# Optics and Spectroscopy (v.88, #4)

Criterion for the accuracy of wave functions of asymmetric atomic and molecular systems by T. K. Rebane

*(475-479)*. From the condition for invariance of the energy under rotations of the Jacobi coordinates, a relationship is obtained that relates the expected values of combinations of degrees of interparticle separations in quantum-mechanical systems. This relationship, which is satisfied for atoms and molecules with like particles identically, because of the permutational symmetry, is an extremely sensitive criterion for the accuracy of the wave functions of asymmetric systems, consisting of unlike particles and having no permutational symmetry. The application of this criterion is illustrated for the example of the asymmetric

^{4}Heμ^{−}e^{−}mesoatom. Formalism of symmetrization operators in the theory of self-broadening of spectral lines by M. R. Cherkasov

*(480-488)*. The operators that symmetrize many-particle states in accordance with the quantum statistics of particles are introduced to construct the theory of self-broadening of spectral lines. In this case, the self-broadening problem becomes formally similar to the problem of broadening by a foreign gas. Comparison is made with papers of other authors.

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation by M. B. Trzhaskovskaya; Yu. I. Kharitonov; V. I. Nefedov; V. G. Yarzhemskii

*(489-497)*. Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons

*E**k*_{ }≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2*p*-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole. Polarization characteristics of the emission of the

^{1}*D*_{2}-state of an oxygen atom obtained as a result of charge exchange of an oxygen ion at a hydrogen atom by S. A. Kazantsev; A. G. Petrashen*(498-501)*. The possibility of significantly polarizing the emission of an ensemble of oxygen atoms obtained as a result of charge exchange of hydrogen atoms at oxygen ions is demonstrated.

*B*

^{2}Σ

_{u}

^{+}excited states of the N

_{+}

^{2}ion and the electron temperature in the discharge afterglow of an Ar-N

_{2}mixture by Yu. Z. Ionikh; N. B. Kolokolov; A. V. Meshchanov; N. V. Chernyshova

*(502-505)*.

The electron energy distribution function in the afterglow of a low-pressure discharge in an Ar-N

_{2}mixture was experimentally found. The values of electron temperature were determined. At the initial stage of plasma decay, the electron temperature was shown to be close to the nitrogen vibrational temperature. A study was made of the afterglow observed in the bands of the first negative system of N_{+}^{2}, and it is shown that this afterglow may be attributed to collisions of argon ions with nitrogen molecules found on higher vibrational levels. Laser photoionization spectroscopy of the zinc atom and the study of zinc sulfide evaporation by O. Tukhlibaev; U. Zh. Alimov

*(506-509)*. The frequencies of 5

*s*^{3}*S*_{1}-*np*^{3}*P*_{1}Rydberg transitions, quantum defects for*n*=15–50, and energies of high-lying*P*states of the Zn atom were measured by three-step laser excitation with subsequent ionization by a pulsed electric field. Free Zn atoms were produced through effusion of Zn vapor from an atomizer during the thermal dissociation of ZnS molecules. The evaporation kinetics was studied, and the ZnS vapor pressure was measured by the detection of photoionic signals of Zn. Satellites of the superfine structure multiplets in the spectrum of saturated absorption of the SiF

_{4}molecule by É. I. Ivanov; I. R. Krylov*(510-521)*. By the method of saturation of absorption of counterpropagating light waves, the gas-phase spectrum of SiF

_{4}is obtained without Doppler broadening of spectral lines. In the frequency range of the generation of a low-pressure CO_{2}laser (the 9.4-μm band), multiplets of the superfine structure (associated with tunneling transitions between the states of rotation about the equivalent symmetry axes of the SiF_{4}molecule) of the spectrum were observed. Weak satellites were observed in the vicinity of the multiplets. Some of the satellites were interpreted as resonances formed by the collisional transfer of the three-photon Bennett holes and peaks. Thermo-and photostimulated luminescence of CaI

_{2}: Tl and CaI_{2}: Pb crystals by S. S. Novosad*(522-526)*. Thermo-and photostimulated luminescence of CaI

