In this paper recent experiments with the one-atom maser or micromaser are described. They deal with the dynamical behavior of the field at parameter values where the field undergoes phase transitions. In the second part of the paper experiments with a single laser-cooled In⁺ ion in a modified Paul trap are discussed. The aim of this experiment is precision spectroscopy and cavity quantum electrodynamics on the basis of quantum jumps.

We have achieved the first realization of a single atom microlaser, a laser oscillator with only one atom in an optical resonator. In the experiment a beam of two-level barium atoms traverses an ultrahigh Q single-mode cavity. The atoms are inverted by a (pi) -pulse field before they enter the cavity. Laser oscillation ((lambda) equals 791 nm) has been observed, with the mean number of atoms inside the mode <N> as small as 0.1, resulting in the mean number of photons in the mode <N> or 0.14. To understand the results quantitatively we used a fully-quantized one-atom microlaser theory adapted from its counterpart micromaser theory. The present theory was found to be in good agreement with the data for small <N> and <n>. Discrepancy between experiment and theory was observed for <n> very much greater than 1 and <N> approximately equal to 1. This discrepancy may be explained by the standing-wave nature of the cavity mode, in combination with the saturation effect occurring at large cavity photon number, as well as by the breakdown of single-atom interaction assumption in the theory for <N> greater than or equal to 1.

Paramagnetic impurities tapped in solid helium matrices are a new experimental sample with outstanding physical properties. One of the most challenging applications of paramagnetic atoms embedded in solid helium is the search for P- and T-violating permanent atomic electric dipole moments. Prerequisites for such an experiment are among others the achievement of a high degree of spin polarization by optical pumping, a long spin relaxation time and the efficient detection of electron spin magnetic resonance. In the present paper we present preliminary results along these lines. We also show that the technique of optically detected magnetic resonance is an efficient tool for the investigation of matrix effects due to anisotropies of the local trapping sites.

The first experimental observation of the sisyphus cooling in an evanescent light wave was carried out. We have observed a reduction of the transverse energy of Na atoms in a beam upon its reflection from the evanescent light wave, associated with the optical pumping between sublevels of the hyperfine structure of the atomic ground state. The initial transverse momentum of 42 $HBARk has been reduced to 28$HBARk in a single reflection event.

We have used matrix continued fraction methods pioneered previously, to solve essentially exactly for the dynamics of the one ⁸⁵Rb atom micromaser. A range of cavity Q values and of average atomic input rates R equals T_p^-1 and of atomic interaction times t_int is studied. For T_p approximately greater than 200t_int the system does evolve to a steady state. And even Q equals 5 multiplied by 10¹⁰ and temperature T equals 0.070 degrees K are apparently insufficient to avoid evolution to a steady state with finite variance of the cavity field when t_int equals 1.54/44 kHz unless T_p is also substantially reduced. Only in this way are actual trapping state dynamics obtained. The field variance v is not a good diagnostic for observing such trapping state dynamics.

In this work we present an investigation of velocity-selective coherent population trapping (VSCPT) in asymmetric three-level schemes. The light force in such schemes is of an intrinsically transient character and should not be described in a quasiclassical approach. Instead, results of the full quantum-mechanical calculations are presented with emphasis on their meaning to the efficiency of subrecoil laser cooling.

We represent a new solution of the set of equations describing laser cooling of atoms by velocity selective coherent population tapping. Our solution is valid at large interaction time t in a full range of atomic kinetic momenta. Referring to this analytic expression we obtain the formula for lowest achievable temperature of cooled atoms for given experimental conditions. We demonstrate that the cooling efficiency decreases as t ^-3/4, when t is greater than or equal to (Gamma) ₁₂^-1, where (Gamma) ₁₂ is the low-frequency atomic coherence decay rate. Also the case of subrecoil laser cooling in vertical direction is examined and the gravitational force influence is estimated.

We examine the laser cooling of three-level (Lambda) -atoms in the field of two standing waves when frequency detunings are considerably greater than natural width of the excited state as well as the Rabi frequencies in the system. It is shown that at the difference of frequency detunings is small when compared to the Rabi frequencies sub-Doppler cooling of the (Lambda) -atom is possible. We present the dependence of the light pressure force on the atoms velocity and dependence of cooled atoms temperature on the parameters of the exciting waves.

