# Optics and Spectroscopy (v.95, #1)

Calculation of the binding energy of a highly excited electron in heavy Be-like ions by M. B. Shabaeva

*(1-5)*. The binding energy of a highly excited electron (

*n*=20–50, where*n*is the principal quantum number) in the Be-like ions Au^{75+}, Pb^{78+}, Bi^{79+}, and U^{88+}is calculated in order to determine the energy of the 2*p*_{1/2}-2*s*transition from experiments on dielectronic recombination in Li-like ions. A formula approximating the calculated data with an error not exceeding 0.04% is proposed. Higher orders in residual two-electron interaction by M. G. Kozlov

*(6-13)*. Precise methods of calculations of many-electron atoms are under intensive development. In such calculations, higher orders of the perturbation theory in regard to residual interaction of electrons should be taken into account. In this study, a model of an atom with two electrons in its core and two valence electrons is considered. In terms of this model, expansion with respect to residual interaction is analyzed for two initial approximations based on the potentials

*V*^{(2)}and*V*^{(4)}. It turns out that the higher order corrections are nearly the same in both cases. At the same time, the potential*V*^{(2)}has a number of advantages. Dynamics of interaction between two-level atoms in a laser field and linear stationary optical dimensional resonances by O. N. Gadomskiĭ; Yu. V. Abramov

*(14-19)*. Formulas for radiative forces acting on the atoms of a diatomic object in a field of external laser radiation are obtained with allowance made for the interatomic dipole-dipole interaction. It is shown that one can control the motion of the atoms by gradually varying the frequency of external laser radiation due to the presence of optical dimensional resonances in the spectrum of the diatomic object.

Quantum mechanical analysis of resonance Raman spectra of thymine by T. G. Burova; G. N. Ten; V. V. Kucherova

*(20-24)*. A direct quantum mechanical calculation of the relative intensities of lines in resonance Raman (RR) spectra of thymine was performed. The method of calculation is based on the adiabatic model in the Herzberg-Teller approximation. It is shown that the basic features of the intensity distribution in the spectra can be explained only by taking into account the vibronic mixing of electronic states and the contribution to the components of the scattering tensor from excited electronic states located close to the resonance state. The calculated results agree satisfactorily with experimental RR spectra of thymine excited by laser radiation at 266, 240, 218, and 200 nm. A comparative analysis of the intensity distribution in the RR spectra of thymine and uracil is carried out.

Specific features of determination of the energy of excited electronic states in the formalism of density functional theory by V. N. Glushkov; A. I. Aprasyukhin

*(25-28)*. Possibilities for application of the theory of subspaces to determination of the energy of excited electronic states are studied in terms of density functional formalism. Specific features of computer implementation of the theory in a basis of spherical Gaussian functions, whose parameters are determined by minimizing the energy of the corresponding subspace of states, are discussed. The results of calculation of the energy of excited states and the excitation energies of simple atoms and molecules are presented to demonstrate the potential of the approach.

Luminescence of water-soluble rh(III) porphyrins by V. V. Vasil’ev; S. M. Borisov; I. V. Golovina

*(29-34)*. The luminescent properties of complexes of rhodium(III) with three water-soluble porphyrins—

*meso*-tetrakis(4-N-methyl pyridyl) porphyrin,*meso*-tetrakis(4-N,N,N-trimethyl aminophenyl) porphyrin, and*meso*-tetrakis(4-sulfonate phenyl) porphyrin—were studied. All three complexes were found to phosphoresce both at 77 K and in deaerated solutions at room temperature, with their fluorescence being very weak. The rate constants of radiative (*k*_{p}=40-60s^{-1}) and nonradiative deactivation of a triplet excited state were determined. It was ascertained that, in aqueous solutions, the phosphorescence is quenched by molecular oxygen via an energy-transfer mechanism that is accompanied by formation of singlet oxygen. The quantum yields of formation of singlet oxygen for all the metalloporphyrins studied were found to be close to unity, which is the quantum yield of formation of their triplet states. Depolarization of luminescence of polyatomic molecules in the gas phase as a method of determining the efficiency of collisional transfer of angular momentum by A. P. Blokhin; M. F. Gelin; I. I. Kalosha; V. V. Matylitskii; V. A. Tolkachev

