# Optics and Spectroscopy (v.96, #2)

Recording of dynamic holograms by nanosecond and picosecond laser pulses in solid-state fullerene-containing matrices by O. V. Andreeva; V. G. Bespalov; A. L. Pyait; V. N. Sizov; A. S. Cherkasov

*(149-156)*. The results of a complex investigation of the recording of dynamic holograms by pulsed radiation with a duration of 20 ns and 300 ps in fullerene-containing media based on porous glasses and polymethyl methacrylate matrices are reported. Spectral analysis of these media in the range 300–700 nm was performed. The efficiency of hologram recording was found to relate with the occurrence of a band at 330 nm in the absorption spectrum of a medium. It is shown that dynamic holograms can be recorded in the fullerene-containing media by nanosecond and picosecond pulses. In the latter case, holograms arise mainly due to a change in the electronic polarizability of fullerene molecules, which is almost inertialess. The results obtained can be used in the development of ultrafast switching devices based on dynamic holograms.

Investigation of the spectral selectivity of volume holograms with femtosecond pulsed radiation by O. V. Andreeva; V. G. Bespalov; V. N. Vasil’ev; A. A. Gorodetskii; A. P. Kushnarenko; G. V. Lukomskii; A. A. Paramonov

*(157-162)*. A method for studying the parameters of high-selectivity volume holograms and photonic crystal structures using ultrashort pulsed radiation in a wide spectral range is developed. The experimental system and measurement procedure are described. The results of determination of the diffraction efficiency and spectral selectivity of holographic gratings with spatial frequencies of 360 and 640 mm

^{−1}are presented. The parameters of the holograms determined by the method proposed and by the conventional techniques based on the use of continuous laser radiation are found to coincide. Dynamic holograms and optical limiting: Asymmetric two-wave interactions by D. I. Stasel’ko; S. V. Kessel’

*(163-167)*. The conditions for obtaining a high efficiency of energy exchange upon two-wave interactions in dynamic holograms are found by analysis and numerical simulation of a system of nonlinear equations. Use of an asymmetric scheme of beam interaction in a medium with two nonlinearities, one of which determines the amplitude and relaxation time of a grating and the other of which provides phase modulation of the interacting beams, is proposed. It is shown that such a scheme in combination with the specific properties of a medium makes it possible to radically reduce the requirements for the nonlinearity of a medium and the intensity of a light flux in limiting systems, as well as to significantly decrease the time of the transition process. As a result, it becomes possible to attain an efficiency of energy transfer higher than 90% and to increase the corresponding attenuation of a high-power beam by almost two orders of magnitude, which is of interest for optical limiting of intense light fluxes.

Study of polarized luminescence in erbium-doped laser glasses by A. S. Rokhmin; N. V. Nikonorov; A. K. Przhevuskii; A. V. Chukharev; A. M. Ul’yashenko

*(168-174)*. A partial polarization of luminescence in laser phosphate and silicate erbium-doped glasses was found to take place for the fundamental laser transition

^{4}*I*_{13/2}→^{4}*I*_{15/2}(λ=1.55 μm) under excitation by linearly polarized laser radiation (532 and 790–990 nm). The shape of the luminescence spectrum depends on the wavelength of the exciting light and on the composition of the glass matrix. The degree of polarization of the luminescence depends on the spectral range of both the excitation and the detection, attaining a maximum of ∼1%. The concentration dependence of the degree of polarization is studied. Analysis of characteristics of interference fringes by nonlinear Kalman filtering by I. P. Gurov; A. S. Zakharov

*(175-181)*. The description of interference fringes on the basis of stochastic differential and difference equations is shown to be adequate. Analytical expressions for obtaining local dynamic estimations of parameters of interference fringes on the basis of the discrete Kalman filtering algorithm are presented. Characteristics of the nonlinear Kalman filter for the noise-immune dynamic estimation of the envelope and unwrapped phases of interferometric signals and the two-dimensional fringe patterns are investigated.

Self-broadening of space-time spectra of few-cycle pulses in dielectric media by V. N. Vasil’ev; S. A. Kozlov; P. A. Petroshenko; N. N. Rozanov

*(182-186)*. The nonparaxial dynamics of spectra of pulses comprising a few cycles of a light field is analyzed in transparent nonlinear media with dispersion. It is shown that the inhomogeneous self-broadening of the time spectrum of a pulse proceeds more effectively into the blue region at all spatial frequencies. A decrease in the energy in the central part of the time spectrum is realized mainly at high spatial frequencies.

