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Showing papers on "Light field published in 1994"


Journal ArticleDOI
TL;DR: In this article, the light field in coastal sediments was investigated at a spatial resolution of 0.2-0.5 mm by spectral measurements (450-850 nm) of field radiance and scalar irradiance using fiber-optic microprobes.
Abstract: The light field in coastal sediments was investigated at a spatial resolution of 0.2-0.5 mm by spectral measurements (450-850 nm) of field radiance and scalar irradiance using fiber-optic microprobes. Depth profiles of field radiance were measured with radiance microprobes at representative angles relative to vertically incident collimated light in rinsed quartz sand and in a coastal sandy sediment colonized by microalgae. Upwelling and downwelling components of irradiance and scalar irradiance were calculated from the radiance distributions. Calculated total scalar irradiance agreed well with the scalar irradiance measured directly by a fiber-optic scalar irradiance microprobe. Close to the sediment surface, the light field was highly anisotropic, dominated by incident collimated light, and the scalar irradiance reached a maximum of 200% of incident scalar irradiance. Below the sediment surface, the light field became diffuse with a forward-biased angular light distribution. A few millimeters into the sediment surface, attenuation coefficients of field radiance, irradiance, and scalar irradiance became identical and independent of depth, indicating that the light field approached an asymptotic radiance distribution. Comparison of light fields in wet and dry quartz sand showed that the lower refractive index of air than of water caused a more forward-biased scattering in wet sand. Light penetration was therefore deeper and surface irradiance reflectance was lower in wet sand than in dry sand. The higher reflectance of dry sand resulted in a higher surface maximum of scalar irradiance. Asymptotic values of average cosines and attenuation coefficients were used to calculate the absorption coefficient in quartz sand and in a coastal sediment with diatoms. Absorption coefficients ranged from 2.5 mm-’ at 450 nm to 1.5 mm-i at 850 nm in the coastal sediment and from 0.8 to 0.4 mm-l in wet quartz sand. Both attenuation spectra and absorption spectra of the coastal sediment with diatoms exhibited a Chl

169 citations


Journal ArticleDOI
TL;DR: In this new technique for mechanical manipulation of atoms, spontaneous emission is suppressed since the atoms evolve in a ``dark'' state that follows the light field, which means that the phase coherence of the atom is preserved so that this technique is useful in the realization of coherent atomic beam splitters and mirrors.
Abstract: We have observed transfer of momentum and ground state population in laser-cooled cesium by adiabatic following of a slowly evolving light field. In this new technique for mechanical manipulation of atoms, spontaneous emission is suppressed since the atoms evolve in a ``dark'' state that follows the light field. This means that the phase coherence of the atom is preserved so that this technique is useful in the realization of coherent atomic beam splitters and mirrors. Our experimental results are in good agreement with optical Bloch equation calculations.

91 citations


Journal ArticleDOI
TL;DR: The dipole force experienced by an atom in a nonresonant spatially inhomogeneous light field is quantized by the discrete nature of the photon by studying the scattering of slow atoms that pass in the evanescent field of a microsphere whispering gallery mode.
Abstract: The dipole force experienced by an atom in a nonresonant spatially inhomogeneous light field is quantized by the discrete nature of the photon. We propose to detect this quantization by studying the scattering of slow atoms that pass in the evanescent field of a microsphere whispering gallery mode. This constitutes an inverse Stern-Gerlach experiment in which the atomic deflection is correlated to the state of the scattering field.

63 citations



Journal ArticleDOI
TL;DR: A study of the mechanical equations of motion suggests an explanation of the very short time scale in terms of oppositely directed field pressures and the speed of light.
Abstract: The electromagnetic field is assigned a self-consistent role in which abrupt slowing of the collapse produces radiation and the pressure of the radiation produces abrupt slowing. A simple expression is introduced for the photon spectrum. Conditions for light emission are proposed that imply a high degree of spatial localization. Some numerical checks are satisfied. A study of the mechanical equations of motion suggests an explanation of the very short time scale in terms of oppositely directed field pressures and the speed of light.

