# Optics and Spectroscopy (v.88, #3)

Heavy atom effect on photophysical deactivation of molecular triplet states by E. A. Gastilovich; S. A. Serov; N. V. Korol’kova; V. G. Klimenko

*(313-315)*. The decrease in the spin-orbit (SO) interaction with increasing number of chlorine atoms in molecules of dibenzo-

*p*-dioxine derivatives is found and explained. The heavy atom effect on components of the rate constant of phosphorescence*k*_{ph}=_{k}_{SO}+_{k}_{VSO}related to SO and vibronic-spin-orbit (VSO) interactions is quantitatively estimated. Analysis of transitions from autoionization states of the Bi III, Bi IV, and Bi V ions by A. N. Ryabtsev; S. S. Churilov; Y. N. Joshi

*(316-320)*. The spectra of transitions from the autoionization states of bismuth ions are studied in the wavelength region from 170 to 500 Å. More than twenty transitions from the levels of configurations accompanied by excitation of the inner 5

*d*subshell in the Bi V, Bi IV, and Bi III ions are identified and their autoionization widths are measured. In addition, transitions from the highly excited 5*d*^{10}*np*levels (*n*=8–11) in the Bi V ion are identified and the ionization potential is refined. Semiempirical calculation of the fine-structure parameters for

*np*^{5}*n*′*p*configurations by G. P. Anisimova; E. L. Kapel’kina; R. I. Semenov; M. Choffo*(321-326)*. The fine-structure parameters are calculated semiempirically in the intermediate coupling scheme for the

*np*^{5}*n′p*configurations of rare gas atoms and a number of ions. The calculation is based on the two-electron matrix of the energy operator, which takes into account, along with the electrostatic interaction, all magnetic interactions. Diagonalizing the energy matrix with the calculated values of the fine-structure parameters yields energy values exactly coinciding with the experimental data, as well as the coupling coefficients and the gyromagnetic ratios. The results obtained are compared with the available literature data. Comparison of four methods for processing data on exponential decay by T. A. Danilova; I. R. Krylov; M. Yu. Razumova

*(327-333)*. Using the decay of a single exponential function to a nonzero level as an example, the following numerical methods for determining lifetimes are considered: the least-squares method, the differentiation method, and two modifications of the method of moments. Domains of efficient application of one method or the other, depending on the form of the noise distribution, are determined on the basis of computer simulation in parameter space of the problem. For the Poisson noise distribution, a domain of parameters is found, where the error of determining the decay rate in the method of moments is smaller than in the least-squares method.

Line phosphorescence spectrum of octachlorodibenzo-

*p*-dioxine at 4.2 K by V. G. Klimenko; R. N. Nurmukhametov; E. A. Gastilovich; S. A. Lebedev*(334-338)*. The line phosphorescence spectrum of octachlorodibenzo-

*p*-dioxine (OCDX) is obtained and interpreted. The symmetry of the lowest triplet state of this molecule is established. The vibrational frequencies found from the vibronic phosphorescence spectrum at 4.2 k are assigned to the vibrational modes of certain symmetry related to individual functional atomic groups of the molecule. The relation between contributions from the spin-orbit (SO) and vibronic-spin-orbit (VSO) interactions to the phosphorescence rate constant*k*_{ph}of the OCDX molecule is found from the vibronic line intensities. It is found that the increase in the number of Cl atoms in OCDX compared to that in tetrachlorobenzo-*p*-dioxine results in the increase in the relative contribution of the VSO interaction to*k*_{ph}. Intramolecular vibrational modes of polychlorodibenzo-

*p*-dioxines of the*D*2*h*_{ }symmetry by V. G. Klimenko; R. N. Nurmukhametov; E. A. Gastilovich; S. A. Lebedev*(339-345)*. The infrared and Raman spectra of the octachlorodibenzo-

*p*-dioxine molecule are measured and all normal vibrational modes of the molecule are calculated. Each vibrational mode was assigned to the vibrations of certain functional groups of atoms in the molecule, taking into account the local symmetry characteristics of the vibration mode. A correlation of vibrational modes by their shape was established in a series of molecules: dibenzo-*p*-dioxine, 2,3,7,8-tetrachlorodibenzo-*p*-dioxine, and OCDX. The influence of substituents on vibrational frequencies was also examined. Properties of low-temperature spectral relaxation of eosin phosphorescence in a glycerol-water mixture by A. V. Pastukhov; V. R. Fogel’; A. I. Kotel’nikov

*(346-351)*. The low-temperature dynamics of the Stokes shift of the instantaneous phosphorescence spectra of eosin in 94% glycerol-water solution is studied upon pulsed excitation. At temperatures

