# Optics and Spectroscopy (v.117, #5)

Spectroscopic determination of Fisher information on vibrational states of diatomic molecules using the example of the

*X*^{1}Σ*g*_{ }^{+}state of a Li_{2}molecule by S. A. Astashkevich*(687-694)*. An expression governing Fisher information of vibrational states of a diatomic molecule is obtained in the first-order Wentzel-Kramers-Brillouin (WKB) approximation, and a quantitative criterion of its applicability is proposed. The expression is determined only by the dependence of energy of vibrational levels on quantum number

*v*and the reduced mass of the molecule; it is not related to any additional model assumptions and does not require knowledge of vibrational wavefunction. It is established that the dependence of Fisher information on*v*attains maximum at certain value*v*_{0}. The efficiency of the obtained expression is demonstrated by calculating the Fisher information of vibrational levels*v*= 0–40 of the*X*^{1}Σ*g*_{ }^{+}state of the^{7}Li_{2}molecule. It is established that*v*_{0}= 23 for this electronic state. Calculation of the Fisher information of levels*v*= 0–38 of this state with the help of the obtained relation is in excellent (within mean-square deviation σ̄ = 0.01%) agreement with the results of calculation based on numerical solution of the Schrödinger equation by using the earlier-published semi-empirical potential curve of this state. At the same time, the expressions available in the literature based on the Wilson-Sommerfeld quantization rule describe the Fisher information of these levels only qualitatively (σ̄ = 18%). It is established that the reason for deviation for levels*v*= 39 (*σ*= 0.3%) and*v*= 40 (*σ*= 1.9%) is not related to using the WKB approximation but is due to the numerical differentiation procedure of strongly nonlinear (in the vicinity of the upper bound of*v*) dependence of the energy of vibrational terms on*v*appearing in the obtained expression. Spin-orbit coupling and dissociation of CO

_{2}molecules by L. B. Ibraguimova; B. F. Minaev; I. S. Irgibaeva*(695-702)*. Potential surfaces of the CO

_{2}molecule for the ground and excited^{3}*B*_{2},^{1}*B*_{2}electronic states are calculated by quantum chemistry methods. The calculation of the spin-orbit coupling in the molecule shows a large the matrix element, which removes the prohibition for the dissociation-recombination process CO_{2}(*X*^{1}Σ) + M ↔ CO(*X*^{1}Σ) + O(^{3}*P*) + M. The barrier on the potential curve for^{3}*B*_{2}, the energy of which exceeds the limit of dissociation into components in the ground states, explains the data on the dissociation and recombination energies measured in experiments with shock tubes. The absorption cross section of CO_{2}molecules in the UV spectral region measured at high temperatures allowed us to plot branches of potential curves near their minima for two upper singlet states assigned to the^{1}*B*_{2}and^{1}*A*_{2}symmetry. Absorption and quantitative characteristics of C-H bond and O-H bond of NIR by Zhisheng Wu; Guoqing Ouyang; Xinyuan Shi; Qun Ma; Guang Wan; Yanjiang Qiao

*(703-709)*. The previous study mainly focused on the interpretation of the relationship between absorption characteristics and quantitative contribution in each near-infrared (NIR) frequency range. Furthermore, the absorption characteristics of NIR mainly cover overtones and combinations of molecular vibrations such as CH, OH, SH, and NH bonds. And it has been know that NIR wavelengths of C-H bond and O-H bond are assigned to different radio frequencies. This paper was intended to investigate the absorption characteristics of bond C-H and O-H bonds in NIR spectral range. Water and acetone which correspond to O-H and C-H bonds have been selected as typical solvents, as well as solutes. Calibration models were established using partial least square regression (PLS) and multiple linear regression (MLR). The parameter of the model were optimized by different spectral pretreatment methods. The result showed that the model set by Savitzky-Golay smooth (SG) in the spectral region of 810–1100 nm could successfully make accurate predictions. Short wave-NIR region has been discovered as optimum characteristic absorption of C-H and O-H bonds.