36 citations


Proceedings ArticleDOI
09 Oct 1994
TL;DR: A portable polarimeter that analyses the linear polarization characteristics of a full image on a single pixel basis is constructed by placing two twisted nematic liquid crystals and a fixed polarizing filter in series in front of a CCD camera.
Abstract: The natural light field has long been known to be partly linearly polarized, and it has been suggested that various objects reflect light that is polarized at a specific orientation. Although humans use polarized light, our inability to see it limits our study and understanding of its distribution in nature and of the information it carries. By placing two twisted nematic liquid crystals and a fixed polarizing filter in series in front of a CCD camera, we constructed a portable polarimeter that analyses the linear polarization characteristics of a full image on a single pixel basis. Two configurations are presented: an autonomous sensor that uses a small camcorder for recording images that are analyzed at a later stage; and an online sensor that uses a digital camera connected to a personal computer which controls and analyses the information. Field measurements reveal possible usage for analyzing spatial orientation of objects or breaking color camouflage. Our new polarimeters provide an opportunity to inspect and understand an aspect of the visual world, currently obscure to our eyes.

35 citations


Journal ArticleDOI
TL;DR: This simple laboratory experiment has several advantages over equivalent direct-detection schemes and has been shown to yield experimentally the theoretically predicted factorial intensity moments that result from zero-mean, circulo-complex Gaussian statistics.
Abstract: In heterodyne detection (such as in coherent lidar) the optical local oscillator defines a single mode of the incoming-signal light field; this single-mode selectivity has been previously predicted to preserve the full fluctuation character of scattered light. This is in contrast with direct-detection schemes, as in photon-correlation spectroscopy, where aperture averaging usually reduces the range of fluctuations. Examples of Gaussian and non-Gaussian statistics in laser light scattered from a moving ground-glass screen have been studied. This simple laboratory experiment has several advantages over equivalent direct-detection schemes and has been shown to yield experimentally the theoretically predicted factorial intensity moments (up to the seventh order) that result from zero-mean, circulo-complex Gaussian statistics.

20 citations


Journal ArticleDOI
TL;DR: In this article, the authors demonstrate a new technique for the mechanical manipulation of atoms with light that may be used to deflect or split an atomic beam, which depends on the existence of an internal superposition state of the atom that is "dark" to resonant excitation by a particular light field.
Abstract: We demonstrate a new technique for the mechanical manipulation of atoms with light that may be used to deflect or split an atomic beam. This technique depends on the existence of an internal superposition state of the atom that is 'dark' to resonant excitation by a particular light field. An atom in a dark state may adiabatically follow a slowly varying light field in such a way that both the internal state and the atom's momentum are changed. Because the dark state never absorbs or fluoresces, the atomic coherence, necessary for atom interferometry, is preserved. We use laser-cooled Cs atoms to demonstrate the transfer of 8 photon momenta from the slowly varying laser field to the atom.

13 citations


Journal ArticleDOI
TL;DR: In this article, the authors used a heterodyne detection technique to observe the intensity fluctuations and statistics of non-Gaussian scattered light, formed by illuminating a rotating ground-glass screen with a tightly focused laser beam.
Abstract: We have used a heterodyne detection technique to observe the intensity fluctuations and statistics of non-Gaussian scattered light, formed by illuminating a rotating ground-glass screen with a tightly focused laser beam. This type of light field contains the characteristic ‘glints’ commonly observed with laser radar systems. It is demonstrated both theoretically and experimentally that the statistics of the fluctuating intensity are significantly altered by spectral filtering of the light. In the limit, when the filter bandwidth becomes much narrower than the overall spectral linewidth of the scattered light, the distribution of intensities tends to that expected for complex Gaussian field statistics (i.e. a negative exponential). We compare this behaviour with that obtained by other workers for spectral filtering within the linewidth of light from a single-mode laser.

