Partially correlated azimuthal vortex illumination: coherence and correlation measurements and effects in imaging

Propagation of Gaussian Schell-model beams in modulated graded-index media

The evolution of partially coherent beams in longitudinally modulated graded-index media is studied. The special cases of Gaussian Schell-model beams and parametric modulation, when the modulation period is half the fiber self-imaging period, are examined in detail. We show that the widths of the intensity and coherence of Gaussian Schell-model beams undergo amplification in parametrically modulated parabolic graded-index media. The process is an analog of quantum mechanical parametric amplification and generation of squeezed states. Our work may find application in spatial and temporal imaging of partially coherent beams in fiber-based imaging systems.

Microscopic phase reconstruction of cervical exfoliated cell under partially coherent illumination

Basic coherent diffraction imaging methods strongly rely on having a highly coherent illumination in order to reconstruct the phase accurately. However, regardless of considering the turbulent transport medium, the instability of the system or the generation mechanism of the light source, partially coherent illumination is more common in real case. In this paper, we proposed an efficient microscopic phase imaging method to study normal and abnormal cervical exfoliated cells. By applying three phase modulations in a single point of the sample's transmitted field, the phase can be retrieved with correspoding three intensities under partially coherent illumination. Compared with intensity map, we can efficiently and clearly judge the proportion of high density shrinking abnormal cells from the phase distributions, which provides a confident analysis and evaluation basis for early medical diagnosis of cervical cancer. This study also has potential applications in noninvasive optical imaging of dynamic biological tissues.

Measuring complex correlation matrix of partially coherent vector light via a generalized Hanbury Brown-Twiss experiment

We introduce an effective method for measuring the spatial distribution of complex correlation matrix of a partially coherent vector light field obeying Gaussian statistics by extending our recently advanced generalized Hanbury Brown-Twiss experiment. The method involves a combination of the partially coherent vector light with a pair of fully coherent reference vector fields and a measurement of the intensity-intensity cross-correlation of the combined fields. We show the real and imaginary parts of the complex correlation matrix can be recovered through a judicious control of the phase delay between two reference fields. We test the feasibility of our method by measuring the complex correlation matrix of a specially correlated radially polarized vector beam and we find the consistence between the experimental results and our general theory. We further show that our complex correlation matrix measurement can be used in reconstructing the polarization states hidden behind a thin-layer diffuser.

Evolution properties of the radially polarized Laguerre-Gaussian-correlated Schell-model beams propagating in uniaxial crystals

In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian-Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

Numerical Approach for Studying the Evolution of the Degrees of Coherence of Partially Coherent Beams Propagation through an ABCD Optical System

In this paper, we propose a numerical approach to simulate the degree of coherence (DOC) of a partially coherent beam (PCB) with a Schell-model correlator in any transverse plane during propagation. The approach is applicable for PCBs whose initial intensity distribution and DOC distribution are non-Gaussian functions, even for beams for which it is impossible to obtain an analytical expression for the cross-spectral density (CSD) function. Based on our approach, numerical examples for the distribution of the DOC of two types of PCBs are presented. One type is the partially coherent Hermite–Gaussian beam. The simulation results of the DOC agree well with those calculated from the analytical formula. The other type of PCB is the one for which it is impossible to obtain an analytical expression of CSD. The evolution of the DOC with the propagation distance and in the far field is studied in detail. Our numerical approach may find potential applications in optical encryption and information transfer.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ₀, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index n_e/n_o of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Measuring vector field correlations using diffraction

We present a method for efficiently measuring the 2 × 2 correlation matrix for paraxial partially coherent beams by using diffraction from small apertures and obstacles. Several representations for this matrix function of four spatial variables are discussed and illustrated with experimental results, including various alternative definitions of the spatial degree of coherence.

Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams

Complicated partially coherent beams (PCBs) are useful in many applications, such as free-space optical communications, particle trapping and optical imaging, while usually it is hard to derive analytical propagation formulae for such beams, and one has to fall back on numerical methods. The conventional numerical methods have some intrinsic drawbacks. In this paper, we introduce an efficient tensor approach (ETA) for simulating paraxial propagation of arbitrary PCBs. The ETA is a direct reconstruction of the propagated PCB without aliasing and rippling problems, and the algorithm is simple and robust with a tensor/matrix multiplication as the main calculation. The validity of ETA is verified through comparing simulation results with analytical results, numerical integration results and experimental results, respectively. The ETA provides a fast and reliable way for simulating paraxial propagation of arbitrary PCBs.

Vector optical coherence lattices generating controllable far-field beam profiles

We introduce partially coherent vector sources with periodic spatial coherence properties, which we term vector optical coherence lattices (VOCLs), as an extension of recently introduced scalar OCLs. We derive the realizability conditions and propagation formulae for radially polarized VOCLs (i.e., a typical kind of VOCLs). We show that radially polarized VOCLs display nontrivial propagation properties and generate controllable intensity lattices in the far zone of the source (or in the focal plane of a lens). By adjusting source coherence, one can obtain intensity lattices with bright or dark nodes. The latter can be employed to simultaneously trap multiple particles or atoms as well as in free-space optical communications. We also report the experimental generation of radially polarized VOCLs and we characterize VOCLs propagation properties.

Vector Hermite-Gaussian correlated Schell-model beam

A new kind of partially coherent vector beam named vector Hermite-Gaussian correlated Schell-model (HGCSM) beam is introduced as a natural extension of recently introduced scalar HGCSM beam. The realizability and beam conditions for a vector HGCSM beam with uniform state of polarization (SOP) or non-uniform SOP are derived, respectively. Furthermore, analytical formulae for a vector HGCSM beam propagating in free space are derived, and the propagation properties of a vector HGCSM beam with uniform SOP or non-uniform SOP in free space are studied and analyzed in detail. We find that the behaviors of a vector HGCSM beam on propagation are quite different from those of a conventional vector partially coherent beam with uniform SOP or non-uniform SOP, and modulating the structures of the correlation functions cannot only modulate the intensity distribution, but also the state of polarization, the degree of polarization and the polarization singularities of a partially coherent vector beam on propagation. Furthermore, we report experimental generation of a radially polarized HGCSM beam for the first time. Our results provide a novel way for polarization modulation.

Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization

Scalar cosine-Gaussian-correlated Schell-model (CGCSM) beams of circular or rectangular symmetry were introduced just recently. In this paper, a new kind of partially coherent vector beam named vector CGCSM beam with radial polarization (i.e., radially polarized CGCSM beam) is introduced. The realizability conditions for a radially polarized CGCSM source and the beam condition for radiation generated by such source are derived. The statistical properties, such as the average intensity, the degree of coherence, the degree of polarization and the state of polarization, of a radially polarized CGCSM beam focused by a thin lens are analyzed in detail. It is found that the statistical properties of a radially polarized CGCSM beam are quite different from those of a conventional radial polarized partially coherent beam with Gaussian correlated Schell-model function. Furthermore, we first report experimental generation of a radially polarized CGCSM beam and measure its focusing properties. Our experimental results are consistent with the theoretical predictions.

Using shadows to measure spatial coherence

We present a very simple method for measuring the spatial coherence of quasi-monochromatic fields through the comparison of two measurements of the radiant intensity with and without a small obscuration at the test plane. From these measurements one can measure simultaneously the field's coherence at all pairs of points whose centroid is the centroid of the obstacle. This method can be implemented without the need of any refractive or diffractive focusing elements.

Vectorial coherence holography

Extension of coherence holography to vectorial regime is investigated. A technique for controlling and synthesizing optical fields with desired elements of coherence-polarization matrix is proposed and experimentally demonstrated. The technique uses two separate coherence holograms, each of which is assigned to one of the orthogonal polarization components of the vectorial fields.