*(35-41)*. The theory of collisional depolarization of luminescence of extended polyatomic molecules in rarefiedgases is considered. The interrelation between the frequency of collisions, the relaxation time of the angular momentum, and the cross section of the luminescence depolarization is established, and the dependence of these parameters on the efficiency of an abrupt change in the angular momentum is calculated. The use of the theory of collisions of solids in the Enskog approximation made it possible to take into account the effect of the shape and mass of colliding molecules on the degree of depolarization. It is established that, in terms of this theory, there exists a limiting efficiency of an abrupt change in the angular momentum, which, however, does not attain the value proposed in the model of strong collisions (

*J*diffusion). The dependence of the depolarization of luminescence of 1,4-di-(2-5-*p*-tolyloxazolyl) benzene molecules on the concentration of a buffer gas (argon) is measured. It is found that about five collisions with Ar atoms are required for randomization of the angular momentum of these molecules. Polarized luminescence of erythrosine molecules adsorbed on a semiconductor-dielectric structure by N. A. Domnina; A. M. Saletskii

*(42-45)*. The dependences of the degree of polarization of fluorescence of erythrosine molecules adsorbed on Ge-GeO

_{2}structures on the thickness of the oxide layer, the surface charge, and the concentration of erythrosine are studied. The values of reorientation barriers and times of vibrational relaxation of adsorbed molecules are found. The effect of the surface charge, the thickness of the oxide layer, and the concentration of water molecules on the rotational-vibrational relaxation of adsorbed erythrosine molecules is revealed. Estimate of lacunarity of vibrational-rotational absorption spectra of water vapor by Yu. V. Kistenev

*(46-48)*. Optical spectra of vibrational-rotational absorption bands of atmospheric water vapor are interpreted in terms of fractal analysis. The main calculation parameter is the lacunarity of the initial spectrum. The variation in the lacunarity makes it possible to estimate the degree of translational and scale invariance of the entire spectrum as some quasi-random frequency function.

Effect of acidification on spectral parameters of solutions of mixed-ligand cyclometalated Pt(II) and Pd(II) complexes by M. V. Puzyk; Yu. A. Ivanov; K. P. Balashev

*(49-51)*. The effect of acidification of water-ethanol solutions of cyclometalated Pt(II) and Pd(II) complexes with ethylenediamine and cyanide ligands is studied. It is found that, unlike the ethylenediamine complexes, the cyclometalated complexes with cyanide ligands are unstable and undergo irreversible decyclometalation.

Specific features of spectra of cyclometalated Pt(II) complexes in polystyrene and polymethyl methacrylate by M. M. Nevdakh; M. V. Puzyk

*(52-53)*. A method of obtaining polystyrene and polymethyl methacrylate films containing cyclometalated complexes of Pt(II) with 2-phenylpyridinate and 2-(2′-thienyl)pyridinate is described. The spectral and luminescent properties of these films at 77 and 298 K are studied. It is ascertained that the Pt(II) complexes in the films are in a monomolecular state.

Overtone transitions of diatomic dimers XH

^{−}-XH^{−}in ionic crystals by K. V. Kazakov; A. D. Afanas’ev*(54-59)*. The resonance interaction of molecular defects XH

^{–}in ionic crystals is considered. In the dipole approximation, the frequencies and intensities of vibrational transitions of diatomic dimers^{m}XH^{−}-^{n}XH^{−}are found for the exact (*m*=*n*) and quasi-exact (*m*≠*n*) resonances. The interaction-atrix elements are obtained with regard to the mechanical anharmonicity in the second order of the theory of perturbation for the case of a linear dependence of the dipole moment of a diatomic molecule on the vibrational coordinate. The expressions obtained are applied to the calculation of overtones in the absorption spectrum of dimers^{m}SH^{−}-^{n}SH^{−}in a KCl crystal. Spectral features of a nematic liquid crystal consisting of biaxial molecules with internal rotation by E. M. Aver’yanov