11 citations


Journal ArticleDOI
TL;DR: In this paper, a new technique called single-mode matching is proposed to suppress the background scattering by matching the refractive indices of the matrix and the confined liquid, but this restricts the applicability to a handful of suitable model systems.
Abstract: Brownian motions in porous media represent a challenging problem not only from a theoretical but also from an experimental point of view. A very powerful technique for the measurement of Brownian motions is Dynamic Light Scattering (DLS). For our problem, however, the classic version of DLS is useless because the porous matrix scatters very strongly and the particles to be measured are completely masked. Sometimes it is possible to suppress the background scattering by matching the refractive indices of the matrix and the confined liquid, but this restricts the applicability to a handful of suitable model systems. We have introduced a new technique which overcomes this difficulty: The keyword is single-mode matching and the idea is to select from the complicated random light field generated by the strongly scattering medium only a single mode so that the contribution from the matrix to the selected mode vanishes because of destructive interference. The first experimental results on the dynamics of latex particles in aqueous suspensions confined in a packing of glass beads are very promising. Their quantitative analysis demonstrates clearly the feasibility of measuring the diffusion coefficient within an opaque strongly scattering porous medium.

9 citations


Journal ArticleDOI
TL;DR: In this article, a quasiclassical approximation of the Schrodinger equation for the electron affected by both Coulomb and light fields under an assumption about slow angular motion is found.
Abstract: In a quasiclassical approximation analytical solutions of the Schrodinger equation are found for the electron affected by both Coulomb and light fields under an assumption about slow angular motion. The applicability conditions of these solutions and approximations are evaluated. The solutions are shown to be valid in a range of light field strengths that includes both weak- and strong-field regions. The quasiclassical Coulomb-Volkov wavefunctions found are used to describe strong-field ionization from Rydberg levels. The theory predicts a qualitatively new behaviour of the ionization rate and of the strong-field atomic quasienergies in their dependence on the light field strength amplitude epsilon 0. In particular, multiple stabilization and destabilization regions following each other are predicted.

Proceedings ArticleDOI
26 Oct 1994
TL;DR: In this paper, a Monte Carlo program was developed to calculate the complete four component Stokes vector for a coupled atmosphere-ocean system which also includes Raman scattering as well as a stochastic interface.
Abstract: We have developed a Monte Carlo program to calculate the complete four component Stokes vector for a coupled atmosphere-ocean system which also includes Raman scattering as well as a stochastic interface. Since the input to this program requires Mueller matrices for all scattering processes as well as the interface we had to derive the correct Mueller matrices for both Raman and elastic fluctuation scattering. We were then able to calculate the radiance, degree of polarization, orientation of the polarization ellipse, and the ellipticity of the radiation field at various levels within the ocean as well as just above the ocean surface. We found that the effect of Raman scattering on the polarization of the light field within the ocean is significant and can be detected by making polarimetric measurements within the ocean.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Book ChapterDOI
TL;DR: In this article, the authors considered the deflection and focusing of atoms in a quantized light field and proposed a method to create narrow atomic wave packets by focusing atoms in the light field.
Abstract: We consider the deflection and focusing of atoms in a quantized light field We study the influence of spontaneous emission on the deflection pattern and propose a method to create narrow atomic wave packets A possible experiment is suggested

Proceedings ArticleDOI
26 Oct 1994
TL;DR: In this article, the authors modeled the light field in reflective tube type absorption meters with Monte Carlo methods and calculated the radiance attenuation as a function of the field of view for several variants of a reflective tube absorption meter.
Abstract: The light field in reflective tube type absorption meters was modeled with Monte Carlo methods. The entrance light field was varied and the systems geometry was varied together with the inherent properties of a test medium. This enabled us to calculate the radiance attenuation as a function of the field of view for several variants of a reflective tube absorption meter. It was found that an instrument with a Lambertian entrance light field and a small field of view measures the sum of absorption and backscattering with an error less than 2 - 5%. This result is independent of the shape of volume scatter functions for surface water. For small fields of view the reflectivity of the cylinder was found not to be critical.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: In this article, a non-linear geometrical model of the probe beam wavefront due to scattering on the thermal lens, which is induced by a pump light field, is proposed.
Abstract: Distortions of the probe beam wavefront due to scattering on the thermal lens, which is induced by a pump light field, are calculated using a non-linear geometrical model. It is shown that when the probe beam light spot is larger than the pump field one, the initial Gaussian distribution of intensities becomes ring shaped. When the probe beam diameter is smaller than the pump field one, the initial Gaussian distribution remains almost Gaussian. The predicted effects are confirmed by a calculation that takes into account the diffraction effects at the far field. Experimental evidence for the effect is shown for the case of light propagation through an ethanol solution of iodine.