We propose a trap based on an evanescent light wave which is formed on the surface of a conical or a pyramidal cavity in a glass substrate. The far blue-detuned evanescent wave acts as a mirror for atoms, bouncing on it in the gravitational field. In addition, fast and deep Sisyphus cooling in the evanescent wave can be organized for alkali atoms. This leads to the cooling of the atoms down to the recoil-limited temperature and their collection in the field- free region near the bottom of the trap, to form an atomic gas of extremely high density.

In this paper we present some new results concerning the observed anomalous frequency properties of the process of the neutral atom scattering in the standing light wave field near the reflecting mirror. The investigations were carried out using the method of scattering of the sodium atomic strip beam, intersecting at right angle the region of the standing light wave field. The standing light wave field was formed by two counterpropagating waves of resonant laser radiation -- incident and reflected from the mirror, mounted at a distance of about 1 cm from the atomic beam. The coherence length of the laser radiation was about 10 cm, that's why the interaction of atoms with the field of two counterpropagating light waves was coherent. The width of the strip atomic beam (a equals 0.02 cm) was much less than the distance to the mirror. The specific feature of the given setup is the use of pulsed laser radiation with the duration (tau) less than 1/(gamma) ((gamma) ^-1- the time of resonant level spontaneous decay), so the atoms are scattered only due to the induced light pressure force. In this paper the detailed investigation of the distance R influence on the scattering process was carried out. With this purpose the mirror was mounted at different distances from the atomic beam. (truncated)

The paper presents theoretical analysis of a Raman velocity selection of three-level atoms in a field of two counterpropagating light waves with time-modulated amplitudes. We demonstrate that in this case additional resonances appear in the atomic velocity distribution on the velocity values corresponding to the frequency of modulation. We have discussed a possible application of such coherent technique in atomic optics for efficient splitting of an atomic wave packet.

The report is devoted to the spontaneous emission of initially excited atom near the surface of semi-infinite dielectric. We predict near field effect in quantum optics which manifests itself to the fullest extent in the near zone with respect to dielectric surface and springs up under consistent description of atomic interaction in the radiation field and under consideration of spatial dielectric structure.

The motion of previously cooled atoms in a spatial grating formed by lin (perpendicular) lin laser field configuration and the static uniform magnetic field is considered in the case of F_g equals 1 yields Fe equals 1 transition. We show that in the case of high intensity laser fields (when Rabi frequency is greater than Zeeman splitting, Doppler shift, natural width, and detuning) atoms are captured in long-lived coherent population trapping (CPT) state while heating, incoherent photon scattering, and atom-atom photon exchange are strongly reduced. The frequency, the damping time of oscillation, and the localization size are obtained for atoms moving near the bottom of potential wells in the frame of harmonic approximation. Narrowing of vibrational spectral lines due to the CPT-effect is predicted.

The effect of P-odd atomic spin rotation in a laser wave with a finite linewidth is considered. We have shown that laser linewidth is the major source of relaxation, limiting the available value of the spin rotation angle. A project of an atomic beam experiment to observe P-odd atom spin rotation is proposed. It is shown that such an experiment would provide better sensitivity than that of the previous ones.

We show that an ensemble of atoms in highly excited states with narrow center-of-mass momentum distribution (cold Rydberg atoms) can be obtained with velocity-selective (pi) - pulses and laser cooling by velocity-selective coherent population trapping (VSCPT). Both methods use three-level cascade systems with the uppermost state being the Rydberg one where the atoms are excited and cooled. Very high fraction of atoms can be cooled to subrecoil temperatures by the use of VSCPT in standing light waves.

Cold atomic clouds were used as a nonlinear medium to reduce the quantum noise of a continuous-wave laser field. The cold atoms were placed in a resonant optical cavity. Quadrature squeezing as high as 40% was measured at the output of the cavity.

We consider polarization-squeezed (PS) light generation in anisotropic homogeneous Kerr medium. The fluctuations of the Stokes parameter either S₂ or S₃ are suppressed in PS light. The influence of initial light depolarization on the fluctuation suppression of the Stokes parameters is analyzed. We show the possibility to transform PS light into light with sub-Poissonian statistics by linear conversion (phase plate and analyzer). The quantum properties of the SH generated by frequency doubling of the PS light are investigated.

