# Optics and Spectroscopy (v.92, #5)

Account of the fine structure of hydrogen atom levels in the effective emission cross sections of Balmer lines excited by electron impact in gases and plasma by B. P. Lavrov; A. V. Pipa

*(647-657)*. The possibility of a correct account of the fine structure was shown for two limiting cases observed in beam and plasma experiments. A significant difference was found in the emission cross sections and the rate coefficients of direct and dissociative excitation of the

*H*_{α}and*H*_{β}lines by electron impact in two limiting cases (e.g., this difference reaches an order of magnitude for dissociative excitation of the*H*_{β}line). The most reliable data on the cross sections and the rate coefficients of direct and dissociative excitation of the*H*_{α}and*H*_{β}lines by electron impact were found for both limiting cases. It was shown that, among the first four lines of Balmer series (rather easily detected), only the first two lines, i.e.,*H*_{α}and*H*_{β}, can be currently employed in plasma spectroscopy studies because of the absence of data on the partial excitation cross sections of hydrogen atom*nl*-sublevels with*n*≥5. Hyperfine magnetic anomaly in the atomic spectra of rare-earth elements by Yu. P. Gangrskiĭ; S. G. Zemlyanoi; D. V. Karaivanov; N. N. Kolesnikov; K. P. Marinova; B. N. Markov; V. S. Rostovskii

*(658-663)*. Hyperfine-splitting constants in the optical spectra of rare-earth elements, Nd, Eu, Gd, and Lu, were measured using the laser-induced resonance fluorescence in a low-divergence atomic beam. Values of the hyperfine magnetic anomaly for different atomic levels were determined by comparing the ratios of the magnetic dipole constants of neighboring isotopes with odd numbers of protons or neutrons. The relation of these values to the special features of the atomic and nuclear structure of the investigated elements is discussed.

Spectral-luminescent properties of Eu

^{3+}ions in inorganic D_{2}O and POCl_{3}-SnCl_{4}solvents by E. A. Seregina; A. A. Seregin*(664-669)*. Absorption and luminescence spectra of Eu

^{3+}ions in D_{2}O and POCl_{3}-SnCl_{4}inorganic solvents were measured. Oscillator strengths and spontaneous radiation transition probabilities for the most intense electron transitions in Eu^{3+}were calculated. Judd-Ofelt parameters, the radiative lifetime of the^{5}*D*_{0}metastable level of Eu^{3+}in D_{2}O-Eu^{3+}and POCl_{3}-SnCl_{4}-Eu^{3+}solutions, and matrix elements for radiative transitions from the^{5}*D*_{0}level were determined. The luminescence lifetime of the^{5}*D*_{0}level of Eu^{3+}in these solutions was measured. The photoluminescence quantum yield for transitions from the^{5}*D*_{0}level of Eu^{3+}in^{5}*D*_{0}and POCl_{3}-SnCl_{4}-Eu^{3+}solutions was found to be 0.32 and 0.88, respectively. The possibility of describing a two-particle quantum system and interparticle correlations in the self-consistent field approximation by D. V. Kulakovskiĭ; A. M. Popov

*(670-675)*. The possibility of determining the energy spectrum and the wave function structure of the stationary states of a model two-particle system is examined in the self-consistent field approximation. The results of exact calculations are compared with the data obtained in the self-consistent field approximation with the use of orthogonal and nonorthogonal orbitals. The possibility of using these approximations for describing the interparticle quantum correlations is discussed.

Resonances at collisions of slow electrons with cadmium atoms and ions by J. E. Kontros; I. V. Chernyshova; O. B. Shpenik

*(676-684)*. Using the crossed-beam method and a hypocycloidal electron spectrometer, the energy dependence of the ionization cross section for the cadmium atom has been studied in the near-threshold region and the elastic scattering of slow electrons at an angle close to 180° by Cd

^{+}ions was studied for the first time. Within the region under study (0–7 eV above the first atomic ionization potential), a resonance structure determined by the contribution of atomic autoionization states is revealed in both the ionization curve and differential cross section of elastic scattering. The structure in the measured curves has been analyzed with the use of data on the ejected-electron spectra obtained under the excitation of autoionization states of Cd atoms, as well as the data on the optical excitation functions for the atomic spectral lines at λ=430.7 nm (5^{1}*P*_{1}-8^{1}*S*_{0}), 515.5 nm (5^{1}*P*_{1}-7^{1}*S*_{0}), 298.0 nm (5^{3}*P*_{2}-6^{3}*D**j*_{ }), and 361.0 nm (5^{3}*P*_{2}-5^{3}*D**j*_{ }). Reconstruction of the

