This paper deals with diode laser applications in high resolution molecular spectroscopy and atmosphere pollutant monitoring. Results of spectral line parameter measuring (frequency, intensity, pressure broadening, and shift) are presented. Diagnostic systems based on diode lasers and IR fibers have been developed. Their use in atmosphere monitoring and some additional applications are considered.

We shall consider a critical phenomenon which corresponds to bifurcation in classical mechanics. It modifies the rotational motion regime due to the appearance or disappearance of the degeneracy in a rotational band at some critical value I equals Ic. The bifurcation is induced by nonlinear effects occurring due to the action of centrifugal or Coriolis forces. It is revealed both as the rearrangement of the rotational multiplet (RM) levels and as a qualitative change of the probabilities of electromagnetic transitions within the band.

An extended geometric symmetry group of HAAH-type molecules is constructed, which includes a point group of these molecules as a subgroup. The extended group has been used within the framework of the concept of a chain of symmetry groups of the models inserted into each other. The models arise in the analytical solution of the problem of the stationary states of the molecule using the perturbation theory. As a result, we have obtained a most consistent and detailed analysis of the symmetry properties of these molecules. Further development of the concept of a chain of symmetry groups is considered.

A molecule is usually classified according to the values of its principal moments of inertia. Following the most widely accepted convention for labelling the moments of inert i a I I I a b c or, alternatively, the rotational constants, A B C-i ii with A(cm ) = 2 etc., 8ir ci a a "spherical molecule" is a molecule possessing identical moments of inertia: I =1 =1 a b c A molecule may then be classified as "quasi spherical" if the principal moments of inertia are similar but not exactly equal. Two limiting cases may be identified: I I = I :prolate a b c I I <I :oblate a b c A few examples of both prolate and oblate "quasi spherical" symmetric tops are collected in the following Table.

The adiabatic and self-consistent field methods are discussed as methods generating various kinds of effective Hamiltonians. The applications of these Hamiltonians in calculations and interpretation of the molecular spectra are demonstrated.

The main tendencies in the up-to-date development of experimental methods of molecular spectroscopy of the atmospheric gases are connected with the increase of spectral resolution, absorption sensitivity of instrumentation as well as the use of new spectral regions and wider applications of research. The high monochromaticity of laser emission used in facilities for atmospheric studies, in combination with the selectivity of atmospheric absorption spectra in the optical range, and large dynamic range in the variations of absorption coefficients (from 10-4 cm-1 at the centers of strong lines down to 10-8 cm-1 for weak lines in the atmospheric transmission windows) require qualitatively new spectroscopic information for solving many practical problems of atmospheric optics. This lecture deals with the discussion of investigations by means of the highly sensitive methods of the laser absorption spectroscopy (intracavity, opto-acoustic, and photometric) as well as of the quantitative data on the highly excited molecular states obtained.

The molecular spectra to which the following pages refer are rotational or rovibrational spectra of small molecules, where the rotational constants are in general fairly large to allow most of the observed lines to be well resolved according to the requirements for high resolution work.

The region of 5 micrometers is one atmospheric window where ozone may be easily observed in solar spectra. It corresponds to the triad 2 (nu)₃, (nu)₁ + (nu)₃, 2 (nu)₁, there (nu)₁ + (nu)₃ is the strongest band. Isotopic bands of (nu)₁ + (nu)₃ of ¹⁶O¹⁶O¹⁶O and ¹⁶O¹⁸O¹⁶O may also be observed. This study is particularly concerned with application to atmospheric transmittance, considering line position, intensity, self-broadening coefficient, air broadening coefficient, and shifts of O₃.

It is well known, that for gases, central portion of an isolated vibration-rotation spectral line contour broadened by collisions is generally described by Lorentzian profile. Nevertheless this prediction of the Anderson theory is restricted by two conditions following from two approximations admitted in constructing this theory.