Relation between the photon correlations in elastic and non-elastic scattering of light and the statistical properties of fluctuations which initiate this scattering is considered. The cases of scattering by dust particles and by ultrasonic waves are investigated experimentally.

Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-II spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in simple beam-splitter (Hanburry Brown-Twiss) anticorrelation and quantum beating experiments. The cancellation of two-photon probability amplitudes as a result of this double entanglement allow us to demonstrate two different types of Bell's inequality violations in one experimental setup.

Some aspects of nonstationary Casimir effect are discussed. A general approach to particle creation in nonstationary conditions is formulated. Statistical properties of nonclassical states which may be related to nonstationary Casimir effect are reviewed.

Solid state laser sources, such as diode-laser pumped Nd:YAG lasers, have given us a cw laser light of high power with unprecedented stability and low noise performance. In these lasers most of the technical sources of noise can be eliminated and thereby allow operation close to the theoretical limit set by the quantum properties of the light. We present progress in the experimental realization of such lasers. These investigations include the control of noise by electronic feedback, passive external cavities; and the reliable generation of amplitude squeezed light through second harmonic generation. At the same time we have developed theoretical models describing the quantum noise properties of coupled systems of lasers and cavities. The agreement between our experimental results with noise spectra calculated with our realistic theoretical models demonstrates the ability to predict the performance of various laser systems.

A nonlocal two-photon quantum effect which surprisingly shows some features analogous to geometrical imaging optics is observed. The remote transfer of two-dimensional analog information with a high degree of security (quantum 'cryptoFAX') is demonstrated.

Light generation, amplification and detection are always followed by noise. Technical noise can be reduced, while quantum noise is unavoidable. In lasers the quantum noise appears as Poissonian fluctuations of output intensity and as a natural width of emitted spectrum. In optical amplifiers the quantum noise appears as a spontaneous emission and may cause a degradation of signal-to-noise ratio. In this paper we present a new type of optical amplifier and oscillator based on light modulation (without stimulated emission). Amplification process in these devices consists of two steps: at first, the input light spectrum is shifted into radio frequency range by a heterodyne photoreceiver, then the amplified rf signal is converted back into initial optical frequencies by means of modulation. The quantum noise in such an amplifier originates from shot noise of a heterodyne photoreceiver. The limitations due to shot noise are studied theoretically and experimentally. Although the physical mechanisms of quantum noise in stimulated emission and heterodyne conversion are different there is deep analogy in resulting equations. When the output of modulation based amplifier is partially transmitted to the input a self-oscillation of the device has been observed. The oscillator is considered as laser light transformer. It may operate as an external frequency or/and intensity stabilize of laser light, which requires no feedback to the laser source.

The non-zero rest mass of confined photon exists due to the standing component of the field and originates from the work performed in opposition to the light pressure of zero-point vacuum fluctuations at raking them together from the free unlimited space (say, into a waveguide or cavity mode).

Quantum cryptography is a new, multidisciplinary technique of distributing information to two or more parties in such a way that can guarantee security against an unauthorized eavesdropping attempt. In the presented paper three schemes of implementation of this goal by means of fiber optics, namely a scheme based on photon polarization, delayed interferometry, and quantum correlations of nonorthogonal states, are discussed. Realization of the proposed schemes is discussed as well as fundamental limits imposed on quantum cryptography by fiber-optics technique.

We discuss the method of parametric excitation of electromagnetic waves in a cavity by creation of a dense plasma layer (which represents the 'mobile' wall of the cavity) due to irradiation of semiconductor film with femtosecond laser pulse. The effect is analyzed for the various initial states including the initial vacuum state. The state of the field produced by this method from initial vacuum state differs from electromagnetic field of another origin because only even quantum levels are populated (similar to Shrodinger cat states) and specific distribution of wave packet in phase space takes place. Besides parametrically excited field has specific angle distribution and appears in shorter time scales than ones required for appearance of radiation of another origin. The instantaneous and adiabatic slow excitation of eigenmodes of the cavity are described. The estimations for experimental detection of the effect are made.

I propose a new approach to generation of sub-Poissonian twin beams. A perturbative analysis shows that frequency dependent redistribution of fluctuations between photorefractively coupled beams results in output beams with sub shot noise intensity correlations.