*(60-69)*. Expressions for the components of the optical permittivity tensor of a nematic liquid crystal consisting of biaxial π-conjugated molecules with a conformational degree of freedom (internal rotation) are obtained. A relationship between the intensity and dichroism of absorption bands in isotropic and nematic phases and the parameters of conformational, orientational, and mixed conformational and orientational orders of the molecules is established. A distribution function for the molecules is obtained that takes into account the mutual correlation of their conformational and orientational degrees of freedom. The effect of this correlation on the above-noted order parameters, the dichroism of the absorption bands, and the dependence of the measured oscillator strengths of molecular transitions on the character and degree of orientational order of biaxial molecules is studied. On the basis of comparison with experimental data, the relative role of different terms in the distribution function that are responsible for the correlation between the conformational and orientational degrees of freedom of the molecules is ascertained.

Optics of helical periodic media in the presence of a wave modulating parameters of the medium: I. New regions of diffraction reflection by A. H. Gevorgyan

*(70-79)*. Reflection and transmission of light through a layer of a helical periodic medium in the presence of a longitudinal hypersonic field are studied. The cases of periodic and aperiodic media are considered in the perturbation theory approximation. Regions of diffraction reflection (RDRs) of different character are shown to appear, including RDRs caused by the helicity of the medium, by its stratification, and simultaneously by the medium helicity and stratification. The results are compared with the exact numerical solution of the problem.

Spontaneous and stimulated low-temperature electroluminescence of GaSe by G. I. Abutalybov; N. A. Ragimova; S. Z. Dzhafarova

*(80-84)*. Stimulated emission of the quasi-two-dimensional layered semiconductor GaSe in high electric fields and at different orientations of the applied electric field relative to the optical axis of samples was observed and studied. The electric field dependences of the polarized spectrum intensity and electroluminescence quantum yield were determined. Three mechanisms of amplification near the fundamental absorption edge, related to combined interaction of defects and free direct and indirect excitons, were identified.

Amplification and photonic band gaps for eigenmodes in two-dimensional photonic crystals with active media by L. A. Mel’nikov; O. N. Kozina

*(85-91)*. The behavior of eigenmodes near the first low-frequency band gap of a two-dimensional squarearray photonic crystal in the presence of amplification has been studied in detail using an approximate analytic solution for the mode dispersion characteristics. A qualitative analysis of the complex propagation constants was conducted for various directions in the crystal, and the frequency regions corresponding to amplification and absence of transmission due to interference-induced wave damping were identified. The enhancement of amplification in a two-dimensional photonic crystal was estimated.

Calculation of refractive indices for the (NH

_{2}CH_{2}COOH)_{2}· HNO_{3}crystal by B. Andriyevsky*(92-95)*. The refraction

*R*of the diglycine nitrate (DGN) crystal, (NH_{2}CH_{2}COOH)_{2}· HNO_{3}, in the para-and ferroelectric phases has been calculated in the model of noninteracting diatomic chemical bonds of the elementary unit cell of the crystal on the basis of the longitudinal and transversal polarizabilities of these bonds. The calculated magnitudes of the principal refractive indices*n**p*_{ },*n**m*_{ }, and*n**g*_{ }and the orientations of the optical indicatrix of the crystal agree satisfactorily with experimentally observed values. Introducing the coefficient of Lorenz-Lorentz interaction*x*into the corresponding formula permits better agreement of the calculated and experimental refractive indices of DGN crystal to be obtained. The temperature changes of these*x*coefficients upon the ferroelectric phase transition in the DGN crystal have been analyzed. Quantitative analysis of the supramolecular structure of metastable polycrystalline films by infrared spectropolarimetry by B. G. Shulitskiĭ; V. V. Filippov; G. G. Fedoruk

*(96-102)*. A method of quantitative estimation of the structural anisotropy of metastable organic polycrystalline films based on infrared spectropolarimetry is used to investigate the structural features films of the α form of copper phthalocyanine. Due to the separation of the inverse problem of reconstruction of the optical parameters of the medium into a number of stages with optimization over no more than two unknown parameters, the graphical tracking of the optimization process and, as a consequence, the minimization of errors and on-line correction of ambiguity are performed at each stage of the solution. It is demonstrated that the structure of copper phthalocyanine films vacuum-deposited onto a substrate can be changed by varying the substrate temperature, the angle of incidence of a molecular beam during the deposition, and the electrostatic field applied to the substrate.