High-power laser radiation propagating in molecular gases strongly affects both the optical characteristics of the medium in the channel of propagation (the absorption coefficient and the index of refraction) and the characteristics of the laser radiation self-action in resonance- absorbing molecular gases. These effects in the atmosphere are of great current interest for atmospheric optics. Over the long atmospheric paths, even comparatively weak nonlinear effects may have significant impact on propagation of high-power radiation. The present paper deals with the results of studying the nonlinear spectroscopy of atmospheric gases and the problems of accounting for nonlinear effects for solving the problems of atmospheric optics.

We describe the high resolution F.T.S. of Reims. In particular we detail the way to obtain the best safety during the working process of the instrument. We also show how to improve the signal/noise ratio by good temporal data acquisition. We finally describe all the softwares used to reduce data.

Let us consider preliminary two situations. In the first of them the monochromatic radiation is absorbing. The increase of its intensity leads to the diminution of an absorption down to zero in a limiting case, i.e. to the effect of saturated absorption. In the second case an absorption of test radiation with a small intensity is observing, while two—level atom is strongly interacting with a perturbing field. This case is characterized by asymmetric dependence of absorption on the frequency difference w- w = A, where w and w are the frequencies of two light waves. As it was shown by Rautian and Sobelman in 19611, the amplification of test radiation arises in a certain range of frequency offsets A instead of the absorption, and the energy transfers from a strong wave to a weak one. In this paper we study the problem which appears from the above situation, when the intensity of test radiation increases. Such an increase leads to new maxima in absorption spectra of test radiation at frequencies A = i n = 2, 3 4 . . . which are additional to the main maxima at n R A = where R the Rabi frequency. These new resonances were observed by Bonch-Bruevich, Vartanyan, and Chigir in 19792 and cal led the subradiat ive structure. We have the following simple approximate expression for R obtained in the case of interaction with two fields: Q =d(?+E2)1"2/h. (1) R 0 1 There are two essential effects in the described situation: the saturation of absorption and the nonlinear interference effect. The last causes the redistribution of an absorbed energy between radiation components, the negative absorption (amplification) without population inversion, and the multiphoton parametric resonances at difference frequencies. The laser generation on the base7of the negative absorption without population inversion was obtained in 1989. The following problems arise from the facts reviewed above: 1. The calculation of absorption coefficients for individual components of a strong polychromatic radiation with an equidistant spectrum. 2. Determining of a generalized Rabi frequency and verification of the simple formula A = In for maxima of resonances. n R The aim of this paper is to solve these problems.

Good examples of combined energy- and time-resolved techniques linked by the theoretical solution of a nuclear problem may be found in investigations of the dynamics of weakly bound Van der Waals (VdW) complexes, such as Ar-OH and He-stilbene. Our report concerns only the theoretical aspect of this complex approach. However, we shall stress the importance of energy-resolved spectroscopy for the dynamics and try to illustrate this with some numerical results.

In the series of articles we have developed a semiclassical self-consistent approach to calculation of the highly excited rotational states in vibration-rotation (VR) spectra of polyatomic molecules. The central idea of the semiclassical approach is based on the introduction of the auxiliary time-periodical fields which transfer interactions between rotational and vibrational molecular degrees of freedom. This procedure leads to separation of variables in the VR Hamiltonian and, as a result, to simplification of the initial problem interpretation, which is reduced now to an independent solution of two nonsteady Schrodinger equations. In the first of them the Hamiltonian describes a motion of the molecular angular momentum J in some time-periodical field and does not depend on the vibrational coordinates explicitly, in the second - the Hamiltonian is a sum of usual vibrational energy and some additives, which describe a motion of the vibrational collective variables in auxiliary fields and do not depend on the angular coordinate explicitly.

To solve the problem of the highly excited vibrational-rotational molecular states it is important to construct analytically the perturbation series for the energies and wavefunctions in the Born-Oppenheimer approximation employing such a representation for the potential function which models the nuclear interaction potential with sufficiently high accuracy at large deviations from the equilibrium configuration of the molecule as well as near the equilibrium point. In Refs.1,2 we have conctructed such a series for a diatomic molecule. The nuclear interaction in the zero-order approximation was described by the Kratzer potential

In this paper we continue to investigate the effective Hamiltonians for the C_4v and D_2d molecules and consider the case of Z-resonances. There exist C_4v and D_2d molecules having strong Coriolis resonances between their fundamental bands. These Coriolis resonances can be classified according to the component of angular momentum in Coriolis interaction operator. It is usual practice to take the main symmetry axis as z-axis of molecular- fixed frame. In this case Z-resonances take place between degenerate or nondegenerate vibrational levels.

