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Showing papers on "Light field published in 2006"


Journal ArticleDOI
Marc Levoy1, Ren Ng1, Andrew Adams1, Matthew J. Footer1, Mark Horowitz1 
01 Jul 2006
TL;DR: The Light Field Microscope (LFM) as discussed by the authors uses 3D deconvolution to produce a set of cross-sections, which can then be visualized using volume rendering.
Abstract: By inserting a microlens array into the optical train of a conventional microscope, one can capture light fields of biological specimens in a single photograph. Although diffraction places a limit on the product of spatial and angular resolution in these light fields, we can nevertheless produce useful perspective views and focal stacks from them. Since microscopes are inherently orthographic devices, perspective views represent a new way to look at microscopic specimens. The ability to create focal stacks from a single photograph allows moving or light-sensitive specimens to be recorded. Applying 3D deconvolution to these focal stacks, we can produce a set of cross sections, which can be visualized using volume rendering. In this paper, we demonstrate a prototype light field microscope (LFM), analyze its optical performance, and show perspective views, focal stacks, and reconstructed volumes for a variety of biological specimens. We also show that synthetic focusing followed by 3D deconvolution is equivalent to applying limited-angle tomography directly to the 4D light field.

818 citations


Proceedings ArticleDOI
26 Jun 2006
TL;DR: This paper develops a prototype integral camera that uses a system of lenses and prisms as an external attachment to a conventional camera and shows examples of novel view synthesis and refocusing where the spatial resolution is significantly higher than is possible with previous designs.
Abstract: An integral camera samples the 4D light field of a scene within a single photograph. This paper explores the fundamental tradeoff between spatial resolution and angular resolution that is inherent to integral photography. Based on our analysis we divide previous integral camera designs into two classes depending on how the 4D light field is distributed (multiplexed) over the 2D sensor. Our optical treatment is mathematically rigorous and extensible to the broader area of light field research.We argue that for many real-world scenes it is beneficial to sacrifice angular resolution for higher spatial resolution. The missing angular resolution is then interpolated using techniques from computer vision. We have developed a prototype integral camera that uses a system of lenses and prisms as an external attachment to a conventional camera. We have used this prototype to capture the light fields of a variety of scenes. We show examples of novel view synthesis and refocusing where the spatial resolution is significantly higher than is possible with previous designs.

367 citations


Journal ArticleDOI
TL;DR: In this article, a method for efficient storage and recall of arbitrary nonstationary light fields, such as single photon time-bin qubits or intense fields, in optically dense atomic ensembles is proposed.
Abstract: We propose a method for efficient storage and recall of arbitrary nonstationary light fields, such as, for instance, single photon time-bin qubits or intense fields, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening and relies on a hidden time-reversal symmetry of the optical Bloch equations describing the propagation of the light field. We briefly discuss experimental realizations of our proposal.

224 citations


Journal ArticleDOI
10 Aug 2006-Nature
TL;DR: Femtosecond time-resolved X-ray diffraction is used to measure the corresponding displacements of ions in ferroelectric lithium tantalate, LiTaO3, to enable studies in complex systems, where electric fields couple to multiple degrees of freedom.
Abstract: The elementary particles of light that propagate through air are photons But when light propagates through condensed matter, it couples to the underlying lattice, resulting in complex particles such as polaritons A new study makes use of ultrafast X-ray diffraction to directly observe atomic displacements that support such optical excitations in a solid In this study, terahertz radiation propagating through the ferroelectric lithium tantalate (LiTaO3) couples to lattice vibrations, resulting in phonon-polariton waves This new X-ray diffraction technique makes it possible to follow the absolute displacements of ions in the lattice that underlie the propagation of these waves Terahertz radiation propagating through ferroelectric lithium tantalate (LiTa03) couples to lattice vibrations, resulting in phonon-polariton waves The new X-ray diffraction technique makes it possible to follow directly the absolute displacements of ions in the lattice that underlie the propagation of these waves In condensed matter, light propagation near resonances is described in terms of polaritons, electro-mechanical excitations in which the time-dependent electric field is coupled to the oscillation of charged masses1,2 This description underpins our understanding of the macroscopic optical properties of solids, liquids and plasmas, as well as of their dispersion with frequency In ferroelectric materials, terahertz radiation propagates by driving infrared-active lattice vibrations, resulting in phonon-polariton waves Electro-optic sampling with femtosecond optical pulses3,4,5 can measure the time-dependent electrical polarization, providing a phase-sensitive analogue to optical Raman scattering6,7 Here we use femtosecond time-resolved X-ray diffraction8,9,10, a phase-sensitive analogue to inelastic X-ray scattering11,12,13, to measure the corresponding displacements of ions in ferroelectric lithium tantalate, LiTaO3 Amplitude and phase of all degrees of freedom in a light field are thus directly measured in the time domain Notably, extension of other X-ray techniques to the femtosecond timescale (for example, magnetic or anomalous scattering) would allow for studies in complex systems, where electric fields couple to multiple degrees of freedom14