On a Gaussian beam in an amplifying medium by N. N. Rozanov

*(103-105)*. The model of a Gaussian beam in an amplifying medium is analyzed within the framework of the paraxial (quasi-optical) approximation. Upon violation of the obtained restrictions, the model leads to a physically inconsistent conclusion about an infinitely high radiation power after a passage of an ordinary Gaussian beam through a layer of the amplifying medium. The importance of a limitation on the transverse dimensions of the amplifying medium or of the introduction of intracavity angular selection is demonstrated. The fundamental mode in the form of a Gaussian beam appears in the model with a quadratic dependence of the gain on the transverse coordinates.

On the possibility of light energy localization in a nonlinear photonic crystal by V. A. Trofimov; E. B. Tereshin; M. V. Fedotov

*(106-109)*. A possibility of the localization of light energy in a one-dimensional nonlinear photonic crystal is demonstrated by means of computer simulation. The energy localized in the crystal may reach up to 50% of the energy penetrating into it, depending on the femtosecond pulse length and intensity. The effect may be used for recording and storing information in three-dimensional optical memory units. The simulation is performed on the basis of an approach proposed by the authors for the class of problems under consideration.

Image reconstruction from amplitude-only and phase-only data in the fractional Fourier domain by T. Alieva; M. L. Calvo

*(110-113)*. Image reconstruction from amplitude-only and phase-only data in the fractional Fourier domain applying the inverse fractional Fourier transform is analyzed on the examples of perfect edges of different contrasts and real-world image.

Communicating with hyperchaos: The dynamics of a DNLF emitter and recovery of transmitted information by V. S. Udaltsov; J. P. Goedgebuer; L. Larger; J. B. Cuenot; P. Levy; W. T. Rhodes

*(114-118)*. It is reported that signal encoding with high-dimensional chaos produced by delayed feedback systems with strong nonlinearity can be broken. The procedure is described and the method is illustrated with chaotic waveforms obtained from a strongly nonlinear optical system used by the authors previously to demonstrate signal encryption and decryption with wavelength chaos. The method can be extended to any systems ruled by nonlinear time-delayed differential equations.

Diffraction longitudinal multidomain structures in a layered nonlinearly absorbing medium by A. V. Vysloukh; V. A. Trofimov

*(119-123)*. The propagation of a diffracting light beam in a layered nonlinear absorbing medium (in which absorbing layers alternate with transparent layers) is analyzed for the case of realization of multidomain longitudinal moving and stationary structures in a continuous medium. The action of Gaussian and ring beams is considered. It is shown that, in a layered medium, stationary multidomain longitudinal structures are formed that, for a rather wide interval of ratios of the lengths of the layers, move together with the nonlinearly absorbing layers.

V.A. Shamburov’s validity criteria for the gyrotropy theory by L. M. Barkovsky; G. N. Borzdov

*(124-130)*. V.A. Shamburov’s attempts to constrain the range of applicability of F.I. Fedorov’s constitutive equations in the gyrotropy theory are shown to be untenable.

Fresnel diffraction by deterministic fractal gratings: An experimental study by D. Rodriguez Merlo; J. A. Rodrigo Martín-Romo; T. Alieva; M. L. Calvo

*(131-133)*. Experimental results are presented for light diffraction under the Fresnel regime by two types of fractal gratings: triadic Cantor bars and Vicsek fractals. It is shown that the evolution of the diffraction patterns in the Fresnel regions reveals the hierarchical structure of deterministic fractal gratings.

Tomographic microscopy of three-dimensional phase objects in spatially incoherent light by G. N. Vishnyakov; G. G. Levin; V. L. Minaev

*(134-138)*. The use of spatially incoherent light is proposed for raising the quality of interference projection data in tomographic microscopy of phase objects. The optical scheme of the tomographic microscope is based on the scheme of a Linnik microinterferometer with an extended source of quasi-monochromatic light. Characteristic features of the tomography of phase objects positioned near flat reflecting surfaces are considered.

