# Optics and Spectroscopy (v.94, #3)

Use of sturmian expansions in calculations of the hyperfine structure of atomic spectra by I. I. Tupitsyn; A. V. Loginov

*(319-326)*. A procedure for calculating hyperfine structure (HFS) parameters using the basis of Sturmian functions is developed. The procedure is used to calculate the HFS parameter

*a*4*d*_{ }^{5}of the 4*d*^{5}levels of the niobium atom. The contributions of the continuous spectrum and higher orders of the perturbation theory are quantitatively estimated by comparing the numerical values of the parameter*a*4*d*_{ }^{10}obtained in the framework of the perturbation theory with the results of direct calculations by the configuration interaction method. Comparison of the results of relativistic and nonrelativistic calculations allows the contribution of relativistic effects to HFS parameters to be found. Excitation of a singly charged Sr Ion by e-Sr collisions by Yu. M. Smirnov

*(327-331)*. Excitation of spectral lines of SrII, including laser lines, is studied experimentally in collisions of slow electrons with strontium atoms. Twenty-one excitation cross sections are measured at an energy of electrons of 30 eV. Five optical excitation functions are recorded at an energy ranging from 0 to 200 eV. Direct-excitation cross sections for the 5

*p*^{2}*P*°_{1/2, 3/2}levels and the contribution to their population by cascade transitions are calculated. Excitation cross sections of two laser transitions in the IR spectral region are determined using known branching ratios. The results obtained are compared with data of previous experiments. Excitation of the BaI

^{1}*P*levels in collisions of slow electrons with barium atoms by Yu. M. Smirnov*(332-337)*. Excitation of the singlet

*P*levels of the barium atom by slow monoenergetic electrons is studied experimentally. In the four series studied, the dependence of the excitation cross sections on the principal quantum number of the upper level was found to be irregular. Such behavior of the cross sections is associated with the fact that the BaI singlet series are strongly perturbed. The absolute excitation cross sections and the branching ratios obtained are compared with the data of previous studies. Diagnostics of a weak magnetic field upon pulse excitation of an ensemble of particles by V. L. Kantsyrev; A. G. Petrashen’; A. S. Shlyaptseva

*(338-342)*. A method of diagnostics of weak magnetic fields, based on the spectropolarimetry of damped radiation from an ensemble of particles excited by a rectangular pulse, is suggested. This method can be used without any assumptions about the dynamics of excitation.

Diagnostics of a magnetic field by X-ray polarization spectroscopy by V. L. Kantsyrev; A. G. Petrashen’; A. S. Shlyaptseva

*(343-345)*. A new method of diagnostics of a magnetic field of a

*Z*pinch, based on the use of three instruments for x-ray spectropolarimetry, is suggested. Dissociative excitation of the 6

*pns*levels of PbI in e-PbCl_{2}collisions by Yu. M. Smirnov*(346-351)*. Dissociative excitation of the 6

*pns*levels of lead atoms in collisions between electrons and lead dichloride molecules is studied experimentally. Thirty excitation cross sections of the transitions from the 6*pns*levels, including three laser transitions, are measured at an electron energy of 100 eV. Five optical excitation functions are recorded at an electron energy ranging from 0 to 100 eV. Cross sections of the population of low laser (metastable) levels by cascade transitions are determined. Possible channels of dissociative excitation at low electron energies are discussed. Remote detection of double nuclear quadrupole resonance spectra by V. S. Grechishkin; R. V. Grechishkina; A. A. Shpilevoi; A. A. Persichkin; Hoon Heo

*(352-353)*. Remote detection of the spectra of double nuclear quadrupole resonance of nitrogen-containing compounds is considered. A comparison is made of this technique with the cross-relaxation method.

Matrix method for the determination of scaling factors for quantum-mechanical force fields by K. V. Berezin

*(354-356)*. A computer-assisted method for the calculation of scaling factors for refining the quantum-mechanical force fields of polyatomic molecules by the Pulay technique is suggested. The method is an iteration procedure and does not involve the calculation of derivatives of the frequencies of vibrations with respect to the scaling factors. The correlation between the experimental and calculated frequencies upon scaling of the force field is discussed.

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules by K. V. Berezin; V. V. Nechaev; T. V. Krivokhizhina

*(357-360)*. The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.