*Q*band spectrum of the 1285-cm^{−1}transition in the CO_{2}molecule from measurements of a pulsed response by A. P. Kouzov; V. B. Morozov; S. A. Mochalov; A. N. Olenin; V. G. Tunkin*(685-689)*. By using the method of nonstationary spectroscopy of coherent anti-Stokes Raman scattering, pulsed responses of the

*Q*band of the vibrational-rotational transition in the CO_{2}molecule at a frequency of 1285 cm^{−1}are measured under conditions of broadening close to the Doppler type. The ratios of the amplitudes of*Q*-band components at known frequencies are obtained by fitting to the measured pulsed responses. A multiwavelength low-pressure radiation source based on argon and xenon chlorides by A. K. Shuaibov; A. I. Dashchenko; I. V. Shevera

*(690-691)*. The characteristics of an excimer radiation source pumped by a subnormal dc glow discharge in an Ar/Xe/Cl

_{2}mixture with the source operating in a spectral range of 160–310 nm were studied. The emission intensities of the 175, 236, 258, and 308 nm bands due to the transitions ArCl (*B-X*), XeCl (*D-X*), Cl_{2}(*D′-A′*), and XeCl (*B-X*), respectively, were optimized in relation to the pressure, composition, and discharge current of the mixture. On the nature of the geometrical symmetry groups in the quantum intramolecular dynamics by A. V. Burenin

*(692-696)*. A hypothesis for the nature of the geometrical symmetry groups that are used in the quantum intramolecular dynamics in the Born-Oppenheimer approximation is considered. It is assumed that they are the dynamic symmetry groups of a more rigorous problem of intramolecular motion. On this basis, the contradictions in the concept of geometrical symmetry groups are removed and a number of new conclusions concerning the general properties of molecular systems are made.

Migration transfer of electronic excitation energy in activated solids by N. V. Selina; E. N. Tumaev

*(697-701)*. An analytic expression for the kinetics of quenching of donor luminescence in the presence of acceptors with allowance for migration of energy over the donor subsystem is derived. An extended criterion for the applicability of the hopping migration model is obtained.

Low-temperature time-resolved vacuum UV spectroscopy of potassium pentaborate crystals by I. N. Ogorodnikov; V. A. Pustovarov; M. Kirm; A. V. Kruzhalov; L. I. Isaenko

*(702-709)*. For the first time, subnanosecond time resolution is attained in the low-temperature (at 7 K) measurements of the photoluminescence (PL) spectra (2–6 eV), the PL excitation spectra (4–32 eV), the PL kinetics, and the reflection spectra (4–21 eV) of undoped potassium pentaborate KB

_{5}O_{8}·4H_{2}O (KB5) crystals under selective photoexcitation by synchrotron radiation. The PL peaks associated with the intrinsic defects of the KB5 lattice are detected. The PL bands resulting from radiative annihilation of the localized and self-localized electron excitations are singled out; these excitations are most efficiently photogenerated at the fundamental absorption edge in the region where the free exciton formation is expected. The difference between the PL spectra of the fast and slow components is revealed. An effective low-temperature energy transport over the KB5 hydrogen sublattice is deduced from a drop in efficiency of PL excitation in the interband-transition region as a result of nonradiative energy loss. Long-term vacuum UV irradiation of a KB5 crystal at 7 K gives rise to defects in the hydrogen sublattice, which facilitate localization of the electron excitations and reduce the effective length of their diffusion. This leads to a decrease in the nonradiative energy loss, thus enhancing the efficiency of the PL photoexcitation in the band-to-band transition region. Optical effects caused by coincidence between the energies of the plasma oscillations and the band-to-band transition in bismuth crystals doped with an acceptor impurity by N. P. Stepanov; V. M. Grabov

*(710-714)*. The energy of plasma oscillations of free charge carriers in bismuth crystals ℏω

_{p}can be qual to the band gap at the*L*point of the Brillouin zone*E**gL*_{ }as a result of doping with an acceptor impurity. Variation in the edge shape and splitting of the minimum in the plasma reflection are observed in experimental studies of reflection under normal incidence of radiation on the crystal. An analysis of the totality of available experimental data shows that the above special features are caused by interaction of elementary excitations (such as the plasma oscillations) with band-to-band transitions. It became possible for the first time to ascertain the composition of the bismuth crystals for which the condition ℏω_{p}=*E**gL*_{ }is satisfied and observe the variation in the characteristics of the plasma oscillations of free charge carriers, which occurs as a result of electron-plasmon interaction. Two-mode nature of the Raman spectrum of lithium niobate crystals by N. V. Sidorov; M. N. Palatnikov; N. N. Mel’nik; V. T. Kalinnikov

*(715-718)*. The ordering of the host and impurity cations in nominally pure (with different values of Li/Nbratio) and doped lithium niobate crystals is studied using Raman spectroscopy. It is shown that depending on the composition-controlled ordering of structural units of the cationic sublattice the crystal may exhibit, in the region of bridge stretching vibrations of the oxygen ions, either single-mode or two-mode behavior. The nominally pure lithium niobate crystals show, within the homogeneity region, single-mode behavior, while the crystals doped with divalent or trivalent cations show single-mode behavior at low concentrations of the dopant and two-mode behavior at higher concentrations.

