Optical coherence is a fundamental characteristic of light that plays a significant role in understanding interference, propagation, light-matter interaction, and other fundamental aspects of classical and quantum wave fields. The study of optical coherence has led to a wide range of applications, including optical coherence tomography, ghost imaging, and free-space optical communications. In recent years, the complex spatial structure of optical coherence embedded in partially coherent light beams has garnered increasing attention due to the novel physical effects it induces, such as self-shaping, self-focusing, and self-splitting of beams in free space. Partially coherent light beams with non-classical spatial coherence structures have found use in many innovative applications, including overcoming the classical Rayleigh diffraction limit in optical imaging, reducing the side effects of atmospheric turbulence in free-space optical communications, coherence-based optical encryption, and robust optical signal transmission. In this article, we present a systematic review of the manipulation and measurement of the spatial coherence structure of optical beams, their propagation and light-matter interaction, as well as the applications of partially coherent light beams with structured optical coherence. We begin with the representation of the cross-spectral density function for a partially coherent light beam using Gori's nonnegative definite condition and Wolf's coherent-mode decomposition theory. We then discuss in detail two different strategies for experimentally manipulating the spatial coherence structure, one based on the generalized van Cittert–Zernike theorem and the other on the coherent-mode decomposition theory. Next, we provide an overview of recent progress in measuring the complex spatial coherence structure of partially coherent light beams using methods based on self-referencing holography, generalized Hanbury Brown and Twiss experiment, and incoherent modal decomposition. We study the novel physical properties of partially coherent light beams with non-conventional spatial coherence structures during their propagation in free space and through a highly focused system, as well as their interaction with atmospheric turbulence. We also discuss the effect of structured optical coherence in reducing the negative effects of atmospheric turbulence. Finally, we present the applications of spatial coherence structure engineering in optical imaging, optical encryption, robust information transmission through complex media, particle trapping, refractive index measurement, beam shaping, and ultrahigh precision angular velocity measurement. Optical coherence structure not only provides a new degree of freedom for light manipulation but also offers an effective tool for novel light applications. 

Research progress on manipulating spatial coherence structure of light beam and its applications

We show how both the ellipticity $\ensuremath{\eta}$ and degree of polarization $P$ influence the extraordinary optical chirality properties of nonparaxial vortex beams. We find that, in stark contrast to paraxial optics and nonvortex modes, extremely rich and tunable spatial distributions of optical chirality density can be produced by an optical vortex beam under tight focusing. We develop a theoretical description of how the optical chirality can be tailored for purpose by altering both the state $\ensuremath{\eta}$ and degree of polarization $P$ of the input vortex mode, along with the magnitude and sign of optical orbital angular momentum via the pseudoscalar topological charge $\ensuremath{\ell}$. We expect that the results will have a significant role in both producing alternative techniques and improving existing methods in chiral nano-optics and structured light photonics. 

/pdf/customized-optical-chirality-of-vortex-structured-light-2cmqzij1.pdf

Customized optical chirality of vortex structured light through state and degree-of-polarization control

We develop a theoretical foundation for the spin angular momentum (SAM) of random, statistically stationary polychromatic light fields within the framework of classical optical coherence theory. The formulation is valid for fields of arbitrary frequency bandwidth and dimensionality. Both temporal and spectral representations are given, and we further elucidate the relationship between the SAM and the polarization characteristics of such fields as compared to monochromatic light. The special cases of quasimonochromatic light and planar fields are analyzed separately. Generally, our paper offers deeper insights into the SAM and polarization structures as well as their interlinked connections in random stationary light, which could be beneficial in exploiting SAM in stochastic optical near fields and tightly focused beams exhibiting complex polarization character. 

Spin of random stationary light

The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wavepackets. Specifically, partially coherent light represents the most common kind of classical light. Here, for the first time, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model unveils the possibility of performing photon-number-resolving detection to isolate the constituent quantum multiphoton wavepackets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wavepackets with up to sixteen photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects, but also establish a fundamental bridge between the classical and quantum worlds.

The Quantum Gaussian-Schell Model: A Link Between Classical and Quantum Optics

Orbit-induced localized spin angular momentum (OILS) has recently garnered significant attention. This paper introduces periodic edge dislocation (PED) into the tight focusing system. The study delves into the tight focusing characteristics of the radially polarized vortex plane beam with PED, demonstrating that PED serves as a straightforward and effective means of manipulating OILS, especially when both the orbital angular momentum and the polarization of the incident beam are fixed. Our findings indicate that the longitudinal OILS reaches its maximum when the difference between the period of PED and the vortex topological charge is equal to 1. Conversely, when the difference is 0, the transverse OILS reaches its maximum, while the longitudinal OILS reaches its minimum. Similar patterns are also observed in linearly polarized vortex beams. This research proposes a simple and practical way to control OILS, contributing to our understanding of optical orbit-spin coupling.

Manipulation of optical orbit-induced localized spin angular momentum using the periodic edge dislocation

In this work, we revisit the tight focusing of a radially polarized partially coherent Gaussian Schell-model beam and examine the effect of spatial coherence of the incident beam on the focal-plane three-dimensional (3D) polarization characters, including the 3D degree of polarization, polarimetric dimensionality, and polarimetric structure. The polarimetric structure and the associated structure for the spin density vector of the tightly focused field are obtained via the 3D characteristic decomposition of the $3\ifmmode\times\else\texttimes\fi{}3$ polarization matrix. We demonstrate that the generated focused field shows the genuine 3D polarization state and a sophisticated spin structure due to the reduced spatial coherence in the incident beam. We find the contributions to whole 3D polarization state of the focused field from the pure state, middle-term state, and 3D unpolarized state in the characteristic decomposition, as well as the contributions to the total spin density vector from the spins of pure state and middle-term state can be controlled by the transverse spatial coherence width of the incident Gaussian Schell-model beam. In addition, the genuine 3D polarization and the spin structure are analyzed in the connection of the recently introduced concept of polarimetric nonregularity. 

Three-dimensional polarization state and spin structure of a tightly focused radially polarized Gaussian Schell-model beam

The transverse spin and orbital-to-spin angular momentum conversion during strong focusing of light beams have attracted wide interest due to the novel physics behind and their broad potential applications. In this work, we study the effect of incident beam’s degree of polarization on the localized spin density of a tightly focused field. By modulating the correlation strength between two orthogonally polarized vortex modes of the incident beam, we find that the magnitude of the focal-plane transverse spin density component changes only slightly, while its spatial shape becomes an isotropic spin vortex with the decrease of the incident degree of polarization. Whereas, the longitudinal spin density, induced by the vortex phase, reduces its magnitude significantly with the decrease of incident beam’s degree of polarization. The behavior of the focal-plane spin density is interpreted with the two-dimensional degrees of polarization among the tightly focused field components. Furthermore, we explore the roles of the topological charge on enhancing the longitudinal spin density for unpolarized incident beam. Our results reveal the feasibility of spin-orbit interaction with partially polarized or even completely unpolarized light, such as the thermal light.

/pdf/effect-of-degree-of-polarization-on-localized-spin-density-2fzg0l0e.pdf

Effect of Degree of Polarization on Localized Spin Density in Tightly Focusing of Vortex Beams

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited].

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Three-dimensional polarization state and spin structure of a tightly focused radially polarized Gaussian Schell-model beam

Effect of Degree of Polarization on Localized Spin Density in Tightly Focusing of Vortex Beams

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited].