Turbulence-induced changes in degree of polarization,degree of coherence and spectrum of partially coherent electromagnetic beams

Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov＇s phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.

Can two partially coherent cosh-Gaussian beams generate far fields with the same spectral degree of coherence?

Taking partially coherent cosh-Gaussian （ChG） beams as an example of more general partially coherent beams, we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is shown that, unlike Gaussian Schell-model （GSM） beams, in the strict sense there do not exist two partially coherent ChG beams which can generate far fields with the same spectral degree of coherence. However, under certain conditions it is possible to find two partially coherent ChG beams with the same spectral degree of coherence in the far field.

Correction of the second-order degree of coherence measurement

The measurement of the second-order degree of coherence [g（2）（t）] is one of the important methods used to study the dynamical evolution of photon-matter interaction systems. Here, we use a nitrogen-vacancy center in a diamond to compare the measurement of g（2） （t） with two methods. One is the prototype measurement process with a tunable delay. The other is a start-stop process based on the time-to-amplitude conversion （TAC） and multichannel analyzer （MCA） system, which is usually applied to achieve efficient measurements. The divergence in the measurement results is observed when the delay time is comparable with the mean interval time between two neighboring detected photons. Moreover, a correction function is presented to correct the results from the TAC-MCA system to the genuine g（2）（t）. Such a correction method will provide a way to study the dynamics in photonic systems for quantum information techniques.

Robust measurement of orbital angular momentum of a partially coherent vortex beam under amplitude and phase perturbations

The ability to overcome the negative effects,induced by obstacles and turbulent atmosphere,is a core challenge of long-distance information transmission,and it is of great significance in free-space optical communication.The spatial-coherence structure,that characterizes partially coherent fields,provides a new degree of freedom for carrying information.However,due to the influence of the complex transmission environment,the spatial-coherence structure is severely damaged during the propagation path,which undoubtedly limits its ability to transmit information.Here,we realize the robust far-field orbital angular momentum(OAM)transmission and detection by modulating the spatial-coherence structure of a partially coherent vortex beam with the help of the cross-phase.The cross-phase enables the OAM information,quantified by the topological charge,hidden in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions and turbulence within the communication link.This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross-phase.We demonstrate experimentally that the topological charge information can be recognized well by measuring the spatial-coherence structure in the far field,exhibiting a set of distinct and separated dark rings even under amplitude and phase perturbations.Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

Robust far-field imaging by spatial coherence engineering

The degree of coherence(DOC)function that characterizes the second-order correlations at any two points in a light field is shown to provide a new degree of freedom for carrying information.As a rule,the DOC varies along the beam propagation path,preventing from the efficient information recovery.In this paper,we report that when a partially coher-ent beam carrying a cross phase propagates in free space,in a paraxial optical system or in a turbulent medium,the modulus of the far-field(focal plane)DOC acquires the same value as it has in the source plane.This unique propaga-tion feature is employed in a novel protocol for far-field imaging via the DOC,applicable to transmission in both free-space and turbulence.The advantages of the proposed approach are the confidentiality and resistance to turbulence,as well as the weaker requirement for the beam alignment accuracy.We demonstrate the feasibility and the robustness of the far-field imaging via the DOC in the turbulent media through both the experiment and the numerical simulations.Our findings have potential applications in optical imaging and remote sensing in natural environments,in the presence of op-tical turbulence.

Scattering of a general partially coherent beam from a diffuse target in atmospheric turbulence

The second-order and fourth-order statistical moments of the speckle field from a diffuse target in atmospheric turbulence are studied which have great influence on the performance of lidar systems. By expanding a general rotationally symmetric beam as a sum of Gaussian-Schell model （GSM） beams, the mean intensity of the general beam propagating over a distance in an atmospheric turbulence is formulated. Expressions for the degree of coherence （DOC） and the normalized intensity variance of the scattered field of a general beam from a rough surface in turbulence are derived based on the extended Huygens-Fresnel principle. The general expressions reduce to the well-known forms for a GSM beam. Another example for the general beam used in this paper is the collimated flat-topped beam. The results of both kinds of beams show that the intensity profile on the target plane is a key factor affecting the statistical characteristics of the speckle field. A larger beam spot on the target plane induces a smaller coherence length and a smaller normalized intensity variance of the received field. As turbulence gets stronger, the coherence length becomes smaller, and the normalized intensity variance firstly increases and declines to unity finally.