A theoretical study of the effect of disorder of the transition dipole moments of molecules on the shape of optical bands of molecular aggregates by D. V. Makhov; A. A. Bagatur’yants; M. V. Alfimov

*(361-368)*. Aggregates with substitutional disorder, in which molecules of different types have different transition dipole moments, are considered. The relations between the absorption spectra of aggregates with disordered and nondisordered transition dipole moments are obtained for two limiting cases: (1) the case when there is no statistical correlation between the transition energies and transition dipole moments of the molecules and (2) the case of total correlation, when the transition energies and transition dipole moments are strictly related to each other. For aggregates that are characterized by substitutional disorder along with diagonal disorder, an effective method of calculation of the optical bands is developed. Numerical calculations of the absorption bands of aggregates consisting of molecules of two types are carried out at different values of the parameters.

Using ion imaging to analyze higher-order moments of the angular distributions of photofragments by O. V. Elyukhina; O. S. Vasyutinskii; J. A. Beswick

*(369-373)*. We investigate the effect of the hexadecapole (

*K*=4) polarization moment on the spatial distributions of angular momenta for atoms produced during the photodissociation of diatomic or triatomic molecules by polarized radiation. We derive general expressions for the angular distributions of the atomic density matrix for*K*= 2, 4 and expressions for the corresponding anisotropy parameters that contain all information on the photodissociation dynamics. We show that these anisotropy parameters can be experimentally determined by using ion imaging. We consider oxygen atoms in the^{1}*D*_{2}state aligned with respect to the orbital angular momentum as an example and provide ion images of the signals that correspond to the population of the atomic magnetic sublevels ¦*m*¦ = 0, 1, 2. We show the contributions from the second-and fourth-rank state multipoles to the angular distributions of the atomic density matrix to be comparable in magnitude and significantly different in form. Vacuum ultraviolet spectra of heteronuclear dimers of inert gases in a direct-current discharge by G. N. Gerasimov; B. E. Krylov; R. Hallin; A. O. Morozov; A. Arnesen; F. Heijkenskjold

*(374-383)*. The emission bands appearing near the resonance lines of Kr and Xe in the spectra of the gas-discharge plasma of binary Xe-X and Kr-Y mixtures (X is He, Ne, Ar, or Kr; Y is He, Ne, or Ar) are experimentally studied. It is concluded that the emission bands investigated are related to electronic transitions in hetero-nuclear dimers. The mechanisms of formation of the spectra under study are analyzed.

Resonance energy transfer in ZnS:Mn crystals in the processes of photoluminescence and electroluminescence by M. F. Bulanyĭ; A. N. Gorban’; A. V. Kovalenko; B. A. Polezhaev

*(384-388)*. The spectra of photoluminescence (PL), electroluminescence (EL), and optically detected magnetic resonance were studied in ZnS single crystals. It is shown that, in ZnS:Mn crystals, PL at λ

_{max}=590 nm excited with light in the extrinsic-absorption region for ZnS (λ = 365 nm) is controlled by the resonance-excitation mechanism; in contrast, the EL can be excited by both the resonance-and impact-related mechanisms. Optical breakdown of alkali halide crystals by S. V. Karpenko; A. I. Temrokov

*(389-395)*. It is shown that the metallization of a dielectric in the region of its interaction with laser radiation is a substantiated mechanism of laser damage of wide-gap dielectrics. Calculations of the radiation pressure produced by high-power laser radiation and the pressure of external bulk compression at which the dielectric energy-gap width becomes zero and which is calculated on the basis of the self-consistent statistical electron theory of ionic crystals have shown that these pressures are of the same order of magnitude.

Reflection of ultrashort pulses from the boundary of a Drude-Lorentz medium by N. N. Rozanov

*(396-399)*. Reflection of ultrashort pulses of electromagnetic radiation from the boundary between a vacuum and a Drude-Lorentz medium (a set of classical linear oscillators with a low concentration) is considered. For the case of two incident pulses, the possibility of interference quenching of reflected radiation is revealed. The quenching occurs when the pulse amplitudes satisfy a certain relation and the pulses follow with an appropriate time delay.