96 citations


Proceedings ArticleDOI
04 Jun 2006
TL;DR: In this paper, a light field camera is sampled with integral photography techniques, using a microlens array in front of the sensor inside a conventional digital camera, and the authors explore computation of photographs with reduced lens aberrations by re-sorting aberrated rays to where they should have terminated.
Abstract: Digital light field photography consists of recording the radiance along all rays (the 4D light field) flowing into the image plane inside the camera, and using the computer to control the final convergence of rays in final images. The light field is sampled with integral photography techniques, using a microlens array in front of the sensor inside a conventional digital camera. Previous work has shown that this approach enables refocusing of photographs after the fact. This paper explores computation of photographs with reduced lens aberrations by digitally re-sorting aberrated rays to where they should have terminated. The paper presents a test with a prototype light field camera, and simulated results across a set of 35mm format lenses.

62 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the motion of the end mirror of a cavity in whose standing-wave mode pattern atoms are trapped and analyze how the dipole potential in which the atoms move is modified due to this back action of the atoms.
Abstract: We consider the motion of the end mirror of a cavity in whose standing-wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this back action of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the back action of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the sideband spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.

61 citations


Proceedings ArticleDOI
26 Jun 2006
TL;DR: The use of hierarchical tensors as the underlying data structure to capture data-sparseness, specifically through local rank-1 factorizations of the transport matrix, enables fast acquisition of the approximated transport matrix and fast rendering of images from the captured matrix.
Abstract: We present a novel technique called symmetric photography to capture real world reflectance fields. The technique models the 8D reflectance field as a transport matrix between the 4D incident light field and the 4D exitant light field. It is a challenging task to acquire this transport matrix due to its large size. Fortunately, the transport matrix is symmetric and often data-sparse. Symmetry enables us to measure the light transport from two sides simultaneously, from the illumination directions and the view directions. Data-sparseness refers to the fact that sub-blocks of the matrix can be well approximated using low-rank representations. We introduce the use of hierarchical tensors as the underlying data structure to capture this data-sparseness, specifically through local rank-1 factorizations of the transport matrix. Besides providing an efficient representation for storage, it enables fast acquisition of the approximated transport matrix and fast rendering of images from the captured matrix. Our prototype acquisition system consists of an array of mirrors and a pair of coaxial projector and camera. We demonstrate the effectiveness of our system with scenes rendered from reflectance fields that were captured by our system. In these renderings we can change the viewpoint as well as relight using arbitrary incident light fields.

60 citations


Proceedings Article
01 Jan 2006
TL;DR: An autostereoscopic display that uses a scalable array of digital light projectors and a projection screen augmented with microlenses to simulate a light field for a given three-dimensional scene is introduced.
Abstract: Ultimately, a display device should be capable of reproducing the visual effects observed in reality. In this paper, we introduce an autostereoscopic display that uses a scalable array of digital light projectors and a projection screen augmented with microlenses to simulate a light field for a given three-dimensional scene. Physical objects emit or reflect light in all directions to create a light field that can be approximated by the light field display. The display can simultaneously provide many viewers from different viewpoints a stereoscopic effect without head tracking or special viewing glasses. This work focuses on two important technical problems related to the light field display: calibration and rendering. We present a solution to automatically calibrate the light field display using a camera and introduce two efficient algorithms to render the special multiview images by exploiting their spatial coherence. The effectiveness of our approach is demonstrated with a four-projector prototype that can display dynamic imagery with full parallax.