Proceedings ArticleDOI
10 Oct 1994
TL;DR: In this article, the amplitude and intensity of the diffracted light field for the incident plane wave light were derived by a 3D grating layer with rectangular cells, using the method of 4D Fourier spectra.
Abstract: The notion that color effects in human vision can be explained as diffraction of light by the 3D grating of retina cells was first proposed by N. Lauinger. To study this new diffraction theory of human vision, we solve the wave equation for light diffraction by a 3D-grating layer with rectangular cells, using the method of 4D Fourier spectra. In the case of weak interaction, we derive analytical expressions for the amplitude and intensity of the diffracted light field for the incident plane wave light. The bandwidth of the diffracted light intensity curves is defined by the width of the grating layer, the size of the grating cells, and the grating period. We show that the geometry of the diffracted light is reciprocal with respect to the geometry of the 3D grating. We compute the wavelength dependence of the diffracted light intensity for incident collimated white light for various geometries of the grating layer and the incident light. Within the visible spectrum range 0.4 - 0.7 micrometers , we obtain three main diffracted light intensity curves for the maxima corresponding to red, green and blue colors, which resemble the fundamental sensitivity curves. The behavior of these curves for non-zero incident angle agrees with the Stiles-Crawford effects.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: In this article, it was shown that phase-sensitive nonclassical effects can be transiently produced via decay of a field mode into a heat bath, and under certain conditions the light field which initially was not fourth-order squeezed may exhibit this non-classical effect.

Patent
04 Nov 1994
TL;DR: In this paper, an outer circumferential section of a terminal section at both ends of a light source is supported to be directly fitted to a recessed support section provided in an internal case.
Abstract: PURPOSE:To improve the picture quality by supporting a light source having no light source in an internal case linearly so as to reduce number of components thereby supporting the light source at a precise position and executing sufficiently light field. CONSTITUTION:An outer circumferential section of a terminal section 3a at both ends of a light source 3 is supported to be directly fitted to a recessed support section 4 provided in an internal case 1. A mirror 5a, a lens 5b, a light receiving element 6 or a photosensing body 7 of an image forming optical system 5 by which a reflected light by the light source 3 is formed to a light receiving section or a photosensing face is arranged to a lower space partitioned by the case 1. Thus, it is not required to provide other light shield plate so as to prevent a light other than the reflected light from the picture face of the original 2 from being made incident on the light receiving face of the light receiving element 6 or the photosensing face of the photosensing body 7 and complete light shield is executed by the case 1.

Journal ArticleDOI
TL;DR: In this article, a quantum statistical theory of light propagation in a twin-core doped optical fiber was developed, where the optical nonlinearity induced by the atomic dopants in the fiber dramatically modifies the quantum fluctuations in the paraxial photon modes.
Abstract: In this paper, we develop a quantum statistical theory of light propagation in a twin-core doped optical fiber. The optical nonlinearity induced by the atomic dopants in the fiber dramatically modifies the quantum fluctuations in the paraxial photon modes. We find that with appropriate arrangement of the device, the input light field with the usual Poissonian photon statistics can be transformed into sub- or super-Poissonian photon statistics. For the sub-Poissonian photon statistics, the quantum noise in the photon numbers in the paraxial modes is reduced below the level of the noise in the usual laser field. >

