Coherence Singularities Research Articles

Evolution of coherence singularities in polarization singular beams.

The evolution of correlation singularities in partially coherent polarization singular beams (PC-PSBs) is investigated. Since PSBs are the superposition of two orthogonally polarized vortex beams, the occurrence of coherence singularities in PC-PSBs is strongly governed by the topological charge of the component vortex beams and the spatial coherence length. Coherence singularities appear in the form of ring dislocations in the modulus of the spectral degree of coherence (SDoC) profile, and the number of ring dislocations is equal to the higher value of the topological charge of the superposing vortex beam. Furthermore, the SDoC phase profile can be used to determine the polarity of a PC-PSB. The findings of the study could be valuable in various applications that rely on the spatial coherence of beams, such as free-space communication and imaging.

Coherence and coherence vortex embedded in partially coherent Gaussian beam background during propagation

This work presents theoretical analysis on coherence vortex of partially coherent vortex beam (PCVB) during propagation. Complex degree of coherence is analyzed to explore the coherence singularity embedded in PCVB in detail. It is shown that observation of coherence singularity is related to position of reference point, and coherence singularities appear in pairs while the reference point is located far from the center. Detailed investigation reveals that it is easy to distinguish coherence singularity for the case of near field and for the case of original PCVB with high coherence.

Coherence singularity and evolution of partially coherent Bessel-Gaussian vortex beams.

For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

Correlation Optics, Coherence and Optical Singularities: Basic Concepts and Practical Applications

The main idea of this review is to trace the interrelations and inter-transitions between the basic concepts and approaches of the correlation optics (including the light coherence) and the singular optics dealing with networks of “exceptional” points of light fields. The principles and examples are described of formation of light fields with required structures (amplitude, phase and polarization distributions, spectral properties as well as the internal energy flows and energy gradients responsible for optical forces) via superpositions of model optical fields of simple standard configurations and under controllable correlation conditions. The theoretical and experimental results, obtained by the authors and other researchers, demonstrate possibilities of the general approach to the complex fields formation with spatial and polarization inhomogeneities. A special topic, considered in more detail, is the interaction of structured optical fields with the media containing suspended micro- and nanoparticles, their inhomogeneous heating by the laser radiation and the accompanying self-diffraction and self-focusing phenomena. Possible light-induced phase transitions and controllable generation of the gas-vapor microbubbles in the medium are discussed. Specific optical singularities in polychromatic light fields are analyzed in connection to the field coherence. Some experimental solutions for revealing the fine structure of optical fields by means of the interference schemes are presented. Practical applications for the micromanipulation techniques, optical diagnostics of remote and random objects, optical treatment and laboratory practice in biology and medicine are described and discussed.

Young's double-slit experiment with a partially coherent vortex beam.

We perform a Young's double-slit experiment with a partially coherent vortex beam (PCVB) and explore its cross-spectral density (CSD) at the focal plane after passing through a double-slit. Our results reveal that the phase of the CSD distribution with respect to an on-axis reference point can simultaneously quantitatively characterize the sign and magnitude of the topological charge (TC) carried by such a beam. In particular, the magnitude of the TC is half of the number of coherence singularities and the sign of the TC is determined by the phase winding of the coherence singularities (i.e., counterclockwise- and clockwise increases correspond to positive and negative, respectively). Based on this property, we present and demonstrate experimentally a simple technique to measure the sign and magnitude of the TC of a PCVB through its CSD distribution after a double-slit. Our method allows for easy measurement of the TC by being conceptually simpler than other methods.

Partially coherent vortex beams: Fundamentals and applications

It has been over 30 years since the concept of optical vortices was first proposed by Coullet et al. in 1989, and the field of structured beams has grown extremely. In the last two decades, partially coherent vortex beams (PCVBs) have received increasing interest in the fields of optical manipulation, optical communication, optical imaging, etc., and great progress has been made in the area of the coherence singularities, generation methods, topological charge measurements, and promising applications of PCVBs. In this review, we firstly outline the basic concepts of PCVBs. We explicate the relationship between the coherence vortices and optical vortices, and the evolution behavior of optical vortices to coherence vortices is summarized in detail. We discuss a special form of coherence singularity, ring dislocation, mathematically and physically. The ring dislocation in the correlation functions under low coherence is dependent on the mode indices, which provide a feasible approach to measure mode indices of PCVBs. Subsequently, we summarize the various methods for measuring the topological charge of PCVBs, highlight the measurement method based on the cross-correlation function, and a physical explanation on the relation between ring dislocation and topological charge is given. After that, we review the recent advances on experimental generation of several kinds of PCVBs. Lastly, we give an overview on the potential applications of PCVBs.