The spectra of H2S molecule and their deuterated species have been subject of several recent studies. The HS absorption spectra have been recorded with a high resolution up to 1.6 jim; rotational constants have been determined for: groun state;1'2 and (010) 7state;3'4 (100),(OO1),(O2O) states;5 (11O),(O11); (11i),(012),(21O) states. As we know no high resolution study at the 1.9 im region has been performed. A previous analysis of H2S spectrum near 2 jim region has been made by H.C.Allenand and E.K.Plyler at low resolution. We report here the high resolution analysis of v1+ V3 and 2v1 bands of H2 S located at 1.9 im region.

The investigations of vibration-rotation spectra of deuterated water vapor are of great importance for the determination of intramolecular potential function, studies of molecular dynamics in excited states, and for some applications in atmospheric optics. In the present paper, the absorption spectrum of HD¹⁶O at 2 micrometers is investigated with a Fourier- transform spectrometer at a spectral resolution 0.0098 cm^-1; energy levels and rotational constants of (011) vibrational state are determined.

Abstract not available.

Two non-polynomial forms of effective Hamiltonian based on Hamiltonian in the principal axes of inertia are proposed to improve extrapolation ability of phenomenological method of description of high-resolution ro-vibronic spectra of polyatomic molecules.

It is known, that parameters of spectral lines (half-width, frequency of transitions, intensity, ets) are determined by the solution of inverse spectral problem. Corresponding methods of calculation of parameters of vibration-rotation high resolution spectrum are effective, if two general conditions are fulfilled: 1. The effective Hamiltonian having good extrapolation properties is establ ished. 2. There are enough experimental data to fit the parameters of this Hamiltonian. The first condition is connected with the achievement of theory of effective Hamiltonians and second one is determined by the development of experimental technique. Sometimes the experimental data on some part of spectrum are absent (highly excited vibration-rotation states, electronic excited states). Ab initio calculations of potential energy surfaces of ground and excited electronic states and ab initio determination of vibration states allow us to weaken these difficulties. On the whole, the success of this task is determined by precision of ab initio calculation of electronic energy. The refined optimization method for solving this problem are given bellow.

There are three usual approaches to the theoretical analysis of absorption and Raman spectra of polyatomic molecules: 1) immediate summation over molecular states, 2) Fourier representation of the cross-sections in absorption and scattering processes, 3) Green function method. In the present paper we discuss advantages and disadvantages of these calculation methods.

The manifestations of rotation-vibration interaction are of fundamental significance for the spectroscopy of highly excited states and weakly bound clusters. In the present report, we wish to analyze the qualitative changes in molecular states and their quantitative description under the variation of some external parameters. For example, the parameters may play the role of integrals of motion such as the energy, the angular momentum, etc. Although there have been several fully quantum-mechanical calculations of rovibrational states for realistic molecular Hamiltonians at low angular momentum, the study of high angular momentum states necessitates a classical (or semiclassical) approach. In standard variational method the basis of harmonic or anharmonic oscillator functions and rigid top wave functions grows quickly with increasing angular momentum quantum number J. The quantum-mechanical methods are also inconvenient for the physical interpretation of rovibrational nonlinear dynamics. A combination of two methodologies (classical and quantum) would be very useful in computations as well as in the interpretation of the behavior of excited molecules. In this report we want to obtain rotational dependences of molecules in the framework of classical approach assuming the adiabatic potential surfaces to be known.

In the present study, three infrared active bands ((nu) ₁₀, (nu) ₇, (nu) ₁₂) are analyzed within the framework of a four-level model, taking into account mutual Coriolis interaction between three infrared active bands and Coriolis interaction with the inactive band (nu) ₄.

For the investigation of the overtone and combination band intensities of the molecules it is important to estimate values of the unharmonic electro-optical parameters such as second and third derivatives of the dipole moment function with respect to the normal coordinates.

