# Optics and Spectroscopy (v.96, #1)

Emission of an atom during its interaction with an ultrashort pulse of electromagnetic field by V. I. Matveev

*(1-7)*. The electronic transitions and emission of an atom during its interaction with a spatially inhomogeneous ultrashort pulse of electromagnetic field are considered. The probabilities of excitation and ionization, as well as the spectra and cross sections of reemission of such a pulse by the atom, are obtained. As an example, the one-and two-electron inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-and helium-like atoms are considered.

Optimal Hamiltonian of internal motion of an atomic-molecular system in a magnetic field by T. K. Rebane

*(8-15)*. The effect of a uniform magnetic field on the state of an atomic-molecular system considered as a united system of

*N*particles (without separation of the motion of acoelightac and particles) is analyzed. It is shown that the Hamiltonian of the internal motion of the system in the magnetic field contains (*N*-1)(*N*-2)/2 arbitrary parameters corresponding to the coefficients of the gauge transformation of the vector potential. A method of calculation of the optimal values of these coefficients based on the requirement for the minimum diamagnetic correction to the energy is proposed. New formulas for the diamagnetic susceptibility of atomic-molecular systems are obtained that take into account the simultaneous perturbing effect of the magnetic field on the motion of all particles. The theory is applied for calculation of the diamagnetic susceptibilities of the H, He, Li, and Be atoms; the muonic analogues of helium atoms^{∞}He^{2+}µ^{−}*e*^{−},^{4}He^{2+}µ^{−}*e*^{−}, and^{3}He^{2+}µ^{−}*e*^{−}; and the positron-containing systems*t*^{+}*e*^{+}*e*^{−}*e*^{−},*d*^{+}*e*^{+}*e*^{−}*e*^{−},*p*^{+}*e*^{+}*e*^{−}*e*^{−}, µ^{+}*e*^{+}*e*^{−}*e*^{−}, and*e*^{+}*e*^{+}*e*^{−}*e*^{−}, with regard for the motion of all particles. Dependence of Doubly Charged Ion Formation by the Two-Electron Mechanism on the intensity of Laser Radiation by I. I. Bondar’; V. V. Suran; D. I. Bondar’

*(16-20)*. Experimental dependences of the doubly charged ion yield

*N*^{2+}on the laser radiation intensity*F*are analyzed for the case of ion formation by the two-electron mechanism. It is shown that the region where the dependence*N*^{2+}(*F*) is characterized by the degree of nonlinearity*K*≈2.5 corresponds to the saturation of the process of doubly charged ion formation. This region is described well by theoretical calculations performed for Gaussian laser beams. Determination of the parameters of the potential well of a diatomic molecule with the use of the experimental spectrum of an electronic transition to a repulsive branch of the state under study by V. S. Ivanov; V. B. Sovkov

*(21-24)*. It is shown that the lack of information on the rotational structure of the vibrational terms of a diatomic molecule in the problem of determination of the potential well of the molecule can be compensated by information on the intensity distribution in the spectrum of a bound-free transition to a repulsive branch of the state under study. The accuracy characteristics of the method proposed are studied on the example of a potential whose parameters are close to those of the state

*a*^{3}Σ_{u}^{+}of the Na_{2}molecule. Semiempirical study of perturbations of the Landé

*g*factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory by S. A. Astashkevich*(25-34)*. Theoretical analysis of perturbations of the Landé

*g*factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the*g*factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an*nl*complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the*g*factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed. Semiempirical study of perturbations of the Landé

*g*factors of electronic-vibrational-rotational levels of hydrogen: II.*i*^{3}_{g}^{−}and*j*^{3}Δ_{g}^{−}states of the H_{2}, HD, and D_{2}molecules by S. A. Astashkevich*(35-46)*. Photoelectron spectroscopy of molecular systems and quantum-chemical calculations in terms of the density functional theory: Iron π complexes L-Fe(CO)

_{3}by I. V. Krauklis; Yu. V. Chizhov*(47-56)*. The HeI and NeI photoelectron spectra of irontricarboniyl complexes with cyclic diene ligands—αmethylstyrene, orthoquinodimethane, and cyclooctatetraene—were obtained. The results of quantum-chemical calculations of the molecules of these compounds in the approximation of the density functional theory (B3LYP/6-31G*) are presented. It is shown that this approximation describes well the excited ionic states of the π complexes under study. The relative ionization cross sections σ

_{π}and σ3*d*_{ }, which characterize the probability of removal of electrons from the molecular π-ligand and 3*d*-metal orbitals, are estimated. The mechanism of the selective coordination of the Fe(CO)_{3}groups to corresponding organic ligands is discussed. The energies of the L-Fe(CO)_{3}chemical bond are calculated. On the mechanism of formation and broadening of the electronic and vibrational spectra of vapors of octaethylporphyrin metal complexes by Yu. S. Demchuk

*(57-62)*. Optical absorption spectra of vapors of metal complexes of octaethylporphyrins known from the literature are analyzed on the basis of notions about sequences as basic elements of the formation of electronic-vibrational bands. According to this analysis, major features of these spectra are explained. These features include considerable half-widths of the electronic-vibrational bands of rarefied vapors, when intermolecular interactions virtually do not affect the broadening; a Lorentzian intensity distribution over the contour of the 0-0 spectral band; long-wavelength shifts of the intensity maxima of bands with increasing temperature; and the origin of a fine structure of the electronic and vibrational spectra at low temperatures. It was concluded that sequential transitions form the basis of the mechanism of formation and broadening of the electronic and vibrational spectra of metal complexes of octaethylporphyrins as representatives of complex biomolecules.

Absorption of cnoidal electromagnetic waves by superlattice electrons in the process of impurity ionization by D. V. Zav’yalov; S. V. Kryuchkov; N. E. Meshcheryakova

*(63-65)*. Absorption of cnoidal electromagnetic waves, which are the most general periodic solution to the sine-Gordon equation, by electrons of a one-dimensional quantum semiconductor superlattice in the process of impurity ionization is studied in terms of the semiclassical approximation. The dependence of the absorption coefficient on the electric field of an electromagnetic wave is found to be nonmonotone with a pronounced peak.

Band structure of α-ZnP

_{2}studied by laser modulation spectroscopy by I. I. Patskun; N. Yu. Pavlova*(66-69)*. A study of α-ZnP

_{2}by two-beam laser modulation spectroscopy is carried out. As a result, five*M*_{0}-type critical points are revealed in the valence band and four*M*_{0}-type critical points, in the conduction band. The energy positions of the critical points are determined. Ultraviolet luminescence of single crystals and single-crystal films of YAlO

_{3}by Yu. V. Zorenko; A. S. Voloshinovskii; G. M. Stryganyuk; I. V. Konstankevych*(70-76)*. The nature of intrinsic emission bands of yttrium orthoaluminate in the UV spectral region at

_{max}=220 nm (5.63 eV) and 330 nm (4.13 eV) is studied on the basis of the luminescence of single crystals and single-crystal films of YAlO_{3}and Ce: YAlO_{3}excited by synchrotron radiation sources with an energy of 3–25 eV at 9 and 300 K. The single crystals and single-crystal films were obtained, respectively, from solution and solution-melt by liquid-phase epitaxy and are characterized by considerably different concentrations of substitutional and vacancy defects. It is found that only the luminescence band at 300 nm, which has the decay time τ=4.1 ns and is excited in a band shifted from the range of interband transitions by 0.25 eV, has exciton-like character. The luminescence band at 220 nm with τ=0.1 µs at 9K, which is observed only for YAlO_{3}single crystals and is absent in the luminescence of single-crystal films, is associated with antisite defects of the Y_{Al}^{3+}type, which are a specific type of cationic isoelectronic impurities. It is shown that the phosphors based on single-crystal films of YAlO_{3}have a simpler scintillation decay kinetics than their bulk analogues due to the absence of channels of excitation energy dissipation associated with the antisite defects of Y_{Al}^{3+}type and vacancy defects. Optical limiting of near-IR radiation in a system based on magnesium phthalocyanine by N. V. Kamanina; I. Yu. Denisyuk

*(77-80)*. Nanocrystals of magnesium phthalocyanine in the β-and

*X*-crystalline forms and the magnesium phthalocyanine C_{60}fullerene system are studied in the near-IR spectral region. The absorption spectra of new nanocomposites are measured. The possibilities of using these systems for optical limiting in the near-IR spectral region (at the wavelength λ=1047 nm) are investigated. The relation between the photoconductivity and nonlinear absorption of phthalocyanine in different crystalline forms is discussed. On entanglement of quantum states of noninteracting subsystems by A. M. Basharov; É. A. Manykin

*(81-85)*. Simple models for measuring the characteristics of a system of two atoms that do not interact with each other are used to show that the nonselectivity of measurement, related to the indistinguishability of the quantum subsystems with respect to some general parameter, leads to entanglement of the atomic states of the subsystem selected in such a way. This entanglement is in no way related to some collective process and is only due to the effective measurement in an entangled basis. An analogy between the preparation of entangled states of a system of subsystems that do not interact with each other by a quantum reduction (a measurement) and a quantum evolution is found.

On the modulation instability of femtosecond light pulses propagating in an optical fiber by A. G. Volkov; V. A. Trofimov

*(86-89)*. The well-known problem of the modulation instability of femtosecond light pulses propagating in a cubic nonlinear medium is considered on the basis of computer simulation with allowance made for the time dispersion of the nonlinear response. The dependence of the maximum perturbation frequency at which the instability takes place on the parameter characterizing the time dispersion of the nonlinearity is studied. The numerical experiments carried out verified the previous conclusion of the authors, based on an original approach to the analysis of propagation of a femtosecond pulse, that the frequency interval of the modulation instability can increase with increasing influence of the dispersion of the nonlinear response. This conclusion is at variance with the conclusion drawn by other researchers on the basis of linear analysis.

Spatiotemporal dynamics of femtosecond pulses in nonlinear optical waveguides with material dispersion by E. A. Romanova; L. A. Mel’nikov

*(90-95)*. The effect of the second-order dispersion on the spatiotemporal dynamics of ultrashort pulses in nonlinear waveguides with infinite parabolic and stepped profiles of the refractive index is studied. It is shown that the leakage of radiation from the core to the cladding of step-index waveguides prevents the formation of a steady spatiotemporal distribution of the field. The possibility of compressing light pulses in a dielectric waveguide with a positive group-velocity dispersion is discussed.

Focusing of singular beams by A. V. Volyar; T. A. Fadeeva

*(96-105)*. The process of focusing of an inhomogeneously polarized beam passed through a system consisting of a uniaxial crystal and a polarization filter is considered. It is shown that the action of this system is equivalent to the action of a phase transparency with a complex relief of the refractive index. In particular, if the angle between the axes of the quarter-wave plate and the polarizer is equal to 45°, this transparency has a helicoidal relief. Simultaneously, two singular beams with different curvatures of their wavefronts arise in the transparency. The action of the lens consists in formation of a combined singular beam having three focal waists. The boundary wave arising upon focusing is able not only to form a new spectrum of toroidal vortices, but also to straighten the focusing region, forming a fairly extended range with a weak divergence.

Permittivity of a randomly inhomogeneous medium by V. L. Kuz’min; V. P. Romanov; I. V. Meglinskii

*(106-116)*. A theory of permittivity of suspension-type systems is developed that allows one to calculate such optical parameters of inhomogeneous systems as the length of scattering and the transport length. It is shown that, in the Born approximation, which takes into account two-particle correlations in the arrangement of scattering particles, the theoretical and experimental data are in agreement only to within tens of percent. The contribution of three-particle correlations to the permittivity of a system of solid spheres is determined. It is shown that, in describing the optical properties of suspensions with a large difference between the refractive indices of the medium and the particles, it does not suffice to replace the Rayleigh-Gans form factor by the Mie form factor, even under a restriction to two-particle correlations.