_{2}: Tl and CaI_{2}: Pb scintillation crystals under optical and X-ray excitation is studied. It is shown on the basis of the results obtained with account for the data of studies of photo-and X-ray-luminescent properties of these scintillators that Tl^{+}and Pb^{2+}ions form complex capture centers with host defects. These centers are responsible for the thermostimulated luminescence in the temperature range of 150–295 K, and the centers of charge carrier trapping are spatially separated from the centers of recombination emission. An assumption is made that thermo-and photostimulated luminescence of CaI_{2}: Tl and CaI_{2}: Pb crystals under optical excitation is observed mainly due to the delocalization of charge carriers from hydrogen-containing centers responsible for the excitation band at 236 nm and the photoluminescence of CaI_{2}with a maximum at 395 nm. The luminescence of CaI_{2}: Tl crystals in the 510-nm band and CaI_{2}: Pb crystals in the 530-nm band is determined by the radiative decay of near-activator excitons. Study of low-frequency polarized spectra of a mixed

*para*-dibromobenzene-*para*-bromochlorobenzene crystal by V. F. Shabanov; M. A. Korshunov*(527-528)*. Polarization studies of low-frequency Raman spectra of a mixed (1: 1)

*para*-dibromobenzene-*para*-bromochlorobenzene crystal are performed. The spectrum of the mixed crystal is similar to the spectra of its components and also exhibits a number of additional low-intensity lines. The experimental results are interpreted using calculations of mixed crystals by the methods of atom-atom potentials and of Dean. It is found that the experimental results better agree with calculations when the disordered distribution of*para*-bromochlorobenzene molecules over*para*-positions is taken into account Perturbation of the spectrum of the Ba atom by radiation from a color center laser in the range from 8400 to 8700 cm

^{−1}by I. I. Bondar’; V. V. Suran*(529-532)*. The perturbation of the Ba atom by radiation from a color center laser in the range between 8400 and 8700 cm

^{−1}is experimentally studied. The study was performed by the method of resonance ionization spectroscopy by simultaneously irradiating a beam of Ba atoms by a color center laser and a dye laser at 17735 cm^{−1}. The dynamic polarizabilities of the 5*d*6*p*^{1}*F*_{0}^{3}and 6*p*^{2 1}*D*_{2}levels are measured. Intraband radioluminescence of LiF crystals by V. V. Tirskiĭ; E. F. Martynovich

*(533-537)*. Spectra of high-energy electrons are calculated in the electron-hole ionization-passive region of lithium fluoride crystals for the conditions of intense irradiation by short pulses of accelerated electrons. The yield of intraband radioluminescence of these crystals is estimated in comparison with the yield of this kind of luminescence of more extensively studied NaCl crystals. The calculations demonstrate that the yield of radioluminescence determined by electron transitions in the conduction band of LiF crystals is two orders of magnitude weaker than the yield of analogous luminescence of NaCl crystals. This is explained, first, by special features of the energy band structure and, second, by the form of the energy dependence of the density of states in the conduction band of LiF crystals. The yield of hole-type intraband radioluminescence is estimated for various assumed relations between the widths of the valence and the forbidden bands.

Photo-and X-ray luminescence spectra of CsPbX

_{3}microcrystals dispersed in a PbX_{2}(X=Cl, Br) matrix by S. V. Myagkota; A. V. Gloskovskii; A. S. Voloshinovskii*(538-541)*. The CsPbX

_{3}(X=Cl, Br) microcrystals are obtained in a PbX_{2}(X=Cl, Br) matrix doped with Cs ions (*C*_{Cs}=0.1–1 mol %). Spectral and kinetic parameters of the intrinsic luminescence of the CsPbX_{3}single crystals are presented. For the CsPbCl_{3}microcrystals, a quantum-confinement effect is detected, which reveals itself as a decrease in the lifetime of the free exciton luminescence. A mechanism of formation of a CsPbX_{3}microcrystal in a PbX_{2}matrix is proposed. Natural electron oscillations in granular indium films deposited on rough surfaces of NaCl and KCl single crystals by I. N. Shklyarevskiĭ; Yu. Yu. Bondarenko; N. A. Makarovskii