Resolution of Two Unequally Bright Points of Apodized Optical Systems with Asymmetric Circular Antenna Arrays

Sparrow criterion of resolution is used for assessment of the resolution of two object points of apodized optical systems under incoherent illumination of light. Semicircular arrays of circular aperture with discrete asymmetric apodization have suppressed side-lobes and a narrower central peak in the image plane termed as PSF good side on alternatively the right and left of the strong spectral point facilitates to detect the presence of weak spectral point in the vicinity of bright spectral point. The results of investigations on optimum discrete pupil function with semicircular arrays on the intensity distributions in the composite image of two object points with widely varying in their intensities under various degree of coherence of illumination have been studied. Sparrow resolution limits and the dip in central intensity as function of degree of coherence of the illumination (γ), intensity ratio (α), degree of asymmetric apodization (b) and number of discrete elements in semicircular array (n). The efficiency of aperture functions is discussed in terms of these parameters. Pupil function capabilities in redistribution of energy in composite image of two object points in close vicinity have been verified for different considerations. Current study has found an improvement in two-point resolution characteristics compared to their unapodized counter part. Fourier analytical properties of an optical system are presented for evaluation of this practical problem.

Propagation Properties of Multi-Hyperbolic Sine-Correlated Beams in Oceanic Turbulence

As a new partially coherent beam, the propagation properties of the multi-hyperbolic sine-correlated (MHSC) beams in turbulent atmospheres have been studied. But as another important medium, the propagation properties of MHSC beams in oceanic turbulence. This paper has studied these questions in detail. The analytical formulas of spectral density and degree of coherence for the propagation are derived and the numerical simulations are represented. It is found that the intensity patterns of MHSC beams will evolve from dark-hollow profiles into Gaussian profiles caused by oceanic turbulence and will degenerate more rapidly with stronger oceanic turbulence. In addition, the coherence region becomes larger with decreasing in the dissipation rate of turbulence kinetic energy in unit mass liquid or increasing in the relative intensity of temperature and salinity fluctuations, mean square temperature dissipation rate. We also find that the degree of coherence of MHSC beams with a higher-order N will decrease more slowly than those of hyperbolic sine-correlated (HSC) beams.

Recent advances in partially coherent beams with prescribed degrees of coherence

Coherence is one of the most salient features of a laser beam,and laser beams which are not completely coherent,the so-called partially coherent beams,are preferred in many applications.The degrees of coherence of conventional spatial partially coherent beams can be described by Gaussian distributions.Currently,more and more attention is being paid to partially coherent beams with prescribed degrees of coherence due to their extraordinary optical properties,such as self-focusing,self-shaping,selfsplitting,periodicity reciprocity,and super-strong reconstruction. Manipulating the structure of the degree of a partially coherent beam provides a novel way for modulating and controlling its propagation properties and is useful in beam shaping,free-space optical communications,optical trapping,optical encryption and image or information transfer through adverse inhomogeneous environments.In this paper,we present a review on the recent advances in partially coherent beams with prescribed degrees of coherence.

Thermal vacuum state corresponding to squeezed chaotic light and its application

For the density operator（mixed state） describing squeezed chaotic light（SCL） we search for its thermal vacuum state（a pure state） in the real-fictitious space. Using the method of integration within ordered product（IWOP） of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals： the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.

Atomic emission spectra and field non-classical properties

This paper studies the interaction of a A-type three-level atom with a single mode field. It discusses the emission spectrum characteristics of the A-type three-level atom driven by the photon-added coherent field. By means of the second-order degree of coherence, it shows some nonclassical properties of the cavity field, such as sub-Poissonian photon- number distribution and the two-time intensity-intensity correlation which violates the Cauchy Schwarz inequality.