Proceedings ArticleDOI
31 Oct 1994
TL;DR: In this article, the results of a series of investigations carried out at the Department to Hydro-optics of SOI during a number of years with the aim of development, design and practical employment of optical instruments of measuring the statistical characteristics of turbulent inhomogeneities in sea water are presented.
Abstract: The results presented in the report are related to a series of investigations carried out at the Department to Hydro-optics of SOI during a number of years with the aim of development, design and practical employment of optical instruments of measuring the statistical characteristics of turbulent inhomogeneities in sea water. The values if magnitude and characteristics scales of refractive index fluctuations caused by turbulent convection in sea water with temperature and salinity stratification, as well as the presence of suspended hydrosol particles, stipulate the choice of devices based on photoelectrical registration of small-angle scattering of light beam propagating through the volume of analyzed medium. The developed modifications of phase- contrast methods (shadow methods) make it possible to detect the variations of light beam angle-of-arrival at the level of 0.03" - 0.05"; the instrument may be mounted on remotely controlled underwater carrier towed by research vessel with the velocity 4-12 knots at the desired depth in the range from 0 to 300 m. The interpretation of registered signals from photoelectrical output of the optical instrument is based on the connection between the signal correlation function or spectrum and the energetic spectrum of refractive index fluctuations. The corresponding relations are obtained with the help of the theory of light propagation in random media, namely, the closed equations for light field statistical moments in parabolic approximation. The results of theoretical analysis allows the optimization of optical scheme to meet the requirements of linearity of the signal relation to the analyzed fluctuations magnitude, high spatial resolution and low sensitivity threshold, as well as sufficient resistance to vibrations and changes in pressure and temperature. A measurement of optical fluctuations spectrum in turbulent flow behind a heated grating in hydrodynamic tube are shown to demonstrate the designed instruments abilities. Some results of in-situ experiments made in calm waters and in turbulized layer near thermocline are presented.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: It is shown that there can be anisotropic cooling-heating forces that will cool the atoms along one field axis while heating them along the perpendicular axis that are associated with the local traveling-wave character of the two-dimensional field.
Abstract: We consider the velocity-dependent light pressure force on a two-level atom interacting with a two-dimensional nearly resonant standing-wave light field. We show that there can be anisotropic cooling–heating forces that will cool the atoms along one field axis while heating them along the perpendicular axis. The force is identified as a spontaneous vortex force associated with the local traveling-wave character of the two-dimensional field. We provide a simple interpretation of this anomalous force in terms of the interplay between the vortical momentum flow of the light field and a motion-induced population transfer between the ground and excited atomic states.

Book ChapterDOI
01 Apr 1994
TL;DR: In this article, the authors examined the properties of the underwater light field and showed that the response of an irradiance meter to parallel radiant flux (wider than the collector) should be proportional to the cosine of the angle (θ) between the normal to the collector surface and the direction of the flux.
Abstract: Having described the nature of the incident radiation flux presented to the aquatic biosphere and the influences to which the light is subject within the water, we shall now consider the kind of light field that results. We shall begin, in this chapter, by examining the ways in which the properties of this light field are studied. The physical definitions of these properties are given in Chapter 1. Irradiance Irradiance meters The most frequently and easily measured property of the underwater light field is irradiance. Knowledge of this parameter is valuable, not only because it provides information about how much light is available for photosynthesis, but also because irradiance plays a central role in the theory of radiation transfer in water. An irradiance meter, since it is meant to measure the radiant flux per unit area, must respond equally to all photons that impinge upon its collector, regardless of the angle at which they do so. With any given meter this can be tested by observing the way in which its response to a parallel light stream varies with its angle to that light stream. As the angle of the radiant flux to the collector changes, the area of the collector projected in the direction of that radiant flux changes, and the proportion of the flux intercepted by the collector changes correspondingly (Fig. 5.1). Thus, the response of an irradiance meter to parallel radiant flux (wider than the collector) should be proportional to the cosine of the angle (θ) between the normal to the collector surface and the direction of the flux. An irradiance collector which meets this criterion is known as a cosine collector.

Journal ArticleDOI
TL;DR: In this paper, a quasiclassical approach is used to construct a theory of atomic transitions induced by a strong light field, and the Coulomb-Volkov solutions of the Schrodinger equation in which both Coulomb and light fields are taken into account.
Abstract: A quasiclassical (WKB) approach is used to construct a theory of atomic transitions induced by a strong light field. This approach is used to find the "Coulomb-Volkov" solutions of the Schrodinger equation in which both the Coulomb and light fields are taken into account. These solutions are shown to be applicable in . a region of low light frequencies, low electron energies and angular momenta.. The found solutions are used to describe two kinds of processes: strong-field photoionization from highly excited (Rydberg) atomic levels, and field-assisted electron-ion scattering. In the photoionization problem the strong-field complex quasi-energies of an atom are found. A problem' of the strong-field stabilization of an atom, as well as the expected behavior of the ionization time in its dependence on the light field strength are discussed.