*(542-546)*. Two plasma resonance bands were simultaneously observed in granular indium films deposited on rough surfaces of NaCl and KCl single crystals; one of them is caused by a combined action of the light-wave field and of the field created by the dipole grains, and the other, by the light-wave field alone with the frequency of natural electron oscillations ω

_{0}in the grains. The indium plasma frequency, calculated from the measured frequencies ω_{0}and known dielectric constants of NaCl and KCl, agrees well with the known plasma frequency of bulk indium. An anisotropy in the plasma resonance band of granular indium films deposited on a rough NaCl surface was found and interpreted. Plasma resonance in granular gallium films deposited on rough NACl and KCl single-crystal surfaces by I. N. Shklyarevskiĭ; Yu. Yu. Bondarenko; N. A. Makarovskiĭ

*(547-550)*. Granular gallium films deposited in high vacuum on the rough surfaces of NaCl and KCl single crystals maintained at 400°C consist of two layers, in which two resonance bands are excited simultaneously. In isolated grains of the upper layer, a band at the normal electron oscillation frequency ω

_{0}is excited. As a result of supercooling, the grains are in the liquid state. The gallium plasma frequency calculated from the measured ω_{0}and dielectric constants of NaCl and KCl coincides with that obtained by other authors by metallooptic methods. In gallium deposited on room-temperature substrates, only one resonance band is excited, with the interband absorption band superposed on its low-frequency edge. Mechanism of dissipation of the excitation energy in garnet oxides doped with rare-earth ions with 4

*f*-5*d*transitions by Yu. V. Zorenko*(551-553)*. Mechanisms of dissipation of the excitation energy in garnet crystal phosphors Y

_{3}Al_{5}O_{12}and Y_{3}Ga_{5}O_{12}doped with rare-earth ions with interconfiguration transitions are studied depending on the Ga concentration. Macroscopic manifestations of specific features of quantum statistics of the radiation field in the spectrum of resonance fluorescence by A. D. Gazazyan; B. V. Kryzhanovskii

*(554-559)*. The fluorescence spectrum of a two-level atom excited by the field, whose state represents a superposition of the coherent states, is investigated. It is shown that to each mode of the quantum-statistical distribution of the incident field, a spectral mode of the scattered radiation corresponds, and one can determine the number of statistical modes of the incident field from the number of spectral modes of the scattered field. This result is a consequence of the fact that in the quasi-classical limit, statistical modes of the superimposed state interact with the atom independently of one another.

Soliton pulses in two-mode periodic fibers by I. O. Zolotovskiĭ; D. I. Sementsov

*(560-563)*. The conditions of the formation and the propagation of soliton pulses in a periodic two-mode non-linear fiber are studied. The analysis takes into account the dispersion of a fiber material and the intermode dispersion of the interacting modes subject to the conditions of their phase matching.

Optical control of longitudinal periodic structures near the boundary of a rarefied resonance medium by T. A. Vartanyan

*(564-567)*. The state of a rarefied gas medium is described theoretically upon reflection of intense resonance light from its surface. Conditions are found under which a longitudinal grating of the excited state population arises in the near-wall region of the medium. A new method for controlling parameters of the arising structure by means of the light is proposed.

Translation symmetry of Fraunhofer diffraction patterns of plane apertures with generalized right angles by V. G. Magurin; V. A. Tarlykov

*(568-575)*. A class of apertures of the simplest shape possessing generalized right angles is considered. Based on the geometrical theory of diffraction, the formation of Fraunhofer diffraction patterns for apertures of this class is analyzed. Conditions of the possibility of observing translation symmetry in the intensity distributions in diffraction patterns are formulated.

Specific features of generation of the quasi-Schrödinger soliton in the CW mode-locked solid-state laser with a semiconductor saturable absorber by V. L. Kalashnikov; D. O. Krimer; I. G. Poloiko

*(576-580)*. The mechanism of mode-locking in the cw solid-state laser with the saturable semiconductor switch caused by the formation of the quasi-Schrödinger soliton is investigated on the basis of the self-consistent laser field theory. The possible regimes of the quasi-soliton destabilization are studied: the sharp transition from the femtosecond to picosecond generation (“the picosecond collapse”), the self-oscillation instability, as well as the breakdown of the pulsed generation. The existence of multistable states and hysteresis phenomena upon the variation in the group-velocity dispersion and the pump power are shown.

Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films by V. V. Filippov

*(581-585)*. A spectrophotometric method is proposed that uses the ratio of envelopes of minima and maxima of the interference reflection spectrum for measuring optical constants of a film on a substrate. Because this ratio does not contain the instrumental function of a spectrophotometer, there is no need in careful calibration of the spectrophotometer. In the case of a transparent isotropic film on an absorbing substrate, the inverse problem has an analytic solution. A simple method is proposed for numerical calculations of the optical constants and thickness of an absorbing film.

Reflection and transmission of light by cholesteric liquid crystal-glass-cholesteric liquid crystal and cholesteric liquid crystal(1)-cholesteric crystal(2) systems by A. A. Gevorgyan; K. V. Papoyan; O. V. Pikichyan

*(586-593)*. Reflection and transmission of light by cholesteric liquid crystal-glass-cholesteric liquid crystal and cholesteric liquid crystal(1)-cholesteric liquid crystal(2) systems were studied. The classical Ambartsumyan method of adding layers and the concept of a sewing function were used. This approach was developed earlier in astrophysics for the theory of radiation transfer. Here, we used a version of this method adapted to wave optics. The Jones matrices are constructed for these systems. The features of the reflection and transmission spectra, optical rotation and ellipticity of polarization were studied for these systems. It is proposed to use these systems as tunable narrow-band filters and mirrors. These systems can be used, for example, to develop a variety of optical elements for lasers and of polarimetric elements in ellipsometry. The specific features of eigenpolarization are also discussed. It is shown that optical rotation of the two layers of cholesteric liquid crystals, which differ from each other only by the sign of the helix, is nonzero, and it becomes substantial in the diffraction reflection region. A unique property of these systems is the degeneracy (coincidence) of eigenpolarizations.

An approximate method for calculating scattering and absorption of light by fractal aggregates by N. G. Khlebtsov

*(594-601)*. A simplified version of the coupled dipole method (CDM) is proposed which allows one to reduce the initial system of 3

*N*×3*N*equations to a simpler system of*N*×*N*equations. The method neglects depolarization effects in the interaction of dipoles but, unlike the mean field approximation, it takes into account local fluctuations of the scalar amplitudes of the excited dipole moments. Simple analytic solutions are obtained for integrated cross sections averaged over aggregate orientations. It is shown by the example of ballistic fractal aggregates that this method provides the accuracy close to that of a standard CDM, being substantially less time-consuming. In the case of biospheres, the approximate method is compared with the exact results of the multipole expansion. Light scattering by a “soft” layered sphere: Analysis by the method of spectral expansion in Kotel’nikov-Shannon choice functions by V. M. Rysakov; M. Ston’

*(602-607)*. Light scattering by a two-layer “soft” sphere is studied. The analysis is made by the method of expansion in the spatial spectrum in Kotel’nikov-Shannon choice functions. In the case where changes of relative refractive indices of the first (Δ

*n*_{1}and the second ((Δ*n*_{2}) layers have the same sign, the scattering indicatrices are found to be close to the indicatrices for a homogeneous sphere with averaged effective parameters, and the integrated cross sections should be close as well. However, in the case where Δ*n*_{1}and Δ*n*_{2}have opposite signs, changes in the indicatrix are stronger. The major lobe becomes weaker and, in certain cases, even vanishes, whereas the side lobes and backward scattering increase in intensity. The physical interpretation of the results that can be used for the analysis of experimental data is given. Specific features of statistical characteristics of photon trajectories in a strongly scattering medium near an object surface by O. V. Kravtsenyuk; V. V. Lyubimov

*(608-614)*. Results of a detailed study of statistical characteristics of photon trajectories in a strongly scattering medium near an object surface are presented. The properties found in the study may be useful for developing an algorithm of reconstruction in real time for the optical tomography of strongly scattering (biological) object.