In this paper we examine the classical mechanics of rovibrational interaction in a model of triatomic molecules, in which a bending mode interacts with the three-dimensional molecular rotation. In the rigid bender model used, both bond lengths are assumed frozen, and rovibrational coupling occurs only via the dependence of rotational constants on the bending coordinate. Although several quantum-mechanical calculations of rovibrational states have been performed for low-lying excited states, the study of highly excited states necessitates a classical approach.

A molecule of 2-chloro-4, 5-dimethyl-1, 3, 2-dioxaphospholene is an asymmetric top the with parameter of asymmetry K=-O.75, i.e. near prolate symmetric top. The dipole moment component b=° due to molecular symmetry (Fig.1). Rotational transitions corresponding to the dipole moment component 11 are permitted. Pure rotational transitions corresponding to i may be a c forbidden by symmetry. The spectrum is peculiar by its band structure. Sufficiently narrow and line crowded bands conform to transitions of J J+1, t a type for every value of 3. It is a matter of difficulty to identify spectral lines (rotational transitions) because:

Microwave spectra of tetrahydroselenophene molecules: αD₄-¹²C₄H₄⁸⁰Se (I), αD₃-¹²C₄H₄⁸⁰Se (II), αD₄-α¹³C- ¹²C₃H₄⁸⁰Se (III), αD₄-β¹³C- ¹²C₃H₄⁸⁰Se (IV), αD₄- ¹²C₄H₄⁷⁸Se (V), were studied in one sample. Rotational transitions with (J less than or equal to 39) in the ground vibrational state were identified in the spectra of this molecules.

In microwave spectrum of 2-chloro-4,5--dimethyl-1, 3,2-dioxaphospholene in the region 7-53 GHz a-type and c-type transitions were assigned for parent molecule and for isotopic species with ³⁷Cl, ¹³C_me, ¹³C_Ring in natural abundance. The rotational transitions were identified on the ground of preliminary calculation of spectra of these molecules, using electron diffraction data. The experimental techniques: radiofrequency-microwave, microwave-microwave double resonance and Stark modulation were used.

A qualitative description of cooling molecules in a pulsed supersonic jet is given on the basis of literature data. Procedure of measurements is described and known relations are presented which allow one to determine the rotational temperature and concentrations of molecules in a jet using the measured intensities of IR absorption lines. The parameters of SF₆ and NH₃ jets have been determined for various pulsed valves by means of tunable diode lasers.

Till now the limited feasibilities of the traditional sources of molecular spectra did not allow one to obtain sufficiently complete information about irradiational spectra of a great number of practically significant molecules, in particular, diatomic oxides, fluorides and chlorides of metals. The search and investigation of the characteristics of new sources of molecular spectra, which allow carrying out the selective excitation of some definite molecules with minimum amount of spectral lines, seem to be perspective. The surface of a solid body being bombarded by keV ions in vacuum can be regarded as one of such sources. As a result of the bombarding the sputtered particles of the material of the target escape the surface, and the part of the excited particles emits the electromagnetic radiation while escaping the surface.

The main peculiarity of liquefied noble gases is their high inertia and transparency in the region from the far ultraviolet to the far infrared. Therefore, a cryospectroscopic technique may be employed not only for determination of basic molecular parameters (vibrational frequencies, isotopic shifts, etc.) but also for the studying of chemically aggressive and unsteady compounds, for investigation of molecular systems produced as a result of complex formation and photochemical reaction, for the determination of a small quantity of impurity in gases (approximately equals 10^-4 - 10^-7%), and for obtaining information concerning molecular of solute dynamics, etc.

Broadening of the hydrogen fluoride R4 ((nu) equals 0 - 2) absorption line by N₂ measured with 1.3 micrometers diode laser was studied. Line parameters (Doppler and Lorentzian half widths, line strength) have been extracted by the least-squares fitting with Voigt function. The spectrum of frequency fluctuations was modeled and its parameters were determined. The line parameters have been improved by taking into account the influence of the diode laser frequency fluctuations.