Raman echo induced by ultimately short pulses under conditions of strong nonresonant pumping by S. V. Sazonov

*(400-410)*. On the basis of quantum-mechanical approach, a theoretical study of the primary Raman photon echo was carried out under conditions of excitation of a medium by pulses with a duration on the order of one period of electromagnetic oscillations (ultimately short pulses) and by strong quasi-monochromatic nonresonant pumping. It is shown that the intensities of the pumps determine to a considerable extent the time of formation of the echo signal, its duration, the direction of emission, and the power and that the use of ultimately short pulses promotes the substantial simplification of the schemes of prospective experiments. The possibilities of echo generation at the Stokes and anti-Stokes frequencies in the regimes of two-, one-, and zero-pulse excitations are revealed. In the last case, the Raman-active transitions are excited by two pumps with different intensities.

Eigenwaves in one-dimensional photonic crystals with gain by L. A. Mel’nikov; O. N. Kozina

*(411-417)*. The dispersion characteristics of a one-dimensional photonic crystal are analyzed in detail on the basis of the exactly solvable Kronig-Penney model for the particular case of a periodic system consisting of an infinite number of insulator-air layers arranged in the direction of propagation of radiation. An analytical solution is obtained, and the behavior of eigenwaves near the edges of the photonic band is thoroughly studied. The behavior of roots on a complex plane is qualitatively analyzed with the use of approximate dispersion characteristics obtained via expanding the solution of the wave equation in series in terms of the harmonics of the lattice spacing. It is shown that, despite the amplifying properties of the material, no gain in the photonic band gap is present, because of the interference quenching of waves.

Specific features of light propagation in a periodic structure with regular arrangement of defect layers by S. N. Kurilkina; M. V. Shuba

*(418-422)*. Specific features of light propagation in a periodic structure with a large number of identical regularly arranged defect layers are considered. Rigorous analytical formulas for the transmittance and reflectance of the structures are derived. It is shown that the presence of periodically arranged inclusions may give rise to new photonic band gaps, with their positions controlled by the dielectric properties and thickness of the defect layers.

Periodic structures induced by scattered light in a photosensitive film on a dielectric plane-parallel substrate by L. A. Ageev; V. K. Miloslavsky; M. V. Pogrebnyak

*(423-427)*. Periodic structures appearing in a thin AgCl-Ag film on a plane-parallel substrate irradiated with a normally incident, focused, linearly polarized Gaussian laser beam λ=633 nm) with a waist spot size of about 0.01 mm have been studied. The structures are formed in the beam spot and its nearest vicinity (with a radius of up to 0.2 mm) as a result of the interference of the incident beam and the waveguide TE modes excited due to the Rayleigh scattering in the film. In the vicinity of the waist spot, the periodic structures develop under the action of a coherent recurrent scattering from back side of the substrate. In addition, periodic structures of ring symmetry have been revealed far (up to 10 mm) from the irradiated spot. It is demonstrated that these structures are due to the interference of radiation scattered from the film and back side of the substrate and reflected from the two boundaries. Interference models are proposed that provide for a good agreement of the interference period, calculated as a function of the distance from the beam center, with the experimental values.

A scalar model of the angular and spectral dependence of scattering from a smooth metal surface: Direct and inverse problems by A. Ya. Khaĭrullina; T. V. Ol’shanskaya; T. A. Zhevlakova

*(428-433)*. Analytical formulas describing the scalar characteristics of scattering (the scattering indicatrix and the diffuse reflectance spectrum) have been derived in the Rayleigh approximation for a smooth metal surface with randomly oriented roughnesses, taking into account their shapes and the correlation in distribution over the surface. Experimentally measured optical characteristics that can provide information necessary for selecting a proper theoretical model are indicated. The efficacy of the proposed theoretical model is demonstrated in its application to a smooth copper surface prepared by optical polishing. It is shown how topological characteristics can be determined from scattering experiments with this system.

On phase-amplitude correlation in reflection spectra of Fabry-Perot Interferometers by P. S. Kosobutskiĭ; M. S. Karkulevskaya; Ya. P. Kosobutskiĭ

*(434-436)*. The correlation between the spectra of phase and reflection of free and fixed Fabry-Perot interferometers is theoretically studied. It is shown that, under certain conditions, the phase of the reflected wave can be determined directly from the reflection spectra.