Solution of a one-dimensional torsion Schrödinger equation with a general periodic potential by V. V. Turovtsev; A. V. Belotserkovskii; Yu. D. Orlov

*(710-712)*. Relations are found for the calculation of eigenvalues and eigenfunctions of the Hamiltonian of internal rotational motion in molecules in the basis of plane waves. The dependences of kinematic coefficient

*F*(φ) and potential*V*(φ) on dihedral angle φ are represented by Fourier series for both symmetric and asymmetric functions, as well as for general periodic functions. If a molecule has symmetry elements, the found solution transforms to that previously known. Calculation and interpretation of vibronic absorption and fluorescence spectra of the first electronic

*n*π* transitions of pyridine and pyrimidine by G. N. Ten; D. M. Kadrov; M. K. Berezin; V. I. Baranov*(713-721)*. We have calculated vibronic spectra of the first electronic

*n*π* transitions of pyridine and pyrimidine in the isolated state using the DFT method in the Franck-Condon approximation. Vibrational spectra for the ground and excited states have been calculated in the anharmonic approximation, which allowed us to refine the assignment of normal vibrations of pyridine and pyrimidine. We have done a complete interpretation of the vibrational structure of the absorption and fluorescence spectra of pyridine and pyrimidine. It has been shown that Fermi resonances between fundamental and combination vibrations and overtones 12 and 16*b*+ 4, 6*a*and 2 × 16*b*affect the formation of the vibrational structure of electronic spectra of pyrimidine. Good agreement between calculated and experimental spectra confirms the correctness of the models of the two molecules in their ground and excited states, which makes it possible to use the models in further investigations of various properties of these molecules in electronically excited states, e.g., tautomerism of pyrimidine bases of nucleic acids. The fluorescence and electronic structure of phenyl-substituted tetraazachlorin molecules by P. P. Pershukevich; D. I. Volkovich; L. L. Gladkov; S. V. Dudkin; A. P. Stupak; V. A. Kuzmitsky; E. A. Makarova; K. N. Solovyov

*(722-740)*. should read ?porphyrazine? instead of ?porphyrazin?;The effect of the addition of phenyl groups to pyrrole rings of tetraazachlorins, a new class of tetrapyrroles, on the photophysical properties and electronic structure of the molecules has been investigated by a complex of experimental and theoretical methods. Characteristics of fluorescence at 293 and 77 K have been determined for phenyl-substituted tetraazachlorins. The objects of this study include unsubstituted tetraazaporphine. The introduction of phenyl groups affords a marked increase in the fluorescence quantum yield. For tetraazaporphine and phenyl-substituted tetraazachlorins, fluorescence buildup occurs as the temperature is decreased from 293 to 77 K, but to a lesser extent than for tetraazachlorins having no phenyl groups, which were earlier studied by the authors. The fluorescence buildup mechanism is discussed. The singlet oxygen generation quantum yield has been determined for the tetrapyrroles examined. This characteristic increases upon tetrapyrrole is phenylation. The electronic structure and absorption spectra of unsubstituted porphine and chlorin, tetraazaporphine, tetraazachlorin, octaphenyltetraazaporphine, and tetramethylhexaphenyltetraazachlorin have been calculated by the INDO/Sm method (original modification of the INDO/S method) with molecular geometry optimization using DFT. The results of the quantum-chemical calculation of the absorption spectra are in good agreement with experimental data for transitions to the lowest excited electronic states

*Q**x*_{ }(*S*_{1}) and*Q**y*_{ }(*S*_{2}).**Keywords:**Macrocycle; Phenyl Group; Fluorescence Quantum Yield; Soret Band; Pyrrole Ring

Q-factor of spherical optical silicon dioxide nanoresonators by A. N. Gruzintsev

*(741-747)*. The Q-factor of the bound optical modes of silicon dioxide spheres with a radius smaller than one micron has been studied in the visible spectrum, showing that local photonic states with a nonzero orbital momentum yield a thin structure in glow spectra, whose maxima positions depend on the diameters of SiO

_{2}nanospheres. A theoretical model to calculate the Q-factor of nanoresonators depending on the wavelengths of bound modes and the radius value of spheres has been proposed. It has been shown that the quality of an optical resonator increases as its diameter grows. The Q-factor values have been calculated for the visible light of the order of 10 for spheres smaller than 1 μm in diameter and 10^{6}for spheres of more than 7 μm in diameter. A dependence of bound modes’ radiation propagation outside of the sphere on their wavelengths and orbital momenta has been detected. Raman scattering for lead telluride-based thin film structures by S. P. Zimin; E. S. Gorlachev; A. V. Baranov; S. A. Cherevkov; E. Abramof; P. H. O. Rappl