I t i 5 we 1 1 known t hat the spectral 1 i ne shape i s def i ned as F(w) = :f P(WWjf)I<fXi<I (1) where i,f denote the initial and final states of the absorbing system, w= wi_ W is the transition frequency, X is the dipole moment operator, p is the density matrix of the system. The system under consideration is the molecular gas in a volume treated as a unified quantum-mechanical object. It can be seen from Eq. ( 1 ) that the 1 me shape is the result of stat ist ical averaging of the delta-function of the argument representing the energy conservation law under the absorption. For calculating F(w) the exact state energies and wave functions of the system or, after transition to the binary approximation, the wave functions and states of two interacting molecules and the characteristics of the statistical ensemble should be available. Usually the expression describing F(c) in term of the correlation function c(t) is used in calculat ions

When molecular collisions are the principal line broadening mechanism the absorption at line centers and in the line wings can be calculated in impact approximation that provides the Lorentz contour for well separated lines. Apart from such lines there are regions in the IR spectra with very dense line structure (Q-branches or band heads for example) where band shape can not be expressed as the sum of Lorentzian lines. These deviations have generally been attributed to line mixing effects. We present here a theory which can be used in shape calculation of overlapped lines if the intermolecular potential is known. The quantum mechanical methods are developed for a limited number of systems and are usually too difficult to be used because of very complicated computations. Instead of this we have used the semiclassical method which can be treated in the simple model representation. The classical impact theory of shape was the basis of our method and then we modernized this theory to apply to a molecular system with discrete spectra. We shall consider here the case of the band shapes for linear molecules.

The absorption coefficient o(w) for the nonpolarized radiation in the isotropic medium is cz(w)-'—Am p(2K+1) { (llK)* P'f+ P// (TLK) R;jf } (1) i:f j'f' where is the reduced matrix element of the resolvent operator I f';if (ilK) _ 1 RjIfI;jf (UK) (UK) w-L —A,, S j f .if L11 and A11 are the matricies of reduced elements of the Liouville and relaxation operators, which are defined in the line space of the absorbing molecule. The diagonal elements of the relaxation operator define the half widths and shifts of the individual lines, the nondiagonal elements are the cross-relaxation parameters responsible for the line mixing. Within the framework of impact approximation the relaxation operator is I' = 1bJd()Tr {[i U(oo_co)] b} (3) where is the thermal bath density and U(oo,-co) is the scattering operator in the combined Liouville space of the absorbing molecule and the bath particle. The averaging is performed over the bath particle states and the classical path parameters. In general the halfwidth and the shift are to be calculated simultaneously, however, usually the former is taken from the experiment or from the isolated line approximation calclations. To calculate the crossrelaxation parameters different models ' or the infinite order sudden approximation method which has only limited application in the molecular spectroscopy, are used.

At pressures about 1 atm well separated rotational-vibrational lines of a gas have Lorentzian shapes. When the lines superimpose the absorption coefficient deviations from the sum of Lorentzian contours are often observed especially in tine wings. These deviations are usually explained by the line mixing effects which can be calculated for the central parts of bands using the impact approximat ion. In this approximat ion the transformat ion of the band shape with pressure is determined by the relaxation Γ-matrix structure.

Great attention of investigators has been recently paid to studying of collision induced line coupling effects (spectral line interference) in vibrational-rotational spectra of atmospheric gases.

The absorption coefficient at a given frequency can be roughly represented as a sum of two terms. One of them accounts for absorption at the nearest line and another represents some background due to absorption at a distant line. This intuitive representation has been used for a long time, especially in studies of the absorption by water vapor. In this case, probably for the first time, special term was introduced for the second term, namely, the continual absorption. The contributions of these two constituents in one and the same spectral region can drastically vary under different thermodynamic conditions.

The values of absorption coefficient κ in the wings of the infrared CO₂ Q-branches significantly differ from those isolated Lorentzian lines. It becomes now traditional to explain these deviations by line-mixing. Actually, presence of the small line separations in the Q-branches are greatly conductive to this point of view. It can be noted, however, that the largest deviations from the Lorentzian line calculations are observed in spectral regions comparatively far from the line centers. Therefore it would be interesting to know whether the line wing theory can be used to describe the observed frequency dependence of κ or not. The present study concerns with the CO₂ Q-branch at 1932cm^-1.

