient and the local inclination of layers in the structure under consideration. The proposed method can also be used, in a quite broad range of wavelengths, for an analysis of analogous waveguide structures made of both dielectric and magnetic materials.

**Keywords:**02.30.Mv; 03.50.De; 07.05.Kf; 42.25.Gy; 42.82.Et

Surface electromagnetic waves at the interface between a homogeneous medium and a system of coupled waveguides by B. A. Usievich; J. Kh. Nurligareev; V. V. Svetikov; V. A. Sychugov

*(585-590)*. An analysis is made of the experimental investigations of the surface waves existing at the interface between a homogeneous medium and a periodically stratified medium that represents a bounded system of coupled waveguides. It is shown that, in all cases of the observation of surface waves, the bounded system of coupled waveguides has its own spectrum of guided modes and a spectrum of leaky modes that become surface waves of the system. It is also demonstrated that a biosensor can successfully operate when two surface waves serve as leaky modes of a Bragg waveguide in which the periodic system of waveguides is used as a distributed Bragg mirror of this waveguide. A structure supporting surface waves is designed on the basis of ten pairs of Nb

_{2}O_{5}-SiO_{2}layers and implemented experimentally. The surface waves are detected with a K8 glass prism according to the Kretschmann scheme.**Keywords:**78.67.Pt

Effect of turning of rays on scattering of light in a layered medium by A. Yu. Val’kov; A. A. Zhukov; V. P. Romanov

*(591-610)*. The problem of the scattering of light by random inhomogeneities in a layered medium whose characteristic scale is large compared to the wavelength of light is considered. The attention is mainly focused on the effect that the turning of incident and scattered waves has on light scattering in such a medium. In the mixed (

*q*_{⊥},*z*) Fourier representation, expressions for normal waves, and Green’s function are found, which can be used both far from the turning point, where the fields are described in the WKB approximation, and near this point, where the fields are described using the Airy function. Based on these expressions and using the Kirchhoff method, a general expression for the scattering intensity in the far field of the sample is obtained, which takes into account the turning of the incident and scattered waves in the fluctuating medium. Physical consequences of the calculation results are analyzed. In particular, it is shown that even a comparatively small gradient of the refractive index in the layer leads to a rather appreciable redistribution of the scattering intensity between the forward and backward hemispheres. In this case, the shape of the scattering indicatrix is rather exotic with sharp discontinuities, peaks, and dips whose amplitude is on the order of the intensity itself.**Keywords:**78.35.+c; 42.25.Fx; 42.25.Dd; 42.15.-i

Current density distribution within a small metal particle in an electromagnetic wave field by I. O. Moiseev; A. A. Yushkanov; Yu. I. Yalamov

*(611-616)*. The eddy current density distribution within a small conducting spherical particle is analyzed in the cases of specular, diffuse, and specular-diffuse interactions of electrons of a metal with the boundary of the sample. The situations with different sizes of particles and different frequencies of incident electromagnetic waves in the absence of the skin effect are considered.

**Keywords:**72.15.-v

A method for retrieval of the profiles of atmospheric backscattering coefficients by three-wavelength lidar and nephelometric measurements by M. M. Kugeiko; S. A. Lisenko

*(617-623)*. A method for retrieval of the profiles of atmospheric aerosol backscattering coefficients β

*a*_{ }along horizontal and inclined paths from the results of three-wavelength probing by laser location systems based on a Nd: YAG laser is proposed. The method uses a power dependence between the spectral values of β*a*_{ }and includes spectral nephelometric measurements of the scattering coefficients by an angle of 33°, which characterize the relative spectral dependence of aerosol extinction. The sensitivity of this method to spatial variations in the above coefficients, to the deviation of β*a*_{ }from the dependence used, and to errors in calibration and measurement of signals is studied. The method is demonstrated to be stable both upon using the absolute calibration of the lidar and at an arbitrary position of the reference point.**Keywords:**42.68.Wt

Effects of angle of incidence and polarization in the chiral photonic crystals by A. H. Gevorgyan

*(624-632)*. Oblique propagation of light through a planar layer of a chiral photonic crystal (CPC) is considered. The problem is solved using Ambartsumyan’s layer-summation method. Specific features of the reflection (transmission) spectra in the presence of dielectric boundaries are studied. Apparent contradictions of the Belyakov-Dmitrienko theory with experiments are discussed. Possibility of the laser emission wavelength control in a CPC layer doped with a laser dye is analyzed. Characteristic features of the light absorption at oblique incidence are investigated.

**Keywords:**42.70.Qs

Measuring the normalized jones matrix of anisotropic samples by means of static ellipsometry by V. A. Shvets; E. V. Spesivtsev; S. V. Rykhlitskiĭ

*(633-638)*. Functional capabilities of the static photometric scheme of ellipsometric measurements proposed earlier are considered as applied to anisotropic reflecting objects. Combination of different positions of the optical elements, as well as addition of two new positions of the polarizer (

*P*= 0° and 90°) to those used before (*P*= ±45°) made it possible to obtain 24 equations for determination of the normalized Jones matrix of an anisotropic sample. For the ideal compensator (ρ*C*_{ }=*i*), this system breaks down to 12 pairs of mutually identical equations. However, in this case, all three elements of the Jones matrix can be determined provided that ρ*pp*_{ }≠ ρ*ps*_{ }ρ*sp*_{ }. Computer simulation of the Jones matrix measurement indicates high accuracy of determination of the elements ρ*pp*_{ }and ρ*ps*_{ }and much lower accuracy for determination of ρ*sp*_{ }.**Keywords:**07.60.Fs

Wavelet profiling of wind velocity using intensity fluctuations of laser beam propagating in the atmosphere by A. L. Afanas’ev; V. A. Banakh; A. P. Rostov

*(639-645)*. A method for the remote determination of the crosswind velocity profile using a wavelet analysis of fluctuations in the intensity of transmitted laser radiation is proposed. Results of an experimental investigation are presented that show how turbulent flow inhomogeneities (intensity fluctuations) localized in separate parts of the path contribute to the total distortions of the intensity distribution in a beam propagating along the path. It is demonstrated that, by separating fluctuations on various scales in the beam intensity distribution and following the evolution of these fluctuations, it is possible to determine the arrangement of turbulent zones along the path of propagation of the laser beam and to evaluate the velocity of motion of the medium in these zones. Wavelet estimates of the wind velocity from fluctuations of the transmitted radiation intensity for a given point of the atmospheric path agree with the results of direct velocity measurements at this point.

**Keywords:**42.25.Dd; 42.68.Bz; 42.68.Wt; 92.60.Gn

The following papers will be published in the October issue of

*Opticheskiĭ Zhurnal*(Journal of Optical Technology), vol. 75, no. 10, 2008 by L. V. Enushevskaya*(646-646)*.**Keywords:**01.10.Cr