Chaotic dynamics in a nonautonomous Dicke model without the rotating-wave approximation by I. L. Kirilyuk

*(719-726)*. The properties of a system consisting of two-level atoms interacting with a mode of the electromagnetic field in a cavity are considered for the case when the cavity detuning or the coefficient of the atom-field interaction is modulated. The consideration is performed with account taken of the Hamiltonian terms that are neglected in the rotating-wave approximation. It is shown that in the semiclassical equations for such a model, the effect of extension (compared to the autonomous system) of the range of variation of the quantity characterizing the number of photons can manifest itself; in this case, the energy oscillations have a chaotic character. The dependence of this phenomenon on parameters characterizing the model is studied. It is numerically demonstrated that with account taken for the relaxation, the system studied can have attractors different from the equilibrium positions, i.e., the number of photons in the mode does not tend to a constant value. The limits of validity of the rotating-wave approximation in the parametrically perturbed Dicke model are discussed.

Fourier synthesization of optical pulses and “polar” light by V. S. Zapasskiĭ; E. B. Aleksandrov

*(727-731)*. It is shown that the direct Fourier synthesization of light beams allows one to create polarity-asymmetric waves, which are able, in the process of nonlinear interaction with a medium, to break its inversion symmetry. As a result, these “polar” waves may show the effect of optical rectification in nonlinear centrosymmetric media by generating light-induced dc electric polarization. At the same time, waves of this type, due to their unusual symmetry properties, can be used for detecting the direction and sign of a dc electric field applied to the medium. The prospects of application of polar waves to data recording and processing are discussed.

Coherent control of the quasi-elastic resonant secondary emission: Semiconductor quantum dots by A. V. Fedorov; A. V. Baranov; Y. Masumoto

*(732-738)*. A detailed theoretical study of the time-integrated signal of spontaneous quasi-elastic secondary emission excited by a pair of phase-locked pulses has shown that coherent control is a promising method for measuring the total dephasing rate of a resonant optical transition. This method may be used to study both the homogeneously and inhomogeneously broadened systems, which is highly important in studies of semiconductor quantum dots. Analysis of components of the secondary emission in the framework of the developed theory has allowed us to find a physically justified criterion for separating the scattering and luminescence signals. The role of spectral filtering of the measured signal in determination of the phase and energy relaxation parameters is elucidated.

Dynamics of solitons in a three-level medium with linear birefringence by A. A. Zabolotskiĭ

*(739-747)*. The dynamics of ultrashort pulses in a three-level or degenerate two-level medium is studied in the framework of integrable systems of the Maxwell-Bloch equations for pulses with a duration much longer than or comparable with the inverse transition frequency, with allowance made for linear birefringence. Using soliton-type solutions, we study the effect of birefringence on soliton conversion for different initial populations of the levels.

Applicability of the

*T*-matrix method and its modifications by V. G. Farafonov*(748-760)*. The range of applicability of the

*T*-matrix method and its modifications for solving the problem if the scattering of electromagnetic radiation by nonspherical, axially symmetric particles is investigated analytically and numerically. The use of this method for calculating the characteristics of scattered radiation in the farfield region (the extinction and scattering cross sections, the scattering indicatrix, etc.) is shown to be appropriate for “weak-Rayleigh-type” particles. This condition is met when the intersection of the analytic continuations of the scattered and internal fields contains a ring with the center at the origin of coordinates. For a reliable calculation of the scattered field in the near-field region, it is necessary that a particle be a “Rayleigh-type” one (i.e., the Rayleigh hypothesis be valid for it). In this case, the singularities of the scattered field must occur inside a sphere lying inside a scatterer. Spheroidal particles are weak-Rayleigh-type ones if their semiaxes ratio is $$a/b < (sqrt {2 + 1} )$$ , and they are Rayleigh-type ones if $$a/b < sqrt 2 $$ . Numerical calculations for spheroids and Chebyshev particles corroborate these conclusions. However, the indicated boundaries are “ spread” (toward the expansion), because the expansion coefficients for the fields are determined with the use of the reduced (i.e., finite) systems. The limiting sizes of the particles for which the*T*-matrix method gives plausible results are primarily determined by their geometry (shape). Specific features of depolarized and polarized light scattering in a solution with a layering isolated region by L. V. Vainshtein; L. L. Chaikov

*(761-764)*. Intensities of depolarized and polarized light scattering in guaiacol-glycerin solutions with layering isolated regions are measured. It is shown that (a) the depolarized scattering intensity is the same above the higher critical point (HCP) and below the lower critical point (LCP), and (b) the polarized scattering intensity below LCP is higher, the higher the HCP. An empirical formula is offered to describe the polarized scattered light intensity. No increase in the single depolarized scattering intensity is found approaching LCP and HCP.