A method for determining the optical constants of an absorbing film entering into the composition of a layered system by E. A. Bondar’; L. P. Shadrina

*(117-121)*. A matrix method of calculating the refractive index and the absorption factor of an absorbing film entering into the composition of a multilayer thin-film system (for example, of the dielectric-metal-dielectric type) from the measured transmission and reflection spectra of the system is proposed. The method is based on solution of the matrix equation for the layered system by the iterative method of continuous differential descent. The method developed was applied to determine the optical constants of a real silver film in the composition of a three-layer energetically efficient titanium dioxide-silver-titanium dioxide coating.

Computer simulation of integral and differential optical characteristics of paints by O. N. Kozakov

*(122-127)*. A method of calculating the integral and differential characteristics of paints is proposed. The method is based on statistical simulation (the Monte Carlo method). For white alkyd enamel formed on the basis of titanium dioxide, the results of calculations of the reflectance, absorptance, covering power, and distribution of the absorbed energy over the layer as a whole, along with the absorptance of the pigment and the binder separately, are presented.

Measurement of mean size and evaluation of polydispersity of gold nanoparticles from spectra of optical absorption and scattering by V. A. Bogatyrev; L. A. Dykman; B. N. Khlebtsov; N. G. Khlebtsov

*(128-135)*. Two methods for determination of the mean size of gold nanoparticles, based on measurement of the wavelengths of the maxima λ

_{max}of side scattering and extinction in the range 400–700 nm, are compared. Four sols with mean particle diameters*d*of about 15, 20, 25, and 30 nm, measured using the dynamic light-scattering technique, were studied experimentally. The slope of the size dependence λ_{max}(*d*) of the spectral position of the scattering peak exceeded that for the extinction peak by a factor of 2.4. This fact ensures a substantially higher accuracy of the scattering method. For simulating polydispersity, mixtures of three colloids with particle diameters of 20, 25, and 30 nm were used: sample S1, with a size distribution close to the normal one of around 25 nm, and sample S2, with equal concentrations of each of the components. The extinction spectra of mixtures S1 and S2 and the initial 25-nm sol (S0) were virtually identical, whereas their scattering spectra showed a pronounced increase in the peak amplitude in the series S0, S1, S2. These results agree with calculations based on the Mie theory. Thus, scattering spectra offer advantages over extinction spectra not only in measuring the mean size of gold particles but also in evaluating their polydispersity. Effect of aberrations in formation of holographic lateral shear interferograms under high measurement sensitivity by A. M. Lyalikov

*(136-141)*. Analysis of the effect of aberrations of a system for recording and optical processing of holograms, as well as of inhomogeneities in hologram bases, on fringe distortion is performed for different methods of holographic shearing interferometry. Different dependences of the degree of fringe distortion in lateral shear interferograms on the measurement sensitivity are revealed. A method of excluding aberrations in formation of shear interferograms is proposed for the cases of single-and double-exposure holograms. Experimental results are reported.

Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry by I. A. Lyavshuk; A. M. Lyalikov

*(142-147)*. A method for increasing measurement sensitivity in the visualization of dynamics of changes in wavefront shape with the use of holographic lateral-shearing interferometry is considered. At the first stage of this method, a photograph of a reference shear interferogram obtained with tuning to closely spaced fringes is recorded under linear conditions. After chemical treatment, the photograph of the reference shear interferogram is installed in exactly its initial position. At the second stage, a series of photographs of lateral-shear interferograms of the wavefront under study is recorded under nonlinear conditions using the photograph of the reference interferogram. The photographs of the lateral-shear interferograms are optically processed by two coherent beams with selection of the highest diffraction orders, which makes it possible to visualize the dynamic component of the wavefront deformation with an increase in the measurement sensitivity (the static component is excluded in this case). The effect of the degree of nonlinearity of photograph recording on the range in which the measurement sensitivity can be controlled during the optical processing of a pair of matched photographs or one double-exposure photograph of interferograms recorded at different values of a lateral shift is analyzed.