Relation for estimating the reflectance of a very rough surface with an approximately one-dimensional distribution of roughness by V. Ya. Mendeleev; S. N. Skovorod’ko

*(437-443)*. A relation for estimating the reflectance of a very rough surface with an approximately one-dimensional distribution of roughness is derived for the case of normal incidence and reflection in the specular direction within the solid diffraction angle. The reflectance values are determined both experimentally and by calculation using the derived relation for two approximately one-dimensional rough steel samples with rms roughnesses of 0.5 and 1.3 μm for a wavelength of 0.6328 μm. The resulting values are found to agree satisfactorily with each other.

A microscopic theory of a quasi-crystalline transition layer on the surface of semi-infinite liquid dielectrics upon brewster light reflection and the near-field effect by O. N. Gadomskiĭ; A. S. Kadochkin

*(444-452)*. An adequate theoretical interpretation of experiments on Brewster light reflection from the surfaces of liquids is given on the basis of the near-field effect in the transition layer. The analysis is carried out in terms of the model of a discrete-continuous dielectric, which takes into account the fields of atomic (molecular) dipoles discretely distributed inside the Lorentz sphere surrounding the point of observation. The liquids under consideration that have anisotropic molecules are characterized by a diagonal polarizability tensor within the transition layer and by scalar polarizability in the bulk of the liquid. It is shown that agreement between theoretical and experimental values of the ellipticity of reflected light is obtained due to a random change within a finite interval of the angle of orientation of molecules in the lattice sites in the transition layer. This makes it possible to conclude that the transition layer in the liquids under consideration is quasi-crystalline.

Interference of speckle fields in the diffraction zone of a focused spatially modulated laser beam by a random phase screen by V. P. Ryabukho

*(453-460)*. The processes of formation of average-intensity interference fringes upon diffraction by a random-phase object of a laser beam having interference fringes and focused on the surface of the object are considered. The dependences of the fringe contrast on the parameters of scattering inhomogeneities of the object and the parameters of the focused laser beam are established in analytical form for various diffraction regimes. Practical possibilities of a method of probing of scattering objects in problems of measuring the parameters of inhomogeneities and problems of interference-pattern formation in optical systems with scattering media are discussed.

Soliton formation in the propagation of phase-modulated femtosecond pulses through an optical fiber with a cubic nonlinearity by A. G. Volkov; V. A. Trofimov

*(461-468)*. A way of soliton self-formation upon propagation of femtosecond light pulses through an optical fiber with a cubic nonlinearity is described with allowance for the dispersion of the nonlinear response of the medium. For soliton formation to occur, a low-frequency phase modulation of the initial pulse is necessary. Several solitons formed in this way differ in both maximal intensities and group velocities. The duration of an individual soliton may be several (up to ten) times smaller than the initial duration of the input pulse.

Radiative characteristics of a two-section laser structure based on a δ-doping superlattice by D. V. Ushakov; V. K. Kononenko; I. S. Manak

*(469-475)*. Spectral characteristics of a two-section laser structure with δ-doping active regions are studied theoretically. The wide range of tuning of the lasing wavelength is primarily related to specific characteristics of the gain spectra of

*n-i-p-i*crystals: the dependence of the effective band-gap width of the superlattice on the level of excitation, the character of variation of the overlap integrals of the electron and hole wave functions, and broadening of the electronic spectra due to fluctuations of the electrostatic potential. Depending on the pumping currents in sections of the laser structure, the lasing wavelength can be tuned over a wide spectral range of the IR region in regimes of cw lasing, the transient regime, and the regime of regular pulsations. In the regime of self-sustaining pulsations, lasing is also possible at two wavelengths spaced well apart. The effect of spatial field distribution on two-mode lasing in a spherical microparticle by H. P. Ledneva; A. V. Korzhov; L. A. Kotomtseva; L. G. Astafyeva

*(476-480)*. It is shown that two steady-state two-mode lasing regimes resulting from nonlinear coupling of the modes and spatial overlap of their fields may exist above the first lasing threshold. With increasing pumping power in one of the modes, the region of their existence is larger the larger the difference in intensities of the spatial structures of the modes.

Erratum: “On measurements of the refractive index dispersion in porous silicon” [

*Optics and Spectroscopy*93 (1), 132 (2002)] by M. I. Strashnikova*(482-482)*.