*(748-752)*. For single-crystal epitaxial lead telluride films, Raman spectra obtained under conditions in which the intensity of incident radiation is minimized in order to suppress photo-initiated oxidative process are presented. The spectra were measured with an InVia Renishaw spectrometer at an exciting radiation wavelength of 514.5 nm and in-line focusing of a 20-μW beam. These measuring conditions allowed us for the first time to experimentally observe a large set of peaks for lead telluride, the positions of which were in line with the theoretical values of harmonics and combinatorial PbTe phonon modes. In order to demonstrate the possibilities of the methodology used, the picture of phonon modes for single-crystal and polycrystalline films of the Pb1 −

*x*_{ }Eu*x*_{ }Te (0.05 ⩽*x*⩽ 0.10) solution was additionally considered. Structural and photoluminescent properties of TiN thin films by M. N. Solovan; V. V. Brus; P. D. Maryanchuk; I. M. Fodchuk; V. M. Lorents; A. M. Sletov; M. M. Sletov; M. Gluba

*(753-755)*. Structural and photoluminescent properties of TiN thin films deposited by dc reactive magnetron sputtering are studied. It is found that TiN thin films are polycrystalline with a grain size of ∼15 nm and have a NaCl-type cubic crystal structure with a lattice constant of 0.42 nm. The TiN films under study exhibit photoluminescence in the spectral range

*h*_{ν}≈ 2.1–3.4 eV at 300 K. On isotropic states in α-LiNH

_{4}SO_{4}crystals by V. Yo. Stadnyk; R. S. Brezvin; M. Ya. Rudysh; P. A. Shchepanskyi; V. M. Gaba; Z. A. Kogut*(756-758)*. The spectral and baric dependences of the birefringence of α-LiNH

_{4}SO_{4}crystals are studied. It is found that the birefringence is rather sensitive to uniaxial compressions. A baric shift of the isotropic point to longer or shorter wavelengths depending on the uniaxial compression direction is observed and a generalized temperature-spectral-baric diagram of the isotropic state is plotted. A possibility of the appearance of a pseudoisotropic state under the action of uniaxial pressure σ*z*_{ }or simultaneous pressures σ*x*_{ }= σ*z*_{ }is shown. Optical absorption spectra and energy levels of Er

^{3+}ions in glassy lithium tetraborate matrix by P. S. Danilyuk; K. P. Popovich; P. P. Puga; A. I. Gomonai; N. V. Primak; V. N. Krasilinets; I. I. Turok; G. D. Puga; V. M. Rizak*(759-763)*. The optical absorption spectra of Er:Li

_{2}B_{4}O_{7}glasses are studied in the range 200–800 nm. The lines corresponding to the direct*f-f*parity-forbidden intraconfigurational transitions from the ground^{4}*I*_{15/2}state to the levels of the excited^{4}*F*_{9/2},^{4}*S*_{3/2},^{2}*H*_{9/2},^{2}*H*_{11/2},^{4}*F*_{7/2},^{4}*F*_{5/2},^{4}*F*_{3/2},^{2}*H*_{9/2},^{4}*G*_{11/2},^{4}*D*_{3/2},^{4}*D*_{1/2}, and^{2}*D*_{3/2}states are found. Optical properties of BiTeI semiconductor with a strong Rashba spin-orbit interaction by A. A. Makhnev; L. V. Nomerovannaya; T. V. Kuznetsova; O. E. Tereshchenko; K. A. Kokh

*(764-768)*. The optical properties of BiTeI crystals in the range of 0.09–5.0 eV are studied by optical spectral ellipsometry. The fundamental characteristics of the electronic structure are determined. The optical gap is estimated to be

*E**g*_{ }= 0.33 eV. The plasma frequency of conduction electrons is determined to be ω*p*_{ }= 0.13 eV. A fine structure of low-energy electronic transitions is found in the range 0.15–0.44 eV between the plasma edge and the intense interband absorption threshold. The singularities at 0.2 and 0.3 eV are related to the transitions between bulk conduction bands split by a strong Rashba spin-orbit interaction. Optical properties of rare earth doped strontium aluminate (SAO) phosphors: A review by D. S. Kshatri; A. Khare