The results of spectral line intensity measurements at resonant frequencies and line shape measurements in the range 54 - 65 GHz are presented. The temperature dependence of oxygen line intensity is studied in the 5 mm band. Experimental data are in a satisfactory agreement with results of theoretical calculations.

While investigating density transformation of middle-IR and far-IR spectra of hydrogen fluoride-xenon gas phase mixture, we discovered the xenon-broadened HF vibrational- rotational lines in the band 1 - 0 to be distinctly asymmetrical, and their broadening coefficients to be the greater in comparison with pure rotational ones the greater J-values are. Previously, the similar effect was observed for argon broadened HF lines. It is collisional perturbation of vibrational motion whose influence on line shape formation is essential in these cases. To reconstruct vibrational line shape, i.e., to characterize vibrationally excited molecular dynamics in dense media, it is necessary to obtain rather accurate absorption data concerning pure rotational line shapes. Recently we have determined pure rotational line shape parameters of xenon-broadened HF lines. Symmetrical Lorentz line shape was assumed because no experimental evidence for asymmetry of pure rotational lineshapes has been obtained. Later we found in some additional researches the symmetry of pure rotational line shapes of hydrogen fluoride broadened by xenon and nitrogen in gas phase at room temperature.

The CO-laser radiation absorption by water-vapor and its mixtures with nitrogen was measured at 26 laser lines in the range from 1906.26 to 1788.40 cm^-1 at temperature Q = 296 +/- 1 K and different partial pressures of H20 and N2 at the optical paths from 2 to 78 m.

The calculations of self-induced H₂O line shift are necessary to determine accurately the position of line center with the different buffer gases, particularly for the reper lines and for the lines in microwave region. The calculations of self-induced H₂O line shift also can be used as the additional test of our calculation method and its predicting capacity because the polarizability of water molecule for 301 vibrational state has been defined in advance from the measured line shifts by air pressure. The calculation method based on Anderson-Tsao- Curnutte (ATC) theory was presented and tested using line shifts by pressure of nonpolar molecules.

The values of broadening and shift coefficients induced by H₂ pressure for the H₂O absorption line centered at 694.38 nm (4₁₄-5₁₅ transition of 000-103 band) were measured. A nonlinear character of the H₂O absorption line center shift dependence on H₂ pressure at its increase beyond 450-500 Torr was experimentally revealed.

Great interest to investigations, both experimental and theoretical, has recently been revealed to the shift of the centers of vibration-rotation absorption lines of atmospheric gases by nitrogen, oxygen and air pressure. A comparison of shift coefficients calculated using Anderson theory with the experimental values gives satisfactory results , but it is clear that the method of calculation has to be further developed to take into account the corrections for trajectories curvature or short range forces contribution.

IR absorption in the region of forbidden molecular transitions is usually considered to be determined by collision-induced mechanisms. Most frequently the absence of any structural features superimposed on the collision-induced background is interpreted as an evidence of the negligible contribution of the bound dimer states. However, in some cases the most important statistical weight belongs to metastable states, rather than bound ones. In general, the dimer molecules highly excited above the dissociation limit have to be considered as metastable molecules. The contribution of metastable molecules to collision-induced absorption must correspond to the portion of the phase-space they occupy and therefore could be considerable. The goal of this paper is to interpret the collision-induced absorption in compressed carbon monoxide as a sum of bound and quasibound dimeric contributions.

The purpose of this paper is an obvious interpretation of complicated fluorescence spectrum, including both discrete and continuous regions, and relating this picture with the geometry of molecular terms.

The problem of a two-level system perturbed by a strong resonant bichromatic field was examined theoretically and later experimentally in the microwave region. The two-level model can be inadequate in the optical region, for example in sodium vapors due to the fine structure of the upper state. The two-level model fails for barium vapor when the linear polarizations of bichromatic fields are different. Consequently, the theoretical investigation of the multilevel case can be a problem of great interest.