*T*<*T**tg*_{ }, where*T**g*_{ }=183–187 K is the glass transition temperature of the solution, the blue shift of the instantaneous phosphorescence spectra is observed. In the vicinity of*T**g*_{ }, the spectral dynamics undergoes inversion, and the red shift of the instantaneous spectra is observed at temperatures between 188 and 210 K, which is caused by freezing out the orientation mobility of the solvent molecules in the first solvate shells of the chromophore molecule. In the temperature range from 230 to 273 K, the enhancement effect was observed at the initial parts of phosphorescence kinetic curves, which is probably explained by cooperative phenomena in the solvent. Special features of spectral and luminescent properties of squarilic dyes in polymer matrices by Yu. A. Skryshevskiĭ; N. A. Davidenko; A. A. Ishchenko; A. K. Kadashchuk; N. I. Ostapenko

*(352-358)*. A study was made of spectral and luminescent properties of a squarilic dye on the basis of 1,3,3-trimethyl-3H-indoline in comparison with the cationic polymethine dye representing a derivative of the same heterocycle. The squarilic dye was introduced into polymer films of poly-N-epoxypropylcarbazole, which is capable of bearing photoproduced charges, and polystyrene, which lacks this ability. Luminescence spectra of films with different dye concentrations at temperatures of 4.2 and 300 K were studied. Spectral and luminescent properties of squarain in both types of polymers were found to be determined by the dye tendency to aggregation. For poly-N-epoxypropylcarbazole, this tendency is less pronounced than for polystyrene, which is associated with the enhancement of specific solvation of a bipolar squarain molecule by polar groups of poly-N-epoxypropylcarbazole. The structure with an angle between chromophore directions of 180° is shown to be the most likely spatial structure of associates. The advantage of this structure is that it is stabilized at both ends of bipolar molecules by electrostatic attractive forces between opposite charges.

Formation rate constant and features of the excited complexes upon concentration quenching of the triplet state of Pd-porphyrins in toluene by V. V. Sapunov

*(359-364)*. The concentration dependence of the phosphorescence spectra and lifetime are studied for a number of Pd-porphyrins in toluene in the temperature range from 293 to 193 K and at 77 K. The conclusion is made that porphyrins in the triplet and ground states form excited complexes. The rates of complex formation were measured, which proved to be smaller than the diffusion constant. This is explained by the successive formation of two types of complexes in solutions. The mechanisms of complex formation are proposed, which describe the corresponding spectral transformations.

Orientation effects in anomalous elastic scattering of polarized X-rays by a linear molecule by A. N. Khoperskiĭ; V. A. Yavna; A. M. Nadolinskiĭ; V. V. Timoshevskaya

*(365-367)*. A strong orientation effect is theoretically predicted in a suggested modified experiment on anomalous elastic scattering of linearly polarized X-rays by free oriented in space HF and HCl molecules near the ionization threshold of the 1s molecular orbital. The analytic expression for the form factor of a linear molecule is determined for the case of one-center nonrelativistic representation of the wave functions of molecular orbitals.

Calculation of the field dependence of nonradiative transition rate from the shape function of optical vibronic transition by S. V. Bulyarskiĭ; N. S. Grushko; A. V. Zhukov

*(368-371)*. An algorithm is suggested for calculation of field dependences of the emission rate from the shape function of the optical transition. Comparison with the experimental data obtained for the

*V*_{Ga}S_{As}complex in gallium arsenide showed that this algorithm is preferable compared to the methods based on the one-coordinate model. Superexchange mechanism of energy transfer between neighboring lanthanide ions in dielectric crystals by V. S. Mironov

*(372-376)*. It is shown that unusually rapid energy transfer between neighboring lanthanide ions in dielectric crystals is caused by the efficient short-range interaction, which is similar to the magnetic superexchange interaction. Both these interactions are related to virtual transition of electrons between lanthanide ions via common bridge ligands. A general method is developed for calculating matrix elements of the effective superexchange Hamiltonian, and the rates of energy transfer in exchange-coupled pairs of lanthanide ions are estimated. The possibility of using the superexchange model of energy transfer for analysis of up-conversion in lanthanide crystals is discussed.

