# Optics and Spectroscopy (v.88, #1)

Resonant multiphoton ionization of the 1

*s*state of a hydrogen atom in a strong laser field by E. A. Volkova; A. M. Popov; O. V. Tikhonova*(1-6)*. The process of resonant multiphoton ionization of a hydrogen atom in the ground 1

*s*state is studied by direct numerical integration of the nonstationary Schrödinger equation for a quantum system in an electromagnetic field. The dependence of photoionization probability on the radiation intensity is found to be nonmonotonic. It is established that the minima of ionization correspond to multiphoton resonances between the ground state and one of the excited (Rydberg) atomic states perturbed by the laser field. It is shown that ionization is suppressed due to rearrangement of Rydberg states in a strong electromagnetic field and is accompanied by efficient Raman Λ transitions, which connect a set of closely lying Rydberg states via the continuum. Signal of collisional beatings of polarization of light as a function of the angular momentum of an excited atomic state by A. G. Petrashen’; V. N. Rebane; T. K. Rebane

*(7-10)*. A comparative study of the beats of circular polarization generated by anisotropic atomic collisions is carried out on the basis of theoretical calculations for the states

*J*=1, 3/2, and 2 of neon atoms and ions excited by monochromatic laser radiation in xenon atmosphere. Contributions made by ordinary alignment and higher polarization moments (octupole orientation and dodecapole alignment) in the collisional generation of orientation and the signal of beatings of circular polarization are compared. Assignment of the 5

*d*6*s*-5*d*6*p*transitions in the PtIX ion: Comparison of two calculations of the 5*d*^{2}, 5*d*6*s*, and 5*d*6*p*configurations in the ion by V. I. Azarov; S. S. Churilov*(11-16)*. The spectrum of platinum is studied in the region from 250 to 1250 Å. The twenty-two 5

*d*6*s*-5*d*6*p*spectral lines of the PtIX are assigned. All levels of the 5*d*6*s*configuration are found. The assignment of the previously known 5*d*6*p*levels is confirmed and their positions are refined. The 5*d*^{2}, 5*d*6*s*, and 5*d*6*p*configurations are theoretically described by the method of orthogonal operators. These calculations are compared with the data obtained by a conventional method using the Cowan program. Exchange between translational and electronic energies of atoms in their impacts with a surface by S. G. Przhibel’skiĭ; V. V. Khromov

*(17-21)*. Electronic excitation of K, Rb, and Cs atoms resulting from their impacts with a sapphire surface is studied experimentally. The spectrum and the intensity of atomic emission are measured as functions of the vapor concentration. The contributions of surface and volume excitations to the vapor emission are separated. The concentration dependence of the intensity of near-wall emission is described as a result of atomic excitation generated at the wall and quenching at it upon diffusion. The probabilities of excitation and deactivation of atoms in their impacts with a sapphire surface are estimated from the measurement results and the values close to unity are obtained.

Adiabatic similarity and dependence of the energy of molecular systems on the masses of particles by T. K. Rebane

*(22-27)*. The dependence of the energy of three-particle molecules on their masses is examined. It is shown that such molecules with the same values of the ratio of the reduced masses for motion in a “fast” and “slow” Jacobi coordinates have the property of adiabatic similarity: In the adiabatic approximation, their energies are proportional to the reduced masses. This allows information on the energy of molecules symmetric in the masses of particles to be extended to asymmetric molecules adiabatically similar to the symmetric molecules. For molecules with arbitrary masses of the particles, an analytic expression for the adiabatic energy and a formula approximating the exact energy are constructed using the principle of adiabatic similarity. Along with the adiabatic energy, which is the lower bound of the exact energy, a simple procedure is considered for determining the upper bound of the energy of asymmetric molecules from the energy of their symmetric counterparts. Based on these results, values of the lower and upper energy bounds are calculated and an approximation of the exact energy is obtained for 43 three-particle molecular systems.