58 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the scattering of an evanescent light field by a single cesium atom outside a nanofiber and showed that the confinement of the field, the presence of the longitudinal field component and the tangential Poynting vector component, the enhancement of spontaneous emission, and the degeneracy of the atomic ground state substantially affect the scattering process.
Abstract: We investigate the scattering of an evanescent light field by a single cesium atom outside a nanofiber. We show that the confinement of the field, the presence of the longitudinal field component and the tangential Poynting vector component, the enhancement of spontaneous emission, and the degeneracy of the atomic ground state substantially affect the scattering process. We find that, in the close vicinity of the fiber surface, the transmittance of the field in the stationary regime can be substantially reduced to 48% due to scattering into radiation modes (with the efficiency as high as 44%) and backward guided modes (with the efficiency as high as 8%).

49 citations


Journal ArticleDOI
TL;DR: Bajcsy et al. as mentioned in this paper presented a detailed analysis of the recently demonstrated technique to generate quasi-stationary pulses of light based on electromagnetically induced transparency.

48 citations


Journal ArticleDOI
TL;DR: A theoretical framework to analyze the rate-distortion performance of a light field coding and streaming system is proposed, revealing that the efficiency gains from more accurate geometry, increase as correlation between images increases.
Abstract: A theoretical framework to analyze the rate-distortion performance of a light field coding and streaming system is proposed. This framework takes into account the statistical properties of the light field images, the accuracy of the geometry information used in disparity compensation, and the prediction dependency structure or transform used to exploit correlation among views. Using this framework, the effect that various parameters have on compression efficiency is studied. The framework reveals that the efficiency gains from more accurate geometry, increase as correlation between images increases. The coding gains due to prediction suggested by the framework match those observed from experimental results. This framework is also used to study the performance of light field streaming by deriving a view-trajectory-dependent rate-distortion function. Simulation results show that the streaming results depend both the prediction structure and the viewing trajectory. For instance, independent coding of images gives the best streaming performance for certain view trajectories. These and other trends described by the simulation results agree qualitatively with actual experimental streaming results.

Journal ArticleDOI
TL;DR: In this article, the entropy evolution property of a singlemode light field interacting with V-type three-level atoms via intensity-dependent coupling has been studied, and the influence of detuning of light field and initial photon number on entropy evolution of field is discussed.
Abstract: The entropy evolution property of a single-mode light field interacting with V-type three-level atoms via intensity-dependent coupling has been studied, and the influence of detuning of light field and initial photon number on entropy evolution of field is discussed. It is found that if detuning is relatively small and initial light field weak, the time-evolution behavior of field entropy is similar to that of Jaynes–Cummings model with single-photon transition, but in case of sufficient large detuning and strong initial light field, the time-evolution behavior of field entropy is similar to the periodic one of field entropy of Jaynes–Cummings model with two-photon transition.

Journal ArticleDOI
TL;DR: Morigi et al. as mentioned in this paper showed that a single trapped, laser-driven atom in a high-finesse optical cavity allows for the quantum-coherent generation of entangled light pulses on demand.
Abstract: We show that a single, trapped, laser-driven atom in a high-finesse optical cavity allows for the quantum-coherent generation of entangled light pulses on demand. We report the detailed description of schemes for generating simultaneous and temporally separated pulse pairs, presented in [G. Morigi et al., Phys. Rev. Lett., 96, 023601 (2006)]. The mechanical effect of the laser excitation on the quantum motion of the cold trapped atom mediates the entangling interaction between two cavity modes and between the two subsequent pulses, respectively. The entanglement is of EPR-type, and its degree can be controlled through external parameters. At the end of the generation process the atom is decorrelated from the light field. Possible experimental implementations of the proposals are discussed.

Journal ArticleDOI
TL;DR: In this paper, the spectral characteristics of the reformation or self-healing of a Bessel beam in the presence of a circular obstruction were investigated and it was shown that the spectral properties of the beam generation and reformation results in a dispersive focal line at the beam centre which is 'white' only over a certain region.
Abstract: Bessel beams are propagation invariant light fields. It has very recently been shown that they may be created with temporally incoherent (white) light. Such fields may have applications in low coherence interferometric imaging for biomedicine and optical micromanipulation. White light Bessel beams may be deemed at first glance to generate a white focal line of light at the beam centre due to the absence of chromatic aberration. We investigate the spectral characteristics of the reformation or self-healing of this light field in the presence of a circular obstruction and reveal that the spectral characteristics of the beam generation and reformation results in a dispersive focal line at the beam centre which is 'white' only over a certain region.