*(769-783)*. After the first news on rare earth (RE) doped strontium aluminate (SAO) phosphors in late 1990s, researchers all over the world geared up to develop stable and efficient persistent phosphors. Scientists studied various features of long lasting phosphors (LLP) and tried to earmark appropriate mechanism. However, about two decades after the discovery of SrAl

_{2}O_{4}: Eu^{2+}, Dy^{3+}, the number of persistent luminescent materials is not significant. In this review, we present an overview of the optical characteristics of RE doped SAO phosphors in terms of photoluminescence (PL), thermoluminescence (TL) and afterglow spectra. Also, we refresh the work undertaken to study diverse factors like dopant concentration, temperature, surface energy, role of activator, etc. Simultaneously, some of our important findings on SAO are reported and discussed in the end. Nonradiative triplet-singlet transfer of electronic excitation energy between dye molecules in the vicinity of the silver-film surface by D. A. Kislov; M. G. Kucherenko

*(784-791)*. Nonradiative triplet-singlet transfer of electronic-excitation energy between molecules of organic dyes (erythrosine and methylene blue) in a polymer film that is deposited on the surface of a silver layer is experimentally studied. It is demonstrated that the energy-transfer efficiency in such a system is lower than the efficiency in the samples without metal layers. The results of the proposed mathematical model are in qualitative agreement with the experimental data.

Dynamics of frequency-modulated soliton-like pulses in an amplifier-modulator-compressor cascade by A. S. Abramov; I. O. Zolotovskii; D. I. Sementsov; D. A. Stolyarov

*(792-798)*. Specific features of the formation of frequency-modulated pulses with large peak powers in amplifier-modulator-compressor cascade schemes based on length-inhomogeneous optic fibers are considered. Optimum profiles of fiber parameters ensuring the most effective amplification and modulation of pico- and subpicosecond frequency-modulated pulses are proposed. It is established that the use of a cascade consisting of active (gain) and passive (modulating) fibers with optimized profiles of the normal group-velocity dispersion and mode area can ensure the formation of pico- and subpicosecond pulses with energies higher than 100 nJ and peak powers above 100 kW.

A ballistic gravimeter with dropping holographic grating by A. L. Dmitriev; E. I. Kotova; E. M. Nikushchenko; A. L. Smirnova; V. T. Prokopenko

*(799-800)*. The principle of operation of a ballistic laser gravimeter based on a dropping holographic diffraction grating is described. The free-fall acceleration of the grating is determined from a change in the frequency of beats that arise during the interference of light beams diffracted on the hologram in the zeroth and first orders of diffraction. An experiment demonstrating this principle of measurement is described. The main distinctive features of the proposed gravimeter are simple design, compact size, and the possibility of using this device for analysis of high-frequency fluctuations in the gravitational-field strength.

Anisotropic light diffraction in crystals with a large acoustic-energy walk-off by V. I. Balakshy; A. S. Voloshin; V. Ya. Molchanov

*(801-806)*. The influence of energy walk-off in an acoustic beam on the characteristic of anisotropic Bragg diffraction of light has been investigated by the example of paratellurite crystal. The angular and frequency characteristics of acousto-optic diffraction have been calculated in wide ranges of ultrasound frequencies and Bragg angles using the modified Raman-Nath equations. It is shown that the walk-off of an acoustic beam may change (either widen or narrow) significantly the frequency and angular ranges. The calculation results have been experimentally checked on an acousto-optic cell made of 10.5°-cut paratellurite crystal.

Network of nano-droplets by a tri-block polymer by Soheil Sharifi; Esmaeil Doodman

*(807-813)*. Mixtures of oil in water nano-droplets with two molecular weights of a tri-block polymer was studied by quasi elastic light scattering and small angle X-ray scattering. The results showed that the size and interaction of droplets didn’t change with increase of the tri-block polymer length but the order parameters increased. The increase of length of the tri-block biopolymer changed the dynamics of the droplets. A network formation is resulted with increase of the amount of tri-block polymer in the microemulsions.

