Higher-order twisted/astigmatic Gaussian Schell-model cross-spectral densities and their separability features

Twisted sinc-correlation Schell-model array beams

We introduce a class of twisted sinc-correlation partially coherent array sources, by applying the construction theory of correlation function. Spectral density of such novel focused beam propagating in free space is analyzed. It is shown that the intensity distribution presents a good twisted effect and splitting phenomenon upon propagation. The array dimension, the intensity distribution and spatial distribution of the lobes can be flexibly regulated by altering the source parameters. We also explore the spatial evolution of multiple correlation singularities of this light field, where the phase distribution appears as a rotational spiral windmill profile during propagation. Furthermore, the coherence orbital angular momentum of the twisted source beam is investigated. These findings could be useful in the particle manipulation and free-space optical communication.

Asymmetrical inseparable coherent structures

A novel, to the best of our knowledge, class of coherent structures of inseparability, incorporating phases asymmetrically cross-coupled by two position vectors, is introduced in theory and experiment. These phases disappear in the environment of complete coherence, but the vanishment is avoidable in the coexistent state of extreme incoherence and full coherence. The radiated beams intrinsically possess a controllable rotation but undergo an intermediate process quite different from the twisted Gaussian Schell-model beams. Analysis shows a novel association between the magnitude and the phase of the coherent structure which displays both synergy and opposition. Our work further reveals the inner mechanism of the inseparable coherent structures and extends a new horizon for the optical twist.

Twisted sinc-correlation Schell-model beams

We introduce a new class of twisted sinc-correlation Schell-model (TSCSM) beams and analyze the statistical characteristics of such novel sources during propagation. Several typical examples are given to specifically explore the distribution and twist effect of spectral density and degree of coherence (DOC). It is shown that the irradiance profile of light intensity always rotates to 90 degree. With appropriate light field adjustment, twist effect of DOC would be diverse. DOC can exhibit unidirectional or non-unidirectional rotation during propagation. Besides, the twist factor can make the spot show a tendency to split. And beam width and coherence length also have an impact on this splitting phenomenon of spectral density.

Generating non-uniformly correlated twisted sources

The inverse method of proving the twistability of cross-spectral density (CSD) inevitably falls into spontaneous difficulties. Based on a nonnegative self-consistent design guideline for generating genuine CSDs introduced by Gori and Santarsiero, we demonstrate a feasible way for twisting partially coherent sources by sticking a Schell-model function to CSDs, which also determines the upper bound of the twisting strength. Analysis shows that the degree of coherence of a new class of twisted pseudo-Gaussian Schell-model beam is neither shift invariant nor shift-circular symmetric. In the presence of a vortex phase, the two different types of chiral phases affect each other and together control the propagation behavior. We further carry out an experiment to generate this non-uniformly correlated twisted beam using weighted superposition of mutually uncorrelated pseudo modes. The result is beneficial for devising nontrivial twisted beams and offers new opportunities.

A New Type of Shape-Invariant Beams with Structured Coherence: Laguerre-Christoffel-Darboux Beams

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.

Twisted space-frequency and space-time partially coherent beams

We present partially coherent sources that are statistically twisted in the space-frequency and space-time domains. Beginning with the superposition rule for genuine partially coherent sources, we derive source plane expressions for the cross-spectral density (CSD) and mutual coherence functions (MCFs) for twisted space-frequency and space-time Gaussian Schell-model (GSM) beams. Using the Fresnel approximation to the free-space Green's function, we then paraxially propagate the CSD and MCF to any plane [Formula: see text]. We discuss the beams' behavior as they propagate, with particular emphasis on how the beam shape rotates or tumbles versus z. To validate our analysis, we simulate the generation and subsequent propagation of twisted space-frequency and space-time GSM beams. We compare the simulated moments to the corresponding theoretical predictions and find them to be in excellent agreement. Lastly, we describe how to physically synthesize twisted space-frequency and space-time partially coherent sources.

Random source for generating Airy-like spectral density in the far field

A stationary beam forming an Airy-like spectral density in the far field is analyzed theoretically and experimentally. The Schell-model source that radiates such a beam is an extended version of a recently introduced source [O. Korotkova, et al., Opt. Lett.43, 4727 (2018)10.1364/OL.43.004727; X. Chen, et al., Opt. Lett.44, 2470 (2019)10.1364/OL.44.002470, in 1D and 2D, respectively]. We show, in particular, that the source degree of coherence, being the fourth-order root of a Lorentz-Gaussian function and having linear and cubic phase terms, may be either obtained from the Fourier transform of the far-field Airy-like pattern or at the source using the sliding function method. The spectral density of the beam is analyzed on propagation through paraxial ABCD optical systems, on the basis of the generalized Collins integral, by means of the derived closed-form expression. We show that the distribution of the side lobes in the Airy beam spectral density can be controlled by the parameters of the source degree of coherence. Further, an experiment involving a spatial light modulator (SLM) is carried out for generation of such a beam. We experimentally measure the complex degree of coherence of the source and observe the gradual formation of a high-quality Airy-like spectral density towards the far field. In addition, the trajectory of the intensity maxima of the beam after a thin lens is studied both theoretically and experimentally. The random counterpart of the classic, deterministic Airy beam may find applications in directed energy, imaging, beam shaping, and optical trapping.

Stochastic complex transmittance screens for synthesizing general partially coherent sources

We develop a method to synthesize any partially coherent source (PCS) with a genuine cross-spectral density (CSD) function using complex transmittance screens. Prior work concerning PCS synthesis with complex transmittance screens has focused on generating Schell-model (uniformly correlated) sources. Here, using the necessary and sufficient condition for a genuine CSD function, we derive an expression, in the form of a superposition integral, that produces stochastic complex screen realizations. The sample autocorrelation of the screens is equal to the complex correlation function of the desired PCS. We validate our work by generating, in simulation, three PCSs from the literature-none has ever been synthesized using stochastic screens before. Examining planar slices through the four-dimensional CSD functions, we find the simulated results to be in excellent agreement with theory, implying successful realization of all three PCSs. The technique presented herein adds to the existing literature concerning the generation of PCSs and can be physically implemented using a simple optical setup consisting of a laser, spatial light modulator, and spatial filter.

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties

We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.