Problem of mixing of stereoisomers in the hydrazine molecule N

_{2}H_{4}by A. V. Burenin*(28-34)*. It is shown that the important consequence of nonrigid motions observed in the hydrazine molecule N

_{2}H_{4}is mixing of stereoisomers, although the geometrical symmetry group, taking into account these motions, similarly to the point group of one equilibrium configuration, has no improper transformations of the molecule as a whole. Here, an important point is that the geometrical group of a nonrigid molecule is the so-called noninvariance dynamical group. The effect of mixing of stereoisomers on the total picture of nonrigid motions is considered using the symmetry methods. In particular, it is shown that a nonrigid molecule exhibits properties of a symmetric top, whereas a rigid molecule represents an asymmetric top. Raman scattering of light by the electroactivated water by V. I. Pastukhov; V. P. Morozov

*(35-37)*. Raman spectra of the electroactivated water and its chemical analogs are studied. The substantial differences are found in the 700–2700-cm

^{−1}region, which are assumed to be related to the presence of a charged hydrogen bond in associates involving excessive H^{+}and OH^{−}ions. Electronic and spatial structures of the hydroxyl ion in LiF, NaF, and KF crystals by A. S. Mysovskiĭ; A. D. Afanas’ev; S. N. Mysovskiĭ

*(38-41)*. The electronic and spatial structures of the impurity hydroxyl ion in LiF, NaF, and KF crystals are studied using a molecular cluster model by the Hartree-Fock-Roothaan method in the semiempirical INDO (intermediate neglect of differential overlap) approximation. The equilibrium geometry of the impurity ion is determined. The hydroxyl ion is oriented in all the three matrices along the 〈110〉-axis, which is caused by the formation of the selected chemical bond between the hydrogen ion and the nearest lattice fluorine ion located on the same axis. The optical absorption energies are calculated.

Vacancy mechanism of the photolysis of aluminum hydride by M. A. Goryaev

*(42-45)*. Within the framework of the thermodynamic model of formation of intrinsic defects in a lattice during the decay of photoexcitations in a solid, the formation of hydrogen vacancies in aluminum hydride is analyzed. The evolution of a system with excess vacancy concentration leads to the formation of micropores under the crystal surface. The results of calculations agree well with the experimental data on photochemically induced absorption obtained in electron-microscopic studies of AlH

_{3}decomposition. Excitation spectra of light-induced electric responses in doped ferroelectric crystals by V. G. Babadzhanyan; G. G. Demirkhanyan; E. P. Kokanyan

*(46-49)*. On the basis of studies of light-induced responses of doped lithium niobate crystals, a new approach to the spectroscopy of polar materials is developed. An experimental technique is described and possible applications and advantages of the approach are discussed.

Nonlinear excitation of AgBr nanocrystals in the field of short light pulses by E. Yu. Perlin; D. I. Stasel’ko

*(50-54)*. Processes of the electron-hole pair generation and excited-state relaxation at earlier stages of the latent image formation in the AgBr nanocrystals are studied theoretically. The experimental dependence of the photographic blackening

*D*in the field of the intense laser light on the light pulse energy*I*is analyzed in the range of pulse durations τ_{i}from 10^{−13}to 10^{−8}s. The values of*I*needed to obtain a fixed blackening*D*at τ_{i}∼10^{−10}s exceeded those at τ_{i}∼10^{−8}s by three orders of magnitude. However, as τ_{i}further decreased to hundreds of fs, these values decreased by two orders of magnitude. It is shown that experimental nonmonotonic dependences can be explained by saturation of the one-photon interband generation of electron-hole pairs accompanied by the development of the two-photon generation. For shortest pulses and, correspondingly, greatest light intensities, the pair generation rate varies more strongly than upon usual two-photon absorption, which is caused by the resonance optical Stark effect. Scattering of surface magnetic polaritons rom order-parameter fluctuations near second-order magnetic phase transitions by V. N. Krivoruchko; T. E. Primak

*(55-62)*. A study is reported of the scattering of surface magnetic polaritons in the vicinity of second-order spin-reorientational phase transitions, which is caused by spatial fluctuations of the order parameter. A four-sublattice antiferromagnet α-Fe

_{2}O_{3}is used as an example to derive expressions for the vacuum-scattered radiation near exchange magnetic-vibration frequencies. The scattering of surface magnetic polaritons is shown to be resonantly enhanced in characteristic regions of their spectrum. Estimates made for α-Fe_{2}O_{3}indicate a possibility of experimental observation of surface magnetic-polariton scattering from fluctuations of the refractive index near second-order spin-reorientational phase transitions. Light scattering by dielectric particles with axial symmetry by V. G. Farafonov

*(63-70)*. A new method is suggested for solving the problem of scattering of a plane electromagnetic wave by dielectric particles with the axial symmetry. The method is based on the separation of fields into two parts: the axially symmetric part, which is independent of the angle of rotation, and the part that is not axially symmetric, which vanishes upon averaging over this angle. The scattering problem is solved separately for each of the parts. In the first case, scalar potentials related to the azimuthal components of electromagnetic fields are used, and in the second case, superpositions of the Debye potentials and vertical components of the Hertz vectors are used. The surface integral equations for these potentials are obtained. They are represented as expansions in the spherical wave functions. The infinite systems of linear algebraic equations are obtained for unknown expansion coefficients. Our calculations demonstrated the high efficiency of the new method.