Interference of plane light waves with different polarizations and the Jones matrix formalism by N. F. Kubrakov

*(814-821)*. A new method is developed to solve the interference problem that involves two plane monochromatic waves of equal frequency provided these waves, in general, have different polarizations and their wave vectors are arbitrarily oriented. Using a three-dimensional generalized Jones vector, we find analytical solutions for the spatial-intensity distribution of the total wave and (at certain orientations of the wave vectors) for the parameters characterizing its polarization state. The results of the work are applied to wide variety of interference problems.

A generator of far-infrared and terahertz radiation in nonlinear metamaterials exhibiting negative index of refraction by I. O. Zolotovskii; D. A. Korobko; R. N. Minvaliev; V. A. Ostatochnikov

*(822-831)*. Laser oscillation conditions are analyzed in nonlinear composite metamaterials exhibiting a negative index of refraction. It is demonstrated that strong quadratic and cubic nonlinearities can be simultaneously realized in such structures. Based on the described composite material, a scheme of an optically pumped parametric generator of terahertz radiation is proposed.

Feature extraction of micro-motion frequency and the maximum wobble angle in a small range of missile warhead based on micro-Doppler effect by M. Li; Y. S. Jiang

*(832-838)*. Micro-Doppler effect is induced by the micro-motion dynamics of the radar target itself or any structure on the target. In this paper, a simplified cone-shaped model for ballistic missile warhead with micro-nutation is established, followed by the theoretical formula of micro-nutation is derived. It is confirmed that the theoretical results are identical to simulation results by using short-time Fourier transform. Then we propose a new method for nutation period extraction via signature maximum energy fitting based on empirical mode decomposition and short-time Fourier transform. The maximum wobble angle is also extracted by distance approximate approach in a small range of wobble angle, which is combined with the maximum likelihood estimation. By the simulation studies, it is shown that these two feature extraction methods are both valid even with low signal-to-noise ratio.

A principal component analysis of transmission spectra of wine distillates by M. V. Rogovaya; G. V. Sinitsyn; M. A. Khodasevich

*(839-843)*. A chemometric method of decomposing multidimensional data into a small-sized space, the principal component method, has been applied to the transmission spectra of vintage Moldovan wine distillates. A sample of 42 distillates aged from four to 7 years from six producers has been used to show the possibility of identifying a producer in a two-dimensional space of principal components describing 94.5% of the data-matrix dispersion. Analysis of the loads into the first two principal components has shown that, in order to measure the optical characteristics of the samples under study using only two wavelengths, it is necessary to select 380 and 540 nm, instead of the standard 420 and 520 nm, to describe the variability of the distillates by one principal component or 370 and 520 nm to describe the variability by two principal components.

Mirrors in optical schemes of ellipsometers by A. S. Gurevich; M. O. Nestoklon

*(844-849)*. Expressions for Mueller matrices describing how the reflection from plane mirrors with an arbitrary orientation of the surface affects the polarization are obtained. The expressions can be useful in considering new ellipsometers’ optical schemes containing plane mirrors, as well as mirrors with a nonzero curvature of the surface.

Methods of IR spectroscopy in monitoring of chemotherapy of oncological pathologies using palladium complexes by G. B. Tolstorozhev; M. V. Bel’kov; I. V. Skornyakov; V. I. Pekhn’o; A. N. Kozachkova; N. V. Tsarik; I. P. Kutsenko; N. I. Sharykina

*(850-854)*. FTIR spectroscopy is used to study mammary-gland tissues of mice with a sarcoma tumor (strain 180). Spectral features that are typical of malignant tumors are revealed in the FTIR spectra in the sarcoma-tumor tissues. Tumor tissues are studied after treatment using coordination compounds based on palladium complexes with 3-amino-1-hydroxypropylidene-1,1-diphosphonic acid and zoledronic acid. A therapeutic effect is not revealed after treatment using palladium complex with 3-amino-1-hydroxypropylidene-1,1-diphosphonic acid. The suppression of tumor growth amounts to 59% when palladium complexes with zoledronic acid are used. Suppression of tumor growth is accompanied by variations in spectral characteristics. With respect to diagnostic features, the FTIR spectra of tumor tissues after treatment with the palladium complexes with zoledronic acid are similar to the FTIR spectra of tissues that are free of malignant tumors. Specific spectroscopic characteristics that make it possible to control the chemotherapy of oncological pathologies are determined.