Photoluminescence spectra of the AgGaTe

_{2}single crystals doped with hydrogen by I. V. Bodnar’; V. F. Gremenok; R. W. Martin; M. V. Yakushev*(377-379)*. The photoluminescence spectra of single crystals of the ternary AgGaTe

_{2}compound obtained by the Bridgman-Stockbarger method are studied before and after bombardment by the 100-eV hydrogen ions of dose 10^{15}cm^{−2}. The spectra were detected in the temperature range from 10 to 300 K at various powers of laser excitation. The spectra exhibit emission bands related to the donor-acceptor recombination, free, and bound excitons. The intensity of these bands in crystals doped with hydrogen is higher than that in undoped crystals. This is explained by the passivation of defects in a crystal lattice by hydrogen. The binding energy of a free exciton and the band gap in AgGaTe_{2}crystals are calculated at 10 K. On the propagation of electromagnetic pulses under the conditions of quasi-resonance by A. M. Basharov; A. I. Maimistov

*(380-386)*. A theory of quasi-resonance for the model of atoms with an arbitrary number of levels is developed by the method of unitary transformation without recourse to Bloch’s equations. Corrections to the results known from the theory of adiabatic following, which refine these results and take into account dispersion of the nonlinear response of the resonant system, are obtained. The condition for quasi-resonance with a single atomic transition is shown to impose stringent limitations on the form of the nonlinear evolution equation for the electric field envelope of the pulse with dispersion of the nonlinear response taken into account, which prohibit the reduction of the equation indicated to familiar, fully integrable systems.

Self-induced transparency in a resonance medium with the dipole-dipole interaction by M. B. Belonenko; V. V. Kabakov

*(387-389)*. Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω

_{0}^{−1}(ω_{0}is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation. Nonlinear susceptibilities of quantum dots by E. Yu. Perlin

*(390-396)*. Within the framework of the simplest model of a material with semiconductor spherical quantum dots, taking no account of excitonic effect, calculations are made of the magnitude and dispersion of the cubic susceptibility χ

^{(3)}in the frequency region found far from the fundamental-absorption edge. Moreover, the dependence of χ^{(3)}on the field strength*E*of a strong electromagnetic wave is studied. This dependence is rather well pronounced for*E*>10^{6}V/cm. It is shown that a substantial contribution to χ^{(3)}is made by a large number of discrete states into which the valence and conduction bands are split in the presence of three-dimensional confinement. If the light frequency is close to resonance with the transition between sublevels of size quantization of one of the bands, χ^{(3)}sharply increases. Under conditions where quantum dots occupy less than 0.1% of the total volume of a material, the nonlinear susceptibility may reach values of the order of ∼10^{−7}CGS electrostatic units for the band gap of the dot material*E**g*_{ }≃ 3 eV, and it increases as*E*_{g}^{−4}with decreasing*E**g*_{ }. Optical vortices in low-mode fibers: III. Dislocation reactions, phase transitions, and topological birefringence by A. V. Volyar; V. Z. Zhilaitis; T. A. Fadeeva

*(397-405)*. Topological birefringence of waves in optical fibers resulting from the spin-orbit interaction in the field of optical vortices is manifested, as a rule, in the form of Rytov-Magnus unified optical effect. At the same time, the field transformations caused by this effect are not explicitly related to the evolution of phase dislocations of longitudinal and transverse components of the electric and the magnetic fields. This relation can be provided by the dislocation reactions proposed by Berry. As opposed to the Berry’s approach, where dislocation reactions at the wavefront surface are considered, it is suggested in this work that topological reactions at the specific characteristic surface of the wave field formed by the coordinate representation of the transverse components of the Poynting vector be considered. Using the action of topological birefringence in a low-mode optical fiber as an example, it is shown that the course of a topological reaction in a vector optical field is accompanied by rigorous conservation of the total topological index of the characteristic surface and does not depend on the presence of an interface (where topological charges can originate and annihilate). The total topological index of a dislocation reaction is found to be equal to the absolute value of the sum of the topological charge and the spirality of the vector wave field.

Modulation instability of light beams and pulses propagating in absorbing media by A. V. Vysloukh; I. S. Ivanova; S. A. Magnitskii; V. A. Trofimov

*(406-414)*. The development of modulation instability of light beams and pulses propagating in an absorbing medium is analyzed. Based on the proposed approach, the domain of increasing perturbations is estimated more exactly. It is shown that, compared to the traditional approach, this domain can be enlarged by 20–50% in frequency and by 50% in the gain increment. For femtosecond pulses, the analysis of the modulation instability is carried out both on the basis of the well-known Schrödinger equation with the time derivative of nonlinear response of the medium and by using the original method of its transformation. It is shown that in the latter case, the nonlinearity dispersion increases the interval of frequencies for which the modulation instability is developed. This more adequate description of the development of the modulation instability in an absorbing medium allowed us to obtain more accurately the frequency intervals of its realization compared to the data available in the literature.

Leaky modes in optical fibers with transverse anisotropy by A. B. Sotskiĭ; L. I. Sotskaya

*(415-422)*. A system of homogeneous integro-differential equations in transverse components of the magnetic field and longitudinal component of the electric field is formulated. The system makes it possible to give a rigorous description of leaky and guided modes of optical fibers with transverse anisotropy. An analysis is made of the leaky modes in fibers with step and graded profiles of the dielectric constant tensor. Examples are given that illustrate the efficiency of the approach.

Conversion of waveguide modes in nonuniformly magnetized planar structures by D. I. Sementsov; A. M. Shutyi

*(423-426)*. An analysis is made of a planar structure with a nonuniform distribution of magnetization throughout the thickness of a waveguide layer that corresponds to the rotation of magnetic momentum in the plane of the layer. The results of the study show the feasibility of efficiently controlling the conversion of orthogonally polarized modes due to the change of thickness of the transition layer and the angle of magnetization rotation across the waveguide layer.

Coupling between elliptic screw polarization modes in single-mode optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random axis twist by G. B. Malykin; V. I. Pozdnyakova; I. A. Shereshevskii

*(427-440)*. An analysis is made of single-mode fiber optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random twist, which shows that, in this case, the coupling of orthogonal polarization modes having elliptic polarization in the screw coordinate system comoving with twist cannot be characterized by one coupling parameter, as differentiated from the case where constant twist is absent. In this case, the coupling between polarization modes is characterized by three independent parameters, which are different in nature and have different effects on the coupling of polarization modes. An estimate is made of the domain of applicability of the classical formula for the

*h*parameter in single-mode fiber optical waveguides without regular twist of anisotropy axes. Light scattering by multilayer ellipsoids in the Rayleigh approximation by V. G. Farafonov

*(441-443)*. A problem of light scattering by multilayer confocal ellipsoids is solved in the Rayleigh approximation. The electric field of a light wave is assumed constant and a set of Laplace equations with the corresponding boundary conditions is considered. The final expression for the polarizability of a particle is represented in the matrix form (2×2 matrices) in terms of parameters of a nucleus and subsequent layers. Numerical calculations of the scattering and absorption efficiencies of small multilayer spheres obtained using the exact (the generalization of the Mie theory) and approximate solutions well agree with each other.

Scattering of laser radiation by multifractal biological structures by O. V. Angel’skiĭ; A. G. Ushenko; A. D. Arkhelyuk; S. B. Ermolenko; D. N. Burkovets

*(444-447)*. Scattering of laser radiation by structured biotissues—histological mounts of bony and muscular tissues and skin, are studied.

Gyrotropy of molecular crystals with vacancies by Yu. G. Pashkevich; S. A. Fedorov

*(448-452)*. A microscopic analysis is made of the gyrotropy of molecular crystals with vacancies. For impurity-free systems with a primitive lattice, the concentration dependence of rotatability in two frequency regions is studied.

Observance of the energy flux balance at the boundary of a crystal for a wave incident at an angle of ϕ≠0, reflected wave, and two natural waves with arbitrary polarization ellipses refracted at angles of ψ

_{1}and ψ_{2}by V. A. Shamburov*(453-454)*. The energy flux balance at the boundary of a gyrotropic transparent crystal is shown to be observed for arbitrary elliptical polarization of the incident wave.

Suppression of background transmission of interference filters by V. Yu. Pervak; Yu. A. Pervak

*(455-458)*. The possibility of manufacturing interference filters with the transmission coefficient no less than 90% in fixed UV, visible or near IR spectral regions and completely opaque at longer wavelengths is shown. The operation of the filter is based on the method of residual rays. Angular dependences of the filter transmission bandshape on the parameters of multilayer coating, such as the thickness, refractive indices, and the number of the layers, are analyzed.

Errors of neural networks by E. I. Shubnikov

*(459-465)*. Errors of associative sampling and recognition in neural networks are determined by methods of the general theory of statistical solutions taking into account statistical variation of the input image, the correlation radius of the image, the number of neurons, and the number of images in the memory. The beta-distribution is proposed to be used as the statistics of image variations. The admissibility of the utilization of the distribution is tested by using temporal variations of real scenes as an example. The error in determining the coordinate is found for networks on the basis of optical correlators.

Solution of the inverse problem for a heterodyne differential microscope for a stepwise profile of a microobject by D. V. Baranov; A. A. Egorov; E. M. Zolotov; K. K. Svidzinskii

*(466-471)*. The solution of the inverse problem for a differential microscope is demonstrated experimentally by the example of an object of the step type. A method for achieving superresolution based on the expansion of the response in the coordinate representation is proposed. The main parameters of the profile (the height and the width) are determined.

Anamorphosis and distortion by A. V. Gitin

*(472-474)*. An analytic relationship between the distortion and the anamorphosis of an anamorphic objective is derived.