Observations of unusual diffraction and interference by two-photon correlation measurements are reported. The signal and idler beams produced by spontaneous parametric down conversion are sent in different directions, and detected by two distant point-like photon counting detectors. A double-slit or a single-slit is inserted into the signal beam. Interference- diffraction patterns are observed in coincidences by scanning the detector in the idler beam.

A theory of generating nonclassical light in a ring resonator is developed. The equations of second harmonic (SH) generation are solved within accuracy of third power of coupling coefficient. The expressions for variances of the quadrature SH are obtained and discussed. The problem of applying quantum operators for field inside the resonator is investigated.

We investigate theoretically the possibility to generate squeezing by the light propagation in thin optical fiber without cover, placed into resonant nonlinear medium. The quantum description is based on the Heisenberg equations of motion for the atomic and field variables. The physical conditions for squeezing are evaluated.

A quantum optical device performing linear transformation of photon creation and annihilation operators is proposed. The action of such a linear transformer on three types of states: Fock state, squeezed and correlated state, and Schrodinger cat state is studied. The two-mode beam splitter is considered as a simple example of a linear transformer. It is shown that the beam splitter can transform subpoissonian Gaussian light into superpoissonian (and vice versa).

The problem of photon creation from vacuum in a cavity with vibrating walls is investigated. Explicit analytical solutions are found in the parametric resonance case (when the frequency of vibrations equals twice the frequency of some electromagnetic mode), both for a one- dimensional model and for a three-dimensional case. A possibility of generating hundreds and even thousands of photons in a resonance mode (with a frequency belonging to the GHz band) of a cavity with Q-factor exceeding 10¹⁰ is predicted. A significant change of the photon statistics and the rate of photons generation due to the interaction with a detector (modeled by an oscillator and a two-level atom) is demonstrated.

An experiment has been carried out in order to observe the effect of 'hidden' polarization in the multiphoton two mode coherent light. This experiment belongs to Brown-Twiss' type experiments and the observed effect was due to the intensity interference of two polarization modes of coherent light.

It is shown on the example of P-odd atom spin rotation in a laser wave that the use of squeezed light allows us to beat the standard quantum limit of parity violation measurements in atoms.

The Wigner function and statistical means are given for special one mode photon states and related generalized Schrodinger cats. The states are generated from the vacuum by exponential operators with exponents containing up to the fourth power of quadrature p. All statistical means are expressed in closed analytical form.

The resonant interaction of A initially unexcited two-level atoms with different quantum fields in a high-Q single-mode cavity (Dicke model) is studied analytically in one of the limits in which the eigenvalues spectrum of the model may be assumed as equidistant. The time evolution of atomic inversion of a single two-level atom coupled to squeezed vacuum or thermal cavity fields (Jaynes-Cummings model) is irregular. Here we show that the dynamical response of the inversion of an assemblage of A two-level atoms to such fields may be regular, i.e., may reveal collapses and revivals and that the properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields.

Hence photons and electrons obey different statistics, information features of noisy photonic and electronic channels are essentially different in quantum limit. For one dimensional channels quantum effects start to influence the information capacity when the signal power is comparable with the equilibrium noise power in a channel. Finite frequency band fermionic channels are limited in respect to the information rate growth. Bosonic channels are free of this limitation.

The calculations and experimental investigation of spontaneous scattering quantum noise influence on the statistics of energy backward SRS at the pump radiation focusing have been fulfilled. The analysis of the calculation results shows that the narrow region of pump power exists where bistable regime of BSRS conversion takes place.

We have discussed the possibilities of correlation spectroscopy (light beating spectroscopy) technique if squeezed light is used as a probe radiation for medium monitoring. The dispersion of the fluctuation of photocurrent spectrum measured in this method is expressed in terms of fourth order photocurrent correlation function. This correlation function is considered and evaluated in assumptions of photodetection theory developed by Glauber in first nonvanishing orders in interaction of probe light with the atoms of a photodetector. We show that fourth order correlation function is determined by all field TN-ordered amplitude correlation functions up to the fourth order. In case of heterodyne detection, when the light incident on photodetector surface is the mix of strong coherent modes of local oscillator wave and weak non-coherent (squeezed) modes, the observable (photocurrent spectrum) as well as its fluctuation (noise of photocurrent spectrum) is expressed in terms of spectrum-dependent Mandel parameter. We have discussed possible improvement of sensitivity limit for correlation spectroscopy in this case.