Journal ArticleDOI
TL;DR: The results suggest that the direction estimation is better with images of evenly distributed intensity gradients than with those of drastically varying gradients, and that the visual system may not take intensity variations due to the surface material or the light field into account in estimating the direction of illumination.
Abstract: We investigated the perception of illumination direction in images of 3-D convex objects under variations of light field and surface material properties. In a first experiment, we used an illumination-matching procedure in order to measure observers' ability to estimate the direction of illumination in images of 3-D polyhedra rendered under different light fields and illumination directions. Match deviations were larger in frontal direction than in rear directions, mainly counterclockwise in azimuth component, and diverged, in elevation component, from the image plane. In a second experiment, we examined whether the direction estimate was affected by the surface material type (BRDF), the light field, and the illumination direction. Angular deviations varied with material surface type and were largest in the test elevation direction 0 degrees. Elevation component deviations also differed with surface type and were larger in hemispherical diffuse lighting than in collimated lighting. These results suggest that the direction estimation is better with images of evenly distributed intensity gradients than with those of drastically varying gradients, and that the visual system may not take intensity variations due to the surface material or the light field into account in estimating the direction of illumination.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate that the evanescent light field in a circular fundamental guided mode can force the atom to rotate around the nanofiber for a macroscopic time.
Abstract: We study the action of the force and torque induced by a guided light field on a cesium atom outside a nanofiber. We demonstrate that the evanescent light field in a circular fundamental guided mode can force the atom to rotate around the nanofiber for a macroscopic time. We find that, due to the action of the torque, the angular momentum of the atom increases with time.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the coherent population trapping (CPT) resonances in Hanle configuration for different polarizations of the exciting light field, on the line of Cs atoms.
Abstract: Coherent population trapping (CPT) resonances study in Hanle configuration is reported for different polarizations of the exciting light field, on the ${D}_{2}$ line of Cs atoms. While for linear/circular polarization dip/peak in the fluorescence is registered, in case of elliptical polarization, a complex shape resonance is evidenced experimentally, whose profile strongly depends on the ellipticity of polarization. A theoretical model is proposed and developed, which includes the influence on the resonance of polarization ellipticity, transverse magnetic field, and spatial intensity profile of the laser beam. Good agreement is found between the theoretical and experimental results. The reported results allow one to accomplish more profound than in previous research analysis of the CPT resonances behavior pointing out their sensitivity to the light polarization and power as well as to transverse magnetic fields. The presented study is of general importance for the wide application of the coherent resonances in high resolution spectroscopy and precise measurements. The purity of linear/circular polarization of the light needed in different applications can be estimated implementing the proposed model.

Book
01 Jan 2006
TL;DR: This lecture focuses on answering two questions regarding light field sampling, namely how many images are needed for a light field, and if such number is limited, where the authors should capture them.
Abstract: Light field is one of the most representative image-based rendering techniques that generate novel virtual views from images instead of 3D models. The light field capture and rendering process can be considered as a procedure of sampling the light rays in the space and interpolating those in novel views. As a result, light field can be studied as a high-dimensional signal sampling problem, which has attracted a lot of research interest and become a convergence point between computer graphics and signal processing, and even computer vision. This lecture focuses on answering two questions regarding light field sampling, namely how many images are needed for a light field, and if such number is limited, where we should capture them. The book can be divided into three parts. First, we give a complete analysis on uniform sampling of IBR data. By introducing the surface plenoptic function, we are able to analyze the Fourier spectrum of non-Lambertian and occluded scenes. Given the spectrum, we also app...

Journal ArticleDOI
TL;DR: In this paper, it was shown that light interaction with planar chiral structures implies a broken enantiomeric symmetry for excitation with circularly polarized light, and that the symmetry can be broken by the polarization state of the exciting light field.
Abstract: Simulations of Maxwell’s equations for electromagnetic waves interacting with planar chiral structures are shown to depend on the polarization state of the exciting light field. These results illustrate generic features of light interaction with planar chiral structures and imply broken enantiomeric symmetry for excitation with circularly polarized light.