01 Jan 1994
TL;DR: In this paper, the authors constructed a portable polarimeter that analyses the linear polarization characteristics of a full image on a single pixel basis, using two twisted nematic liquid crystals and a polarizing filter.
Abstract: lhe natural light field has long been known to be partly linearly polarized, and it has been suggested that various objects reflect light that is polarized at a spec@ orientation. Although humans use polarized light, our inability to see it limits our study and understanding of its distribution in nature and of the information it carries. By placing two twisted nematic liquid crystals and afied polarizingfilter in series in pant of a CCD camera, we constructed a portable polarimeter that analyses the linear polarization characteristics of a full image on a single pixel basis. Two configurations are presented: an autonomous sensor that uses a small camcorder for recording images that are analyzed at a later stage; and an on-line sensor that uses a digital camera connected to a personal computer which controls and analyses the information. Field measurements reveal possible usage for analyzing spatial orientation of objects or breaking color camouflage. Our new polarimeters provide an opportunity to inspect and understand an aspect of the visual world, currently obscure to our eyes.


Book ChapterDOI
01 Jan 1994
TL;DR: In this paper, a microscopic theory for semiconductor lasers and amplifiers is presented, which applies nonequilibrium quantum mechanical (Green's function) techniques to derive a set of coupled equations for the light field and carrier distribution functions.
Abstract: In this final chapter we discuss results for semiconductor lasers and amplifiers that go beyond the quasiequilibrium assumption made in the previous chapters. First, in Sec. 11-1 we outline a microscopic theory for semiconductor lasers that treats both the light field and the carrier system quantum mechanically. This approach applies nonequilibrium quantum mechanical (Green’s function) techniques to derive a set of coupled equations for the light field and carrier distribution functions. It allows us to analyze the stationary and dynamical responses of the interacting photon and electron-hole systems in semiconductor lasers and amplifiers including many-body effects of the electron-hole plasma and the photon system.

Proceedings ArticleDOI
21 Dec 1994
TL;DR: In this article, a generalisation of the phase screen model is applied for studying light scattering on atmospheric paths and extended light source image properties, where the random phase at the screen by integration along a broken line between source, point on the screen and observer is obtained.
Abstract: The generalisation of phase screen model is applied for studying light scattering on atmospheric paths and extended light source image properties. The random phase at the screen by integration along a broken line between source, point on the screen and observer is obtained. The optimal position of the screen surface and its connection with altitude dependence on atmospheric turbulence is discussed. The limiting conditions for phase screen model application and some possibilities of its improving are considered. The random light field in the observing plane as a sum of light beams scattered by different parts of screen is represented. The local coherent structures, connected with each beam, are described. The random (partial averaged) correlation function for light field local properties studying is applied. The second moment of this function is calculated and its dependence on model parameters is studied. The connection between random correlation function and short exposure image of light source intensity is shown. The second moment of image intensity is studied and conditions of maximal contrast image are obtained. The approach to phase on the screen reconstruction is considered.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: In this article, the authors analyze the mechanical action of a quantized light fleld on a non-resonant atom using this concept and derive the equation of motion for the Wigner function of the atom.
Abstract: In classical mechanics a phase space distribution contains the complete information about a dynamical system. This concept carries over to the quantum world: a prominent distribntion is the Wigner function [1]. This representation of quantum mechanics gives immediate insight into the dynamics of a quantum system. In the present paper we analyse the mechanical action of a quantized light fleld [2] on a non-resonant atom using this concept [3]. The paper is organized as follows. In Sec. 2 we present the model [Λ] describing the motion of a non-resonant atom in a single mode of a quantized light fleld. Starting from the Schrodinger equation for the state vector for the atomic motion and the fleld we derive the equation of motion for the Wigner function of the atom. The latter tuus out to be the sum of the Wigner functions corresponding to the motion of the atom in the individual number states, weighted with the photon statistics. In Sec. 3 we give an analytical solntion for the equation of motion of the Wigner function for the case when the wavelength of the light is much larger than the de Broglie wavelength of the atom [5]. Making use of this small parameter we expand the actual light potential in a Taylor series up to second order and obtain a first order differential equation solvable exactly. We devote Sec. 4 to a discussion of the distribution of atoms after the interaction with the light fleld. Following the evolution of the Wigner function we note that each individual hock state deflects