Arbitrary engineering of spatial caustics with 3D-printed metasurfaces.

Caustics occur in diverse physical systems, spanning the nano-scale in electron microscopy to astronomical-scale in gravitational lensing. As envelopes of rays, optical caustics result in sharp edges or extended networks. Caustics in structured light, characterized by complex-amplitude distributions, have innovated numerous applications including particle manipulation, high-resolution imaging techniques, and optical communication. However, these applications have encountered limitations due to a major challenge in engineering caustic fields with customizable propagation trajectories and in-plane intensity profiles. Here, we introduce the "compensation phase" via 3D-printed metasurfaces to shape caustic fields with curved trajectories in free space. The in-plane caustic patterns can be preserved or morphed from one structure to another during propagation. Large-scale fabrication of these metasurfaces is enabled by the fast-prototyping and cost-effective two-photon polymerization lithography. Our optical elements with the ultra-thin profile and sub-millimeter extension offer a compact solution to generating caustic structured light for beam shaping, high-resolution microscopy, and light-matter-interaction studies.

Resolving an inverse problem through a momentum flow within the framework of electromagnetic scattering.

Although there have been many approaches to inverse problem in the classic theory of potential scattering, they are implicitly confined to the analysis of the scattered electric field, and thus the magnetic counterpart of the scattered wave is ignored, which limits the further application of those approaches to some extent. Here, we propose a new, to the best of our knowledge, technique for an inverse problem within the framework of electromagnetic scattering. This technique aims at reconstructing the correlation function of the scattering potential of a random medium through measuring the electromagnetic momentum flow of the scattered field in the far zone. As illustrative examples, we use the technique to determine the correlation functions of the scattering potentials of homogeneous, isotropic, and Gaussian-correlated spheres. Our new inversion approach works both microscopically and macroscopically.

Polarization resonance with sub-wavelength switching of random light self-interfering in open-end cavity.

Following recent work [Sci. China Phys. Mech. Astron.66, 274213 (2023)10.1007/s11433-023-2097-9] that revealed the sub-wavelength scale resonance phenomenon in scalar random beams counterpropagating in an open-end cavity, we extend the analysis to the vectorial domain and show a similar effect for the polarization properties. We found that, in contrast with the changes in the scalar properties, being of harmonic nature, changes in polarization involve alternating regions of constant values followed by sharp and complex changes.

Rigorous full-wave calculation of optical forces on microparticles immersed in vector Pearcey beams.

We present the electromagnetic fields of vector Pearcey beams by employing the vector angular spectrum representation. The beams maintain the inherent properties of autofocusing performance and inversion effect. Based on the generalized Lorenz-Mie theory and Maxwell stress tensor approach, we derive the partial-wave expansion coefficients of arbitrary beams with different polarization and the rigorous solution to evaluate the optical forces. Furthermore, we investigate the optical forces experienced by a microsphere placed in vector Pearcey beams. We study the effects on the longitudinal optical force arising from the particle size, permittivity and permeability. This exotic curved trajectory transport of particles by vector Pearcey beams may find applications in the case where the transport path is partly blocked.

Relationship between Hanbury Brown-Twiss effect and spectral degree of polarization in light scattering from a collection of particles of $\mathcal {L}$ types.

We consider the vectorial extension of the recently developed matrix theory for the correlation between intensity fluctuations (CIF) of the scattered field generated by a collection of particles of $\mathcal {L}$ types [Y. Ding and D. M. Zhao, Opt. Express 30 46460, 2022]. In the spherical polar coordinate system, we establish a closed-form relation that connects the normalized CIF of the electromagnetic scattered field with the pair-potential matrix (PPM), the pair-structure matrix (PSM), and the spectral degree of polarization $\mathcal {P}$ of the incident field. Based on this, we pay much attention to the dependence of the normalized CIF of the scattered field on $\mathcal {P}$. It is found that the normalized CIF can be monotonically increasing or be nonmonotonic with $\mathcal {P}$ in the region [0, 1], determined by the polar angle θ and the azimuthal angle ϕ. Also, the distributions of the normalized CIF with $\mathcal {P}$ at polar angles and azimuthal angles are greatly different. These findings are explained mathematically as well as physically, and may be of interest to some related fields, especially where the CIF of the electromagnetic scattered field plays important roles.

Matrix treatment for the correlation between intensity fluctuations of light waves on weak scattering from a collection of particles with L types.

We report a new approach to the correlation between intensity fluctuations (CIF) of light waves on weak scattering from a collection of particles with L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly formulate the CIF of the scattered field for the first time. We show that the CIF equals the squared modulus of the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices provide sufficient amount of information to determine the CIF of the scattered field. Based on this, we further analyze the normalized version of the CIF of the scattered field. It is found that the expression of the normalized CIF can have pretty compact and profound forms in three special cases: (I) the spatial distributions of the scattering potentials of particles of different types are similar (II) the spatial distributions of the densities of particles of different types are similar (III) both the scattering potentials and the densities of particles of different types are similarly distributed in space. Finally, the effects of the off-diagonal elements of the PPM and the PSM on the normalized CIF of the scattered field are illustrated by two examples. The results show that the non-zero cross correlation between particles of different types can induce intense changes in the normalized CIF of the scattered field.

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.

Controllable Laguerre Gaussian wave packets along predesigned trajectories.

We introduce controllable Laguerre Gaussian wave packets (LGWPs) with self-accelerating and self-focusing properties along their predesigned parabolic trajectory via phase modulation. Numerically and experimentally recorded intensity patterns of controllable LGWPs with topological charges are obtained, and it is obvious that they agree well with the theoretical model. Furthermore, spatiotemporally controllable LGWPs can propagate stably along predesigned trajectories for many Rayleigh lengths. This paper not only provides a theoretical propagation model for these multi-dimensional controllable LGWPs, but also promotes further development of the basic research into self-bending and autofocusing structured light fields.