Applicability of quasi-static and Rayleigh approximations for spheroidal particles by N. V. Voshchinnikov; V. G. Farafonov

*(71-75)*. Expressions are obtained for the efficiency of absorption and scattering of radiation by uniform spheroids in the quasi-static approximation and the region of their applicability is studied. The prolate and oblate nonabsorbing particles with refractive indices 1.1≤

*n*≤10 and axial ratios 1.1≤*a/b*≤100 were studied. The approximation expressions are found for the particle size at which the efficiency factors are calculated in the quasi-static approximation with an accuracy of 1%. Light scattering from a waveguide structure with a sinusoidally corrugated boundary modulated by a weak roughness by I. Aubrecht; M. Miler; I. Mokhun’

*(76-84)*. Results are reported of the analysis of light scattering from a waveguide structure with a periodically and randomly distorted boundary. The method is based on the assumption of single scattering. The field inside the waveguide is analyzed within the framework of the geometrical optics approach. Results of a computer simulation are presented.

Influence of spatial dispersion of the first and the second orders simultaneously on the parameters of natural waves in a uniaxial crystal by V. A. Shamburov

*(85-89)*. It is found for the first time that the coexistence of two principal and two additional natural waves and only one additional wave (in the absence of the second one) is impossible in the exact solution and in the approximate solution, respectively, of the problem formulated in the title, because Fresnel’s general equation beaks up into two independent equations for two principal and two additional waves. A probable relationship is found between the small parameters of spatial dispersion of the first (γ) and the second (α

_{0}) orders (α_{0}/γ≈1) for the spectral region far from resonances, for which the refractive index of the third additional wave for α_{0}=0 is approximately equal to the refractive index of one of two additional waves for α_{0}≠0 and γ≠0, when the wave normal is directed along the optical axis of a uniaxial crystal. Mikhel’son effect in a plasma by A. E. Dubinov; S. A. Sadovoi; V. D. Selemir

*(90-95)*. An analysis is made of the parametric frequency shift of an electromagnetic wave traveling in a plasma (isotropic collisionless, isotropic collisional, and magnetized collisionless) with time-varying parameters (Mikhel’son effect). Different situations corresponding to the growth of plasma concentration, a change of collision frequency, and a change of magnetic field are considered.

Diffraction of an ultrashort pulse by a slit by I. É. Suleimenov; Yu. A. Tolmachev; M. K. Lebedev

*(96-101)*. An analysis of a specific feature of the interaction of an ultrashort pulse with a slit is made. Analytical expressions for a monochromatic wave in the form of an ultrashort pulse diffracted by an infinite slit are obtained.

Determination of the resolving power of optical systems in the formation of speckle images by G. N. Mal’tsev

*(102-106)*. Relations for the calculation of the limiting resolvable spatial frequency of a speckle image of a line mira used as a test object in the determination of the optical power of optical systems are presented. The influence of the speckle structure on the extraction of information about the shape of the object observed from the image recorded is taken into account by using the equivalent modulation transfer characteristic of the optical system than determines the transfer of spatial frequencies of the envelope of the speckle image and the threshold characteristic of speckle noise conditioned by fluctuations of the amplitudes of individual speckles. Conditions, in which the prevailing influence on the quality of the image recorded is exerted by the speckle structure, atmospheric phase distortions, and discretization noise, are determined.

Diffraction method for checking geometrical parameters of a spiral fiber by P. G. Shlyakhtenko

*(107-112)*. Monochromatic small-angle Fraunhofer diffraction from a spiral is studied as a function of its stretching. A simple relation between locations of the principal maxima and geometrical parameters of a spiral is obtained. Diffraction from a spiral is analyzed theoretically in the linear approximation of the boundaries of the profile of a periodic unit. An analytical expression for the light intensity at any point of a screen is derived, and analytical relations between locations of the principal maxima and geometrical parameters of a spiral, which are identical to the relations established experimentally, are obtained. The possibility for utilizing the results obtained in the development of systems of automatic control of the main geometrical parameters of spiral objects in the process of their production is demonstrated by the example of the analysis of diffraction patterns from a standard metallic screw and a twisted capron fiber.