Phase detection of coherence singularities and determination of the topological charge of a partially coherent vortex beam

In the theory of partial coherence, coherence singularities can occur in the spectral degree of coherence (SDOC): in case the fields at two different points are completely uncorrelated, the phase of the SDOC is undefined. For a partially coherent vortex beam, the detection of coherence singularities is linked to the measurement of topological charge, whose magnitude equals the number of ring dislocations in its far field amplitude. However, the phase distribution of coherence singularities is rarely mentioned in the literature and the amplitude distribution can hardly reflect the sign of topological charge. In this letter, we present a phase-analysis method for measuring the coherence singularities by introducing a movable perturbation at a certain point in an illumination window of a finite size. Using the proposed method, we measure experimentally the coherence singularities of a partially coherent vortex beam in the focal plane. From the results, the magnitude and sign of the topological charge can be determined simultaneously from the phase distribution of the coherence singularities. Our results can find application in information transmission.

Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.

It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated. This arrangement serves to clarify the relationships between the different singularity types, and provides a simple tool for further exploration.

Evolution of coherence singularities of Schell-model beams.

We show that the propagation of the widely used Schell-model partially coherent light can be easily understood using the ambiguity function. This approach is especially beneficial for the analysis of the mutual intensity of Schell-model beams (SMBs), which are associated with stable coherent beams such as Laguerre-, Hermite-, and Ince-Gaussian. We study the evolution of the coherence singularities during the SMB propagation. It is demonstrated that the distance of singularity formation depends on the coherence degree of the input beam. Moreover, it is proved that the shape, position, and number of singularity curves in far field are defined by the associated coherent beam.

Correlation singularities in partially coherent electromagnetic beams

We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for both interference experiments and correlation of intensity fluctuation measurements performed with such beams.

Measurements of spatial coherence of partially coherent light with and without orbital angular momentum

We study the spatial coherence of a partially coherent beam before and after being transmitted through a spiral phase plate that changes the overall orbital angular momentum of the field. The two-point coherence function is measured and directly visualized on a CCD through interference in a Mach-Zehnder interferometer equipped with an image rotator. We show, in particular, how the coherence singularities associated with Airy rings are strongly affected by the spiral phase plate.

Evolution of singularities in a partially coherent vortex beam

We study the evolution of phase singularities and coherence singularities in a Laguerre-Gauss beam that is rendered partially coherent by letting it pass through a spatial light modulator. The original beam has an on-axis minumum of intensity--a phase singularity--that transforms into a maximum of the far-field intensity. In contrast, although the original beam has no coherence singularities, such singularities are found to develop as the beam propagates. This disappearance of one kind of singularity and the gradual appearance of another is illustrated with numerical examples.

Coherence singularities in the field generated by partially coherent sources

We analyze the coherence singularities that occur in the far field that is generated by a broad class of partially coherent sources. It is shown that for rotationally symmetric planar quasihomogeneous sources the coherence singularities form a two-dimensional surface in a reduced three-dimensional space. We illustrate our results by studying the topology of the coherence singularity of a partially coherent vortex beam. We find that the geometry of the phase singularity can be associated with conic sections such as ellipses, lines, and hyperbolas.

Phase and coherence singularities generated by the interference of partially coherent fields

A condition for the complete destructive interference of partially coherent fields emerging from pinholes in an opaque screen is derived, with the assumption of symmetry in both their geometric positions and coherence properties. We use this condition to theoretically investigate the simultaneous production of phase singularities of the optical field and of the spectral degree of coherence. We find that in cases where the number of point sources is even, a new type of mixed field/correlation singularity is observed.