Journal ArticleDOI
TL;DR: In this paper, the effects of longitudinal purely spatial coherence of light and the results of observation of these effects in an interference experiment are considered under the condition that the length of temporal coherence l�� c676 ≪ ρ is considerably smaller than the length and the time of coherent (free) path of the wave train.
Abstract: The effects of longitudinal purely spatial coherence of light and the results of observation of these effects in an interference experiment are considered under the condition that the length of temporal coherence l c is considerably smaller than the length of longitudinal spatial coherence ρ‖ of the field. It is shown that, for l c ≪ ρ‖, the longitudinal purely spatial coherence of the light field in fact governs the coherence of the wave train in the process of its propagation. The length and the time of coherent (“free”) path of the wave train are considered as new spatial and temporal scales of a partially coherent light field.

Patent
20 Sep 2006
TL;DR: In this paper, the distribution of elasticity and viscosity in a measurement object without contact is measured by using a light probe, and the position information of the target area in the measurement object is acquired by photographing light spots of guide light with a camera provided to the light probe.
Abstract: Brillouin scattered light is used to measure the distribution of elasticity and viscosity in a measurement object without contact and in a noninvasive and simpler manner. Measuring light emitted from a light source is directed from a light probe onto a measurement object, and scattered light is received by the light probe. A control computer analyzes the light spectrum of scattered light received by the light probe, calculates at least one parameter selected from the center frequency and the linewidth of the elastic wave scattered components as viscoelastic information, matches the viscoelastic information with the position of a target area in the measurement object, and outputs image information. The position information of the target area in the measurement object is acquired by photographing light spots of guide light with a camera provided to the light probe.

Journal ArticleDOI
TL;DR: The principal aims are the development of a theory for intracavity four-wave mixing in complex molecular media in conditions of scattering from dynamic gratings and resonator feedback and the introduction of novel nonlinear-optical methods to control the characteristics of light beams.
Abstract: This work presents theoretical and experimental studies of the processes of light field transformations upon frequency-nondegenerate four-wave mixing (NFWM) in a nonlinear Fabry-Perot interferometer (FPI). The principal aims are the development of a theory for intracavity four-wave mixing in complex molecular media in conditions of scattering from dynamic gratings and resonator feedback; determination of a mechanism of light field transformations in dynamic holograms, and also by nonlinear interferometers; working out and introduction of novel nonlinear-optical methods to control the characteristics of light beams. High diffraction efficiency (up to 13.5%) with simultaneous infrared-to-visible frequency conversion of coherent images has been experimentally obtained by intracavity NFWM.

Patent
13 Jan 2006
TL;DR: A light source system comprises a light source disposed within a non-imaging optical element as mentioned in this paper, which does not produce a direct image of the light source, and the output light field at the output surface of the non-IMAGING optical element has an intensity that is substantially uniform over the area of the output surfaces.
Abstract: A light source system comprises a light source disposed within a non-imaging optical element. The non-imaging optical element does not produce a direct image of the light source, and the output light field at the output surface of the non-imaging optical element has an intensity that is substantially uniform over the area of the output surface. A light source system of the invention is therefore smaller and lighter than a prior art system of the same output power, since there is no need to provide further components, such as an integrator, to homogenise the output light field.

Patent
24 Jan 2006
TL;DR: A light field control device comprises a control unit to which the groups of light-emitting diodes are connected by means of adjusters each of which is connected to a power supply unit.
Abstract: The inventive surgical light comprises a body provided with main light-emitting diodes and additional light-emitting diodes arranged therebetween, which are spaced on said body and fixed thereto, wherein said additional light-emitting diodes are grouped and are characterised in that the spatial orientation thereof differs from the spatial orientation of the main light-emitting diodes. A light field control device comprises a control unit to which the groups of light-emitting diodes are connected by means of adjusters each of which is connected to a power supply unit. The main light-emitting diodes are fixed to the light body in such a way that the optical axes thereof cross the light axis in the center of a light spot. The additional light-emitting diodes are fixed to the light body in such a way that the optical axes thereof form a concentric light spot in the form of a ring around the main light spot.