Scattering of light waves from a collection of particles of L types.

A new, to the best of our knowledge, pathway is paved within the first-order Born approximation to access light scattering from a collection of particles of L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly characterize the scattered field. We show that the cross-spectral density function of the scattered field equals the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices allow us to determine all the second-order statistical properties of the scattered field. Based on this, the spectral degree of coherence (SDOC) of the scattered field is further analyzed. In a special case where the spatial distributions of the scattering potentials of particles of different types are similar and the same is true of their density distributions, it is found that the PPM and the PSM will reduce to two new matrices whose elements separately quantify the degree of angular correlation of the scattering potentials of particles and their density distributions, and the number of species of particles in this special case will appear as a scaled factor to ensure the normalization of the SDOC. The importance of our new approach is illustrated by an example.

Self-focusing vortex beams.

A class of wide-stationary optical sources with a specially designed degree of coherence profile is introduced for radiating spectral densities with a vortex whose core's location and size can be controlled at a specified range. This is achieved by modeling of the source coherence state as a combination of a helicoidal separable phase and a Cartesian phase factor, depending on the separation between the $ n $th power of the radius-vectors of two points.

Partially coherent Pearcey-Gauss beams.

We investigate the dynamics of partially coherent Pearcey-Gauss beams propagating in free space, theoretically and experimentally. They are produced by introducing the degree of coherence (DOC) function with Gaussian Schell-model correlation into the light source in the frequency domain. Under a nearly incoherent state, the oscillation of the sidelobe turns smooth, and the intensity distribution concentrates on the mainlobe. Particularly, partially coherent Pearcey-Gauss beams would maintain the inherent properties of autofocusing performance and inversion effect without diminishing the autofocusing distance and form-invariable propagation. Moreover, the opening angle and the shift of peak intensity of the beams can be controlled by the binary parabola in the spectrum distribution of the Pearcey function. Our experimental results are in great agreement with the theoretical analysis.

Twisted anisotropic electromagnetic beams with Laguerre Gaussian-Schell model correlation.

A class of twisted anisotropic electromagnetic beams with Laguerre Gaussian-Schell model correlation is introduced as an extension of the scalar beams into electromagnetic domain. The analytical formula for the cross-spectral density matrix of such a beam on propagation has been derived. Then the degree of coherence, the degree of polarization and the state of polarization are discussed in detail. Our results reveal that it is feasible and efficient to engineer the characteristics of beams via setting the anisotropy of the beam source, the topological charge, and specially the twisted factor. This provides us a method for synthesizing fields presenting peculiar coherence and polarization patterns.

Random sources generating hollow array beams.

A novel class of partially coherent light sources that can yield stable optical lattice termed hollow array in the far field is introduced. The array dimension, the distance of hollow lobes intensity profile, the size and shape of the inner and outer lobe contours and other features can be flexibly controlled by altering the source parameters. Further, every lobe can be shaped with polar and Cartesian symmetry and even combined to form nested structures. The applications of the work are envisioned in material surface processing and particle trapping.

Propagation of Gaussian Schell-model beams through a jet engine exhaust.

Theoretical predictions of light beam interactions with jet engine exhaust are of importance for optimization of various optical systems, including LIDARs, imagers and communication links operating in the vicinity of aircrafts and marine vessels. Here we extend the analysis previously carried out for coherent laser beams propagating in jet engine exhaust, to the broad class of Gaussian Schell-Model (GSM) beams, being capable of treating any degree of coherence in addition to size and radius of curvature. The analytical formulas for the spectral density (SD) and the spectral degree of coherence (DOC) of the GSM beam are obtained and analyzed on passage through a typical jet engine exhaust region. It is shown that for sources with high coherence, the transverse profiles of the SD and the DOC of the GSM beams gradually transition from initially circular to elliptical shape upon propagation at very short ranges. However, such transition is suppressed for sources with lower coherence and disappears in the incoherent source limit, implying that the GSM source with low source coherence is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence. The physical interpretation and the illustration are included.

Experimental generation of a kind of reversal rotating beams.

A kind of reversal rotating beams with astigmatic phase is proposed, whose spectral density and degree of coherence both follow anisotropic Gaussian distribution. Unlike a general rotating beam, the spectral density and the degree of coherence of this beam can be reversal rotated during propagation, that is, the direction of rotation could change automatically. Such a beam can be viewed as having two elements with astigmatic phase and partial coherence of the beam, which can reshape the cross-spectral density, corresponding to two directions of rotation. We generated this beam successfully in experiment and observed the expected phenomenon, which is basically consistent with the result of the numerical simulation. The reversal rotating beam has certain requirements on the astigmatic phase, which is analyzed and verified. The effect of the main parameters in astigmatic phase on the reversal rotation is further studied from both simulation and experiment.

Elliptical Laguerre Gaussian Schell-model beams with a twist in random media.

A class of partially coherent elliptical sources with twisted Laguerre Gaussian Schell-model (TLGSM) correlation function is proposed, which are capable of producing beams whose intensity profiles may vary substantially. This kind of beam can be viewed as the generalization of the LGSM beams. Properties of the spectral density during propagation in free space and atmospheric turbulence are investigated with varying quantities related to the beam source and the medium. It is shown that the elliptical TLGSM beams evolve in a manner that is much more complex compared to the LGSM beams. In addition, the behaviour of the rotation angle is further analysed by quantitative examples.

Maintenance of the coherence of a light wave on weak scattering.

In the light of the perspective of statistical similarity, we examine the maintenance of the second-order coherence of a light wave on weak scattering from a random medium