Self-energy correction to the wave function in the effect of parity violation for the amplitude of the 6

*s*–7*s*transition in the^{133}Cs atom by I. A. Goĭdenko*(187-191)*. The quantum electrodynamic self-energy correction to the wave function in the effect of parity violation for the amplitude of the 6

*s*–7*s*transition in the^{133}Cs atom is calculated in explicit form without using the nonrelativistic approximation for the self-energy operator. The result obtained refines some previous estimates and indicates that the correction to the parity violation may be comparable with the corresponding correction to the vacuum polarization. The necessity of taking complete relativistic account of all the quantum electrodynamic corrections in calculations of the electroweak charge*Q**W*_{ }in atomic systems is shown. Calculation of optical characteristics of atoms with a closed shell by the Hartree-Fock-Roothaan method by M. N. Adamov; Yu. B. Malykhanov; V. V. Meshkov; R. M. Chadin

*(192-194)*. The transition frequencies, oscillator strengths, and Cauchy moments of the dipole dynamic polarizability are calculated for the Ar, Ca, Sr, and Xe atoms and their isoelectronic sequences.

Elastic scattering of a photon by the neon atom near the

*K*ionization edge by A. N. Khoperskiĭ; V. A. Yavna; A. M. Nadolinskiĭ; D. V. Dzyuba*(195-197)*. A precision theoretical investigation of the differential cross section of elastic photon scattering by the neon atom near the

*K*ionization edge is performed. The calculation results have a predictive character. Rotational dependence of the broadening of lines of the ν2 band of H

_{2}O induced by nitrogen pressure by N. N. Lavrentieva*(198-204)*. A semiempirical method for calculating the coefficients of broadening of spectral lines of H

_{2}O molecules subjected to nitrogen pressure is developed. The method involves different corrections associated with deviations from the Anderson approximation. The parameters of the method are determined from the adjustment of the coefficients of broadening to experimental data, which makes it possible to predict fairly accurately the parameters of the contour of a line whose measurements were not performed. On the basis of numerous calculations in terms of this method, a numerical analysis is made that allows one to conclude that the rotational dependence of the half-widths of the lines is more complex than was previously believed and to reveal the basic trends of this dependence. Theoretical study of the spectral and structural parameters of van der Waals complexes of the Li

^{+}cation with the H_{2}, D_{2}, and T_{2}isotopomers of the hydrogen molecule by V. P. Bulychev; K. M. Bulanin; M. O. Bulanin*(205-216)*. The three-dimensional vibrational problem for the isolated binary complexes formed by the Li

^{+}cation with all the isotopomers of the hydrogen molecule is solved by the variational method using sufficiently exact nonempirical adiabatic surfaces of the potential energy and the dipole moment. Information on the largeamplitude vibrations was obtained for the first time, and the anharmonic effects caused by the interaction of the different internal degrees of freedom in these weakly bound van der Waals complexes were consistently taken into account. The frequencies and intensities of many spectral transitions are determined, and the average values of geometrical parameters and the dipole moment are calculated for the ground and excited vibrational states. Calculation of the IR spectrum of ethylbacteriochlorophyllide (A) by the density functional method by V. V. Nechaev; K. V. Berezin

*(217-220)*. The structure, the frequencies of the normal vibrations, and the absolute IR intensities of ethylbacteriochlorophyllide (A) are calculated in the approximation of the hybrid density functional B3LYP with the 6–31 G(d) basis set. The scaling of the quantum-mechanical force constants is performed by the Pulay method. The effective force field of ethylbacteriochlorophyllide (A) in the redundant and nonredundant coordinates is obtained. The vibrational IR spectrum is modeled. On the basis of the calculations performed, the experimentally determined IR spectrum of bacteriochlorophyll (A) is interpreted.

Kinetics of a photoinduced NH tautomerism of free-base porphyrins in crystalline matrices at low temperatures: Computer simulations and experiment by I. V. Stanishevsky; K. N. Solovyov

*(221-229)*. Photoinduced NH tautomerism, along with the reaction pathways of phototautomerization in tetrabenzoporphin and porphin free bases in