An interpretation of quantum fluctuations sources in quantum optical systems in terms of correlation of recycling times is suggested. An appropriate recycling time operator is defined. It is shown that the degree of correlation of the recycling times is a measure of the quantum feature of the field.

We have considered general polarization-sensitive correlation measurement of light intensity fluctuations based on a Hanbury Brown and Twiss interference detection scheme for probe radiation passed through angular momentum polarized atomic ensemble put into external magnetic field. The general theory is applied to the correlation spectroscopy of the atomic medium with spin ground state characterized by large relaxation times. We show and discuss the possibility of squeezing effect in transmitted light that can be caused by polarization- dependent interaction of the probe radiation with oriented atoms.

It's shown that the complex quantum structure of nonclassical superposition states is reflected in instability of resonance fluorescence driven by an optical field being initially excited into the superposition of two phase shifted coherent states.

We derive c-number Bloch-Maxwell (B-M) type equations from a quantum theory for 2-level atoms occupying a macroscopic slab-like region V of width L stimulated by a coherent-state electromagnetic field of radial frequency (omega) plus a broad-band correlated squeezed vacuum field with carrier frequency (omega) _p. The squeezed vacuum field is in principle of arbitrary 3-dimensional geometry including geometries created by an optical parametric oscillator. The c-number spatially dependent B-M equations are solved self-consistently and 'exactly' in terms of a nonlinear dispersive refractive index m((omega) ) while the slab V acts, also self-consistently, as a natural Fabry-Perot cavity of finite spacing L. Very preliminary results for optical bistability in the squeezed vacuum and more exact results for anomalous dispersion and absorption in the squeezed vacuum in linearized approximation are reported. Finally we compute the effect of the dielectric on the free-field modes of the squeezed vacuum.

It is shown that the additional irradiation of thin film of resonant atoms by squeezed light causes the bistability depending on phase of resonant coherent light.

We have calculated the 1¹S, 2¹S, and 2³S state energies of helium atom described by the nonrelativistic Schrodinger equation, and obtained (in atomic units): E(1¹S) equals -2.9037243770330010, E(2¹S) equals -2.1459740460540720, E(2³S) equals -2.1752293782367900. We have estimated the relative accuracy of the order of 10^-12 minus 10^-13 for the 1¹S and 1²S states, and 10^-15 minus 10^-16 for the 2³S state. The importance of calculations of helium for high resolution laser spectroscopy is emphasized.

Laser photoelectron projection microscope with the magnification of 10⁵ and spatial resolution of up to 30 nm has been developed. Photoelectron images produced due to the laser photoselective ionization of light absorbing centers on LiF:F₂ needle tip surface when irradiated by cw argon ion laser have been investigated and single color centers on its surface have been observed for the first time. In some experiments spectral dependence of photoelectron image on laser radiation wavelength has been observed. The results of the experiments can be regarded as a first realization of such a surface studying method which makes it possible to study the surfaces at a high spatial resolution and at the same time to identify some specific small structures in surfaces, i.e., has a high 'chemical selectivity.'

The quantum limit for resolution of small force using optical transducer displacement with coherent nonmodulated pump is proved to be less than standard quantum limit if one measures quadrature amplitude in output wave, squeezed by the ponderomotive nonlinearity mechanism. This squeezing has spectral dependence and we propose the procedure allowing to reveal it.

The quantum limit for resolution in force measurement using active interferometric optical transducer of displacement is proved to be less than the standard quantum limit (SQL) if one measures not the phase but a specially chosen quadrature amplitude in the output wave, squeezed by a mechanism of ponderomotive nonlinearity. Consideration of two types of active transducer having three-level atoms gain and parametric gain is given. Noises of spontaneous emission, fluctuations due to losses in mirrors and effect of radiative friction are taken into account.

The possibility of formation of polarization-squeezed light in the case of the interaction of two orthogonally polarized waves in the spatio-periodical Kerr medium is considered. It is shown that at the output of such a nonlinear medium fluctuations of one of the Stokes parameter can be less than ones incoherent state. For the first time a procedure of quantum nondemolition measurement (QND) of the Stokes parameters of light is offered and analyzed.