Simulation of scattering of optical radiation by a metal surface with nanometer irregularity by A. Ya. Khaĭrullina; T. V. Oleĭnik; A. F. Sinyuk; V. A. Babenko; A. N. Ponyavina; T. A. Zhevlakova

*(615-618)*. Within the framework of the model of a limited electron free path, the scattering indicatrix for spherical nanoparticles was calculated. The calculations were made by an example of silver and supersmooth surfaces, which were modulated by a monolayer of spherical nanoparticles taking into account the correlation in the distribution of particles and the size effect within the framework of the interference approximation. As follows from the calculations, the inclusion of the size effect into consideration leads to a noticeable change of the scattering intensity, both for separate particles and a surface, near the plasma resonance wavelength. Because of this, the spectral dependences of the refractive index calculated with and without allowance for the size dependence of optical constants differ in the resonant region by more than an order of magnitude.

Simulation of shadings in systems of opaque particles by D. G. Stankevich; Yu. G. Shkuratov; K. O. Muinonen; O. V. Miloslavskaya

*(619-622)*. Results of computer simulation of the shading effect in systems of opaque spherical particles scattering light in accordance with the Lambert law are presented. Two types of systems are studied: a semi-infinite medium and statistically uniform clusters of a finite number of particles. The simulation makes it possible to obtain photometric characteristics of systems with an accuracy better than 1%. The phase dependence of the shading effect is shown to become steeper as the packing density of particles in clusters decreases and their number increases. For statistically uniform media, the following relation takes place: The lower the packing density, the more pronounced the shadow decrease in brightness with an increasing phase angle.

Dynamic optical transfer function of an acoustooptic modulator with a damped sound wave by A. S. Zadorin

*(623-629)*. Based on a spatially dependent dynamic optical transfer function of an acoustooptic modulator, a dynamic model of light modulation by a sound signal under conditions of acoustic damping is developed. A system of equations describing the dynamics of the acoustooptic interaction is given. Solutions of this equation for arbitrary power level and spatial-time structure of a sound signal are found. It is shown that acoustooptic damping has the strongest effect in a nonlinear modulation regime. Here, the dissipation of an acoustic signal suppresses the higher harmonic of the dynamic optical transfer function. An analytical model of the dynamic optical transfer function for a low level of acoustooptic coupling is given. It is shown that when the pump beam aperture is much greater than the spatial size of an acoustic signal, the time response of the acoustooptic modulator response is identical within a phase factor to the amplitude profile of a pump beam apodized by the exponential dependence of the amplitude of a damped sound wave. Otherwise, the sound damping produces almost no distortions of a plane top of the acoustooptic modulator response to a pulsed signal and shows itself only under phase mismatch conditions. Here, the asymmetry of overshoots at the edges of the acoustooptic modulator response is observed. Calculated plots are presented, which illustrate the aforementioned specific features of the transient process under conditions of acoustic damping in the acoustooptic interaction in paratellurite.

Results of the use of generalized coupling equations in the original Fresnel theory and original theory of spatial dispersion in a gyrotropic uniaxial crystal by V. A. Shamburov

*(630-633)*. The generalizations of the original Fresnel theory and original theory of natural gyrotropy as manifestations of the first-order natural dispersion in uniaxial crystals are considered. The generalizations are made for magnetic crystals, taking into account the magnetic gyrotropy. The region of application of the corresponding generalized theories is found to be restricted by a particular case of the wave normal s directed parallel to the optic axis

*C*of a uniaxial crystal. Correction of wavefront distortions and depolarization in solid-state laser amplifiers by R. A. Ganeev; A. A. Gulamov; Sh. R. Kamalov; T. Usmanov

*(634-636)*. Results are reported of the study of systems averaging the azimuthal inhomogeneities of gain and suppressing aberration and polarization wavefront distortions formed in active amplifying elements of a repetitively pulsed Nd:YAG laser. A twofold decrease of depolarization in the amplified radiation was obtained. An optimum filling of active elements due to correction of radiation distortions in the near field was realized.