Only for optically thin layers and plane waves may the intensity of a light wave be unambiguously expressed in terms of the nonlinear susceptibility of the medium. In aperture limited light beams the saturation parameter and the Stark shifts are local variables, while the output intensity of the pump and probe beams is an integral characteristic of the transmission process. The output spectrum is affected by diffraction, nonlinear refraction, and saturated absorption. The nonlinear refraction is a cause of a spectral line asymmetry which is well- known in saturation spectroscopy. In addition to usual line broadening, the saturated absorption causes specific beam effects, related to the formation of a self-induced transparency channel. The diffraction of the beam due to this self-induced aperture may result in the enhancement of the on-axis intensity, which is not a result of the self-induced lens effects. All these factors are taken into account by the mathematical model suggested in the present work. The propagation of the near-resonance saturating pump and non-saturating probe beams of various initial profiles through a homogeneously broadened two-level gas is simulated numerically. The calculations carried out make it possible to analyze the contribution of the propagation phenomena, mentioned above, to the output spectra of the beams.

One of the optical problems of quantum optics is interaction of an atom or molecule with a strong harmonic electrical field. It has acquired a new importance in connection with a deep ani6interesting phenomenon of dynamical chaos discovered in this systems lately. This phenomenon take place only in nonlinear systems. The conception of "nonlinear systems" is widespread in quantum mechanics. But first of all it is necessary to attract attention to one important point : the equat ions of quantum mechanics are 1 inear in a rigour statement of a problem, but they might be nonl inear in phenomeno logical theories such as Ginzburg-Landau theory of superconductivity. The nonlinearity of equations of quantum mechanics relative to the electric field or other characteristics of the Hamiltonian can not lead to bifurcations and thus to the dynamical chaos . Therefore the quantum chaos , i . e. the dynami cal chaos in quantum systems, can take place only in the classical limit in which the appropriate equations are nonlinear.

The subject of this work is the accurate mathematical algorithms of absorption solar radiation by the earth's atmosphere and a description of the scattering processes. These algorithms are based on a combination of the Monte-Carlo method used for scattering simulation, and the line-by-line accurate accounting for the selective gaseous absorption on the basis of Spectroscopic Data Compilation Atlases.

The first results on simultaneous measurements of carbon oxide and carbon dioxide in expired air with the help of tunable diode laser spectroscopy are presented. Exact preliminary data on high resolution absorption spectra of these gases in 4 - 5 microns spectral region provides a simple technique for such investigations. Application of tunable diode lasers for the analysis of human exhalation ensures high sensitivity, accuracy, and a fast rate of measurements; it could therefore be promising as a new method for medicine diagnostics.

In this work the atmospheric transmission spectra T equals f((lambda) ) were determined experimentally by the balloon experiments in the region of 8.0 - 12 micrometers with resolution about 5 cm^-1. The balloon-borne spectrometers have three optical channels. Two channels are used for simultaneous registration of two solar spectra, the third one serves for the uninterrupted registration of the solar intensity during all the time of the flight in the two narrow spectral regions (0.02 micrometers ) obtained with the use of the interference filters at (lambda) equals 0.5 micrometers or (lambda) equals 0.8 micrometers . All the measurements were performed during lifting the apparatus at the positive sun heights h_radii > 0 and during gliding at altitude about 30 km firstly at the positive and then at the negative solar heights.

The differential absorption method is the best one from the point of view of its potentialities in applications to solving the problems of sensing atmospheric gaseous pollutants. The middle IR spectral range from 2 to 14 micrometers is most attractive for measurements since well-resolved absorption spectra of almost all the atmospheric gases are observed here. This paper presents some results of monitoring several trace atmospheric constituents, including CO, C₂H₄ and NH₃ using a gas analyzer, based on the use of two CO₂ lasers and a set of frequency converters. The gas analyzer with a discretely frequency-tuned CO₂ laser was taken as the basic device for this study. Use of a ZnGeP₂ monocrystal for frequency doubling enables one to measure CO concentration in addition to concentrations of ethylene, water vapor, ammonia under field conditions.