Transformation of spatial modulation of a light field into amplitude modulation in the interaction of a superposition of transverse modes of a He-Ne laser with iodine-127 vapors by A. V. Mironov

*(113-117)*. The observation of “spatial-modulation” resonances of saturated absorption in the interaction of iodine-127 vapors with a superposition of frequency-nondegenerate TEM

_{01}and TEM_{10}transverse modes of a linear laser is reported. The modulation of the total radiation power of the probing wave, recorded at twice the beating frequency of transverse modes of the laser, is interpreted to be the result of the transformation of modulation of the spatial distribution of the field into its amplitude modulation under the action of nonlinearly absorbing iodine vapors. Resonances of saturated absorption of the weak line*R*(127)11-5 of iodine-127 (633 nm) in an extracavity cell are observed by the method proposed. An explicitly solvable case of the construction of the fundamental cavity mode in the form of a Gaussian beam with a complex astigmatism by V. N. Kudashov; A. B. Plachenov; A. M. Radin

*(118-120)*. An analysis is carried out of the ring cavities whose fundamental modes represent Gaussian beams with complex astigmatism. The analysis is made for the case where the block

*B*or*C*in the cavity ray matrix*ABCD*of dimension 4×4 is a symmetric nondegenerate matrix. Explicit formulas are obtained, which permits the expression of beam characteristics directly in terms of the cavity ray matrix without the laborious process of finding its eigenvectors. The results obtained in the study can be used for controlling astigmatism in lasers and laser systems, the calculation of polarization of three-dimensional active media in linear and ring optical cavities of complex configuration, etc. Optical beams with complex astigmatism in the case of coincident eigenvalues of the cavity ray matrix by V. N. Kudashov; A. B. Plachenov; A. M. Radin

*(121-126)*. An analysis is carried out of the optical cavities whose natural modes have the form of Gaussian beams with complex astigmatism. In the case of coincident eigenvalues of the cavity ray matrix, the wave beams were found to be determined not only by the geometrical optics characteristics of a cavity, but also by additional cavity-independent parameters. A detailed analysis is given for the fundamental mode of such cavities. Concrete cavities possessing these properties are noted.

Narrow saturated absorption resonances in the transmission band of an active interferometer by S. N. Bagaev; A. A. Kurbatov; E. A. Titov

*(127-131)*. The shape of the transmission band of an active interferometer, a resonator with amplification and absorption cells excited by an external signal, is studied. Upon tuning the external signal frequency, the narrow saturated absorption resonances can be observed in the transmission band of the interferometer. It is shown that, by varying the gain, the resonance absorption amplitude can be compensated for one order of smallness in pressure. The effect of amplitude and frequency noises of the external signal on the results obtained is studied.

Splitting of oscillation frequencies of a ring gas laser caused by the diffraction lens effect: II. Nonlinear theory by T. V. Radina

*(132-138)*. An analysis is made of the problem of generating the fundamental mode in a laser cavity containing a weakly nonlinear active medium and an aperture. Frequency-dependent nonlinear loss of counterpropagating waves is calculated. The loss was found to have a jumpwise decrease at the boundary of the lasing region. An explanation is given regarding the mechanism responsible for the asymmetry of loss about the central frequency of the transition. It is shown that counterpropagating waves differ in loss, as well as in the phase velocity, which is one of the reasons of that the counterpropagating waves of a ring laser, without special nonreciprocal devices, have different frequencies and intensities.

Effect of perturbations in an active medium on the instability of the difference frequency of laser radiation by V. E. Privalov; M. A. Fedotov; E. G. Chulyaeva

*(139-142)*. A frequency-stabilized helium-neon laser with Zeeman frequency splitting in the magnetic field was studied. A series of pulses with repetition frequency equal to the frequency difference caused by the splitting of the gain profile by the magnetic field was used as a reference signal for a laser interferometer. The modulation of discharge current by electric noise or natural oscillations of the discharge current were found to lengthen the edges of these pulses, which decreases the accuracy of measurements with a laser interferometer.

E. G. Loewen and E. Popov

*Diffraction Gratings and Their Applications*(Marcel Dekker, New York, 1997) by D. A. Zhuravlev*(143-144)*.