Effect of absorption of multiply scattering media on the degree of residual polarization of backscattered light by D. A. Zimnyakov; Yu. P. Sinichkin; I. V. Kiseleva; D. N. Agafonov

*(765-771)*. The effect of absorption in a scattering medium on the degree of residual polarization of backscattered radiation is studied in the case of probing of multiply scattering media by a linearly polarized light. An approximate expression describing the dependence of the degree of residual linear polarization of the backscattered radiation on the optical characteristics of a multiply scattering medium is derived within the framework of the phenomenological approach, based on the concept of the distribution of the optical paths of partial components of the scattered optical field under the conditions of multiple scattering, and with the use of the ideas about the similarity of statistical moments of the multiply scattered optical fields. The cut-off of the partial components, characterized by a large value of the optical path, because of their absorption, results in a substantial increase of the degree of residual polarization for the bands of the selective absorption caused by the presence of chromophores in the scattering medium. The results of experiments with model scattering media (whole milk) and biological tissues (human skin

*in vivo*) are presented. Dynamical halo scattering from photorefractive crystals by A. N. Morozovskaya; V. V. Obukhovskii

*(772-779)*. The effect of formation of a dynamical halo in scattering from photorefractive crystals was studied theoretically. The characteristic features of this effect, the formation of a conic spatial structure and pulsed temporal behavior are adequately described within the framework of the model of multibeam interactions in crystals with cubic nonlinearity with due regard for the transverse inhomogeneity of the interacting beams.

The effect of a surface layer on determination of the dielectric functions of ZnTe films by the ellipsometric technique by V. A. Shvets; M. V. Yakushev

*(780-783)*. By means of spectroellipsometric technique, the dielectric functions of zinc telluride films, 0.1–1.7 µm thick, grown by molecular beam epitaxy (MBE) are studied. The presence of a thin layer on the surface of the films, noticeably affecting the results of measurements, is established. The analysis of spectra of the ZnTe dielectric functions available in the literature shows that the surface layer was present in all samples studied, regardless of the method of preparation. It is shown that studying the interference oscillations of the pseudodielectric function makes it possible to detect this layer and to correct properly the measured spectra of the dielectric functions.

Special features of absorption of electromagnetic radiation by a cylindrical particle by E. V. Zavitaev; A. A. Yushkanov; Yu. I. Yalamov

*(784-789)*. The cross section of electromagnetic radiation absorption by a cylindrical metal particle was calculated. No limitations were imposed on the relation between the electron mean free path and the particle size. Specific absorption cross sections of cylindrical and spherical particles are compared. The results of the numerical calculation are presented graphically.

Transverse effects under four-wave coupling in the nonlinear Fabry-Perot interferometer by O. G. Romanov; A. L. Tolstik

*(790-794)*. Specific features of the light-beam transverse structure transformation in the process of four-wave coupling in the Fabry-Perot interferometer with a resonant nonlinearity under conditions of bifurcation of the symmetry breaking and optical bistability are analyzed. The asymmetric regimes of the interaction, characterized by a difference both in the integrated transmission functions of the nonlinear interferometer for two light beams with equal intensities and in the spatial intensity distribution at the exit of the interferometer, are considered.

Mode theory of three-dimensional superposed holograms: II. The wave field arising from the reconstruction of a superposed hologram by V. V. Orlov

*(795-799)*. The wave field arising in the volume of superposed holograms is obtained with allowance for multiple wave diffraction on holographic cross-modulation gratings. It is shown that cross-talk interference waves are generated as a result of multiple diffraction, and their intensity depends on the degree of mutual orthogonality of hologram object waves.

Synthesis of multifrequency optical holograms of rotating objects by T. V. Bogdanova; V. P. Titar’; E. Ya. Tomchuk

*(800-812)*. A two-channel system for synthesizing two-dimensional complex multifrequency optical holograms of rotating objects was developed. In the object irradiation (longitudinal) direction, a hologram is synthesized due to multifrequency laser radiation, and in the transverse direction, the synthesis is provided by object rotation. The object image is reconstructed in the plane coinciding with the plane of its rotation. The resolution of the synthesized hologram in the longitudinal direction is determined by the frequency bandwidth of the laser radiation, and in the transverse direction, the resolution is determined by the initial laser-radiation frequency and the angle of object rotation during the time of hologram synthesis. Using a digital simulation, the degree of isoplanarity of the multifrequency system for synthesizing holograms of rotating objects and its noise immunity under conditions of phase noises were analyzed.