A simulation scheme for the photodetection process of two-mode fields with the continuous measurements of one and both modes is presented. Continuous reduction of the two-mode field during the measurement is described. Analytical expressions for statistic characteristics of the monitored radiation are obtained.

High sensitive polarization-modulation microscopy of transparent objects with the use of single mode squeezed light and spatially multimode squeezed light is discussed. Criterion for the evaluation of threshold sensitivity and resolving power of polarization measurements is suggested.

We demonstrate the quality factor Q equals (0.8 plus or minus 0.1) multiplied by 10¹⁰ of whispering-gallery modes in fused silica microspheres at 633 nm, close to the limit determined by fundamental material attenuation. The lifetime of ultimate Q is limited by adsorption of atmospheric water. Optical effects of adsorption are investigated and conditions for fabrication of long-lifetime microspheres are clarified.

We present the simple and very effective radio frequency lock-in technique for precise measurements with cw-pumped mode-locked lasers. The technique is applied for the photodeflection transient spectroscopy that allowed to reach the sensitivity to surface displacement about one femtometer. We use the method for probing hypersound generation and propagation in a semiconductor plate.

For the first time depolarization degree of the diode-pumped monolithic ring Nd³⁺:YAG laser has been measured. The obtained value of depolarization degree equals 3 (DOT) 10^-3. It has been shown that the dominant mechanism of the intracavity losses and the output light depolarization is diffraction on random inhomogeneities of birefringence in the laser media.

Here is theoretical research and experimental implementation of systems to change the polarization state of light with wave length tuning. The systems consist of several birefringent plates with different orientation.

The results of photon flux noise measurements in a quantum well semiconductor laser with 1.3 micrometer wavelength and antireflection coating on the front surface are presented. The results are compared with the theory based on quantum mechanical Langevin-Heisenberg equations.

One of the main challenges in the development of the MSM PD (metal-semiconductor-metal photodiode) structures is to obtain a short impulse response. The time-dependent behavior can be best studied in terms of device simulations. We analyze the performances of GaInAs interdigital MSM PD structures by simulating the electron and hole movement with a two- dimensional self-consistent time-dependent technique. The model provides a clear understanding of high-speed dynamic processes in structures with micron and submicron spacing. Several ways of improving the high-speed impulse response of GaInAs MSM PD are proposed.

The optical train and design of an automated two-coordinate laser polarization interferometer to measure linear displacements in the nanometer range are discussed. The interferometer can be used for two-coordinate measurements of displacements of the needle of scanning tunneling or atomic-force microscopes in the study of surface topology.

The new method and new set-up are developed for accurate (approximately 1 divided by 5%) measurement of the width of submicrometer structures (slit, groove, wire). The method is based on the measurement of the shifts of the interference fringes depending on the width of structure. The interference pattern is obtained by interference of the diffracted beams in a two- beam interferometer. The comparison of the shifts of the fringes from reference and investigated width is made.

The method of the response interpretation of heterodyne differential phase microscope (HDPM) to submicron groove has been developed. The proposed procedure is based on an expansion of the averaged reflection coefficient in terms of object shape function moments. These moments define the major profile parameters (width, depth, etc.). Two types of a groove were considered: a groove with a geometric profile in homogeneous material and a phase groove in heterogeneous material. The influence of object parameters and a transfer function on the phase response of the microscope has been studied. It has been shown that the limiting lateral resolution may reach 0.1 micrometer if a signal to noise ratio (SNR) exceeds unity. The fluctuation limit of lateral resolution runs to 0.02 micrometer according to our estimation. The sizes of a 0.4 multiplied by 0.06 micrometer squared groove in magnetic video-recording head have been experimentally determined.

We review the ways of performing super high resolution optical microscopy of opaque samples using surface electromagnetic waves (SEW) for the cases when the light signal is detected in the near or in the far field. An immersion method of SEW excitation is presented. The method enables one to perform the superhigh resolution SEW-microscopy of conducting and semi conducting opaque sample surfaces.

A new interferometric method for control of refractive index distribution in a plane-parallel section cut from a gradient-index (GRIN) lens blank is described. It uses a standard double- pass interferometric scheme modified to provide single passing of the beam through the investigated GRIN sample. The two-dimensional dependence of refractive index in transverse dimensions along the sample surface is measured with the accuracy better than 1 multiplied by 10^-4.