Journal ArticleDOI
TL;DR: In this paper, a method to characterize the polarization state of a light field in the continuous-variable regime is presented. But instead of using the abstract formalism of SU(2) quasidistributions, the authors model polarization as the superposition of two harmonic oscillators of the same angular frequency along two orthogonal axes, much in the classical way of dealing with this variable.

Journal ArticleDOI
TL;DR: In this paper, the theoretical aspects of the diffractive optic synthesis and analysis of light fields, and present some recent applications of diffractive optical elements for information, nano-, and biotechnologies are reviewed.
Abstract: The synthesis and analysis of light fields having specific properties are the main issues in diffractive optics Light field synthesis technology with diffractive optical elements can provide actual solutions for various applications that require extraordinary optical functions Also, the rigorous analysis of a light field is an essential element for the design and application of micro- or nanoscale diffractive optical elements In this paper we review the theoretical aspects of the diffractive optic synthesis and analysis of light fields, and present some recent applications of diffractive optical elements for information, nano-, and biotechnologies

Patent
13 Apr 2006
TL;DR: In this article, a broad band stop filter was used in combination with a band pass filter, a first light field and a second light field to improve the color gamut of an image display device.
Abstract: The color gamut of a image display device is improved by the introduction of a broad band stop filter in combination with a band pass filter, a first light field and a second light field. The first light field is generated by a first and a second light source, emitting blue and green light, respectively. The second light field is generated by said second light source and a third light source emitting red light. The color gamut is improved since the band pass filter facilitates a displacement of the color point of said second light source towards shorter wavelengths, as the band pass filter transmits some of the blue light in the first light field. Similarly, a displacement towards longer wavelengths is facilitated, as the filter transmits some of the red light of said second light field. Hence, four primary colors are generated by only three light sources.

Journal ArticleDOI
TL;DR: In this article, it was shown that there exists a possibility of controlled aggregation of silver nanoparticles in an external light field, as a result of the dipole-dipole interaction of particles, whose energy has a minimum at a certain particle configuration and at corresponding frequency and polarization.
Abstract: Using simplest two-and three-particle models, it is shown that there exists a possibility of controlled aggregation of silver nanoparticles in an external light field. The aggregation occurs as a result of the dipole-dipole interaction of particles, whose energy has a minimum at a certain particle configuration and at corresponding frequency and polarization of the field.

Journal ArticleDOI
TL;DR: In this paper, the distribution of polarisation of a light field in the cross section of a beam at the sum frequency was investigated upon the collinear interaction of two elliptically polarised Gaussian beams in a nonlinear isotropic gyrotropic medium, and it was shown that the ellipticity, the angle of rotation of the principal axis of the polarisation ellipse and the rotation direction of the electric field vector of radiation at the beam cross section strongly depend on the angle in the polar coordinate system.
Abstract: The distribution of polarisation of a light field in the cross section of a beam at the sum frequency is investigated upon the collinear interaction of two elliptically polarised Gaussian beams in a nonlinear isotropic gyrotropic medium. It is shown that the ellipticity, the angle of rotation of the principal axis of the polarisation ellipse, and the rotation direction of the electric field vector of radiation at the sum frequency in the beam cross section strongly depend on the angle in the polar coordinate system. The ranges of parameters of elliptically polarised fundamental Gaussian beams are found where the cross section of the sum-frequency beam is divided into sectors with different rotation directions of the electric field vector. The equations of the straight lines determining the boundaries of these sectors contain parameters specifying the shape and orientation of polarisation ellipses of the fundamental waves and the ratio of their wave vectors. In the case of opposite circular polarisations of these waves, the ellipticity of the sum-frequency beam does not change in the beam cross section and the principal axes of polarisation ellipses of the light field are oriented perpendicular to the radius in polar coordinates.

Journal ArticleDOI
TL;DR: In this paper, the influence of the strength of the light field and the phase angle between the two coherent states on the field entropy is discussed by using numerical calculations, and it is shown that the degree of entanglement between two-level atoms and the three different states of light fields is equal.
Abstract: The field entropy can be regarded as a measurement of the degree of entanglement between the light field and the atoms of a system which is composed of two-level atoms initially in an entangled state interacting with the Schr?dinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke?Stoler coherent state and it is minimum in a system of the two entangled atoms interacting with an even coherent state.