Memory-efficient algorithm for lens distortion compensation by K. D. Kozmin; K. Hyyppä

*(139-141)*. Distortion introduced by a lens in a measurement system based on an image sensor usually must be compensated. The memory used for distortion compensation by a lookup table is proportional to the image sensor size. To reduce the memory usage, a compression algorithm is proposed and implemented.

Ultrahigh-density magneto-optical recording based on the effect of plasmon excitations by V. G. Kravets

*(142-147)*. The analysis of ultrahigh-density recording in magneto-optical media formed with the use of granular CoAg(Au) films is performed. Due to excitation of plasma oscillations of electrons in granular CoAg(Au) films, the latter make it possible to perform additional focusing of recording radiation and to significantly decrease the size of memory cells. It is suggested that two-layer film CoAg(Au)/TbFeCo/substrate systems be used as recording media for magneto-optical recording. It is shown theoretically that the angle of the Kerr rotation of the plane of polarization θ

_{K}upon magnetization of such a two-layer structure increases significantly in the range of incident-photon energy from 2 to 4 eV in comparison with the case of TbFeCo magnetic film. Some specific features were detected experimentally in the spectra of θ_{K}in the region of excitation of plasma oscillations in nanogranular CoAu and CoAg films at ℏ ω*P*_{ }≈ 2.5 and 3.5 eV, respectively, as well as in two-layer CoAg(Au)/TbFeCo film systems. On the Fresnel diffraction pattern of phase holographic gratings by A. M. Nastas

*(148-153)*. The Fresnel diffraction pattern of phase diffraction gratings is studied on the example of idealized sinusoidal relief-phase plane holographic thermoplastic gratings. It is shown that, in the region of low spatial frequencies, which are more than two times lower than the inverse wavelength of the reading coherent radiation, the intensities of the main diffraction maxima, the diffraction efficiency, and the light-scattering power are independent of the spatial frequency of the phase gratings under investigation, which are characterized by a sinusoidal law of modulation of the reading-radiation phase. It is established that the range of spatial frequencies at which a plateau is observed in these dependences increases with decreasing amplitude of the phase modulation of the reading light. These dependences are also observed to have similar character for the thermoplastic holographic gratings under study. Calculations were performed to analyze the influence of real profiles of thermoplastic strain on the diffraction efficiency and light-scattering power of such gratings. On the basis of analysis of the results obtained, recommendations on using holographic and raster techniques of recording data on phase carriers are given that make it possible to improve the quality of the restored optical image.

Optimum conditions for the generation of the second harmonic of intense laser radiation by U. K. Sapaev

*(154-157)*. A generalized approximation of strong interactions of waves is suggested for the theoretical analysis of second-harmonic generation under conditions of self-action. On the basis of the method suggested, approximate solutions for the efficiency of second-harmonic generation are obtained with regard to the influence of higher nonlinearities, depletion of pumping radiation, and linear phase mismatch. The effects of the phase mismatch and the spatial distribution of the amplitude of the fundamental harmonic on the efficiency of second harmonic generation by intense laser radiation is analyzed. The results obtained with the approximate method developed are shown to be in good agreement with known experimental data and numerical calculations. Optimum conditions for second harmonic generation are determined in a wide range of laser radiation intensity and at different spatial distributions of the fundamental harmonic amplitude.

The coherence and spectra of a Bose condensate generated by an atomic laser by A. V. Kozlovskiĭ

*(158-164)*. The first-order coherence dynamics of a Bose condensate generated by a cw atomic laser with evaporative cooling is analyzed. For the atomic-laser multimode model, the coherence functions and atomic field spectra are calculated by the master equation technique. Elastic collisions in the trapped atomic gas lead to significant broadening of the atomic laser line, a shift of its center, and a multi peak structure of the spectra. The oscillatory time dynamics of the atomic-field coherence function is studied. For the atomic laser, the free phase diffusion of the field typical of optical lasers, and characterized by monotonically decreasing mean field with a constant mean phase, is absent due to elastic collisions.