*n*-octane polycrystalline matrices at 77 K, is studied by simulation of kinetic processes and their experimental observation. The simulation of the processes is performed by the numerical solution of the system of kinetic equations describing the populations of electronic levels and transitions between them. Kinetic dependences are obtained by measuring the perturbation of stationary fluorescence of one component of the 0-0 doublet origin upon pulsed selective photoexcitation of the other component. For two tautomeric forms related by the reversibility of the photochemical reaction, under the assumption of synchronism of the NH rearrangement, (i) analytical solutions governing the reaction rate are found, (ii) a method of measuring the rate constants of the proton rearrangement is suggested and the constants themselves are estimated, and (iii) direct evidence of the participation of*T*_{1}levels in the photochemical reaction is obtained. With the aid of numerical simulations, the specific features of kinetic manifestation of an asynchronous mechanism of the photoinduced NH rearrangement are studied. The efficiency of formation of primary radiation defects in LiF and MgF

_{2}crystals by L. A. Lisitsyna; V. M. Lisitsyn; V. I. Korepanov; T. V. Grechkina*(230-234)*. Processes of radiation formation of primary defects—

*F*centers and self-trapped excitons—in lithium and magnesium fluorides, which have crystal lattices of different types and similar widths of the band gap and valence band, have been studied in a wide temperature range (11–500 K). It is shown that, along with qualitative similarity of the regularities of formation of the defects under study, LiF and MgF_{2}crystals are characterized at low temperatures (11–100 K) by different relationships between the energy dissipation channels for self-trapping electronic excitations and the types of self-trapped excitons arising. Polymorphism of phthalocyanine nanocrystals: β→

*X*→β polymorphous transformations by I. Yu. Denisyuk; N. V. Kamanina*(235-239)*. Polymorphous transformations of crystalline modifications of phthalocyanine nanocrystals in coordinating solvents are studied. The possibility of obtaining the

*X*-crystalline form of nanoparticles of various metal phthalocyanines by transformation from the iβ form in an alcohol-water mixture is investigated. The transformation conditions and the optical absorption spectra of the obtained nanoparticles of the*X*form are analyzed. The thermally induced*X*i→iβ transformation is considered. Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: X. Verification of the ergodic hypothesis for fiber ring interferometers by G. B. Malykin; V. I. Pozdnyakova

*(240-257)*. The problem of the validity of the ergodic hypothesis as applied to a fiber ring interferometer (FRI) is considered on the basis of a comparison between magnitudes of the zero drift of an FRI calculated upon changing temperature of the fiber and upon random realizations of inhomogeneities in a single-mode optical fiber (SMF). The physical nature and statistical characteristics of random inhomogeneities in an SMF, types of polarization nonreciprocity in an FRI, and thermo-optical parameters of an SMF are analyzed. An algorithm for calculation of the zero drift of an FRI on changing temperature is proposed. The conditions under which the ergodic hypothesis is satisfied in an FRI are formulated. In particular, it is shown that many random inhomogeneities have to be placed on the depolarization length of polychromatic radiation in the SMF loop of an FRI; otherwise, the zero drift of the FRI calculated by the method of averaging over an ensemble of independent realizations may significantly exceed its actual value. Numerical estimations are made. It is shown that thermostabilization of an FRI with a polychromatic radiation source may significantly reduce its zero drift.

On the theory of superradiant scattering of light from a Bose-Einstein condensate of dilute atomic gases by E. D. Trifonov; N. I. Shamrov

*(258-264)*. The theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas, which was earlier proposed by one of the authors, is used to study the spectral-kinetic characteristics of scattered radiation and the evolution of populations of coherent atomic states.

Correlation of the energies of photons emitted in cascade transitions by P. S. Antsiferov

*(265-267)*. New details of a well-known physical process—cascade transition—have been considered. The wave function of a system of two photons emitted in a cascade transition in the absence of a shift of the phase of the intermediate state was studied. The joint energy distribution density for two such photons is obtained by numerical calculation, and a correlation between their energies at certain probabilities of radiative transitions is ascertained. This phenomenon can be used to diagnose the plasma density.

Spectral heterodyne tomography by Yu. T. Mazurenko; G. V. Papayan

*(268-274)*. A novel method of optical coherent tomography—spectral heterodyne tomography—is proposed. Spectral heterodyne tomography is based on parallel heterodyne detection of a multitude of frequencies of the light backscattered by an object under study. The result of this detection is a spectral distribution of the amplitude and phase of the scattered radiation. Subsequent numerical processing allows one to find the distribution of scattering centers over the depth corresponding to the point of entrance of the incident light. The proposed method is potentially characterized by a higher efficiency as compared with the most successful approach to optical coherence tomography, based on heterodyne scanning interferometry.

A new algorithm for processing turbidity spectra based on multibranch calibrations by S. L. Shmakov

*(275-280)*. A new algorithm for processing turbidity spectra using calibrations several branches or corridors is proposed. The method does not require determination of the wave exponent and makes it possible to estimate the degree of polydispersity of the system under study. Some examples of calibrations for an FÉK-56 photoelectrocolorimeter are presented.

Mathematical modeling of the Magnus effect in the geometrical optics approximation by N. D. Kundikova; V. G. Nikolaev; N. R. Sadykov; M. O. Sadykova

*(281-284)*. The Magnus effect in multimode fibers with triangular and parabolic refractive index profiles (RIPs) is simulated in the geometrical optics approximation. The calculations confirm the linear relation between the angle of rotation Δϕ and the fiber length

*z*. The results of calculations for a spiral path with constant radius are compared with the analytical solution obtained. For a fiber with a parabolic RIP, the value of Δϕ obtained in this work is one-half the result obtained in the wave approach. Application of the neural network method for determining the characteristics of homogeneous spherical particles by V. V. Berdnik; R. D. Mukhamedyarov; V. A. Loi˘ko

*(285-291)*. The problem of reconstructing the characteristics of disperse particles from measurements of scattered radiation is considered. To solve this problem, the neural network method, based on the approximation of the parameters of particles by a linear combination of the results of measurements, is used. The capabilities of the method are studied on the examples of the reconstruction of the radius and the refractive index of spherical particles from measurements (for example, in flow-type cytometers) of the luminance of radiation scattered by individual particles, as well as the reconstruction of the mean radius, the coefficient of variation, and the refractive index from measurements of the luminance of radiation scattered by an ensemble of particles. Errors in the reconstruction of the characteristics of disperse particles depending on the structure of the neural network and the parameters of particles are studied.

Light scattering by the surface of amorphous alloy ribbons modified by annealing and cryogenic treatment by L. V. Poperenko; S. I. Lysenko; K. L. Vinnichenko

*(292-297)*. The modification of the microrelief and structure of the surface layers of ribbons of an amorphous metal alloy based on iron and cobalt after thermal treatment at elevated and cryogenic temperatures and under the action of an external magnetic field is studied by the method of light scattering. The parameters of the surface roughness were calculated from the experimentally found indicatrices of light scattering. It is shown that heating of the metal ribbons to

*T*=650–750 K partially relieves stresses arising in the course of the ribbon preparation and reduces the surface roughness as compared to that of freshly prepared samples. Cryogenic treatment at*T*=78 K increases the surface roughness, and application of a magnetic field to a ribbon causes anisotropy in the surface layer due to the magnetostrictive effect. Intensity of optical field inside a weakly absorbing spherical particle irradiated by a femtosecond laser pulse by A. A. Zemlyanov; Yu. 'E. Geints

*(298-304)*. Using the Fourier technique in combination with the Mie theory, we study numerically the spatiotemporal evolution of the intensity of the internal optical field inside micron-sized weakly absorbing spherical particles upon diffraction by these particles of a femtosecond laser field. A number of specific features of the dynamics of the spatial intensity distribution of the femtosecond pulses inside the particles are found to depend on the pulse width, the shape of the laser beam, the size of the particles, and the geometry of their irradiation. It is shown that, under conditions of nonstationary diffraction, the internal optical field is usually excited in a resonance way, with the eigenfrequencies of one or several high-

*Q*resonance modes of the particle falling into the central part of the original pulse spectrum. This causes a time delay of the light in the particle and a reduction of the absolute maximum in the time dependence of the internal field intensity as compared with a stationary regime. The greatest reduction of the peak occurs at exact resonance. In this case, the decrease in the peak intensity may reach several orders of magnitude. Irradiation of a particle by a narrow Gaussian beam of femtosecond duration directed toward the particle center enhances the internal field intensity as compared with the case of near-edge incidence. Saturated dispersion resonance observed in the width of a He-Ne laser beam with an intracavity neon cell by A. G. Druzhinin; A. V. Mironov

*(305-311)*. A narrow dispersion-like resonance is found in the width of the beam of a He-Ne laser with an intracavity neon cell. The width of the beam was determined by measuring the difference between the power in its axial circular zone and in an adjacent coaxial zone of annular shape. The zones were selected by spatial division of the beam power in half by a mirror with a circular aperture. The resonance obtained is spectrally locked to the center of the neon absorption line and is interpreted as a result of action of the nonlinear lens of the refractive index in the neon. By comparing the experimental data with the numerical model of Gaussian beam formation, the nonlinear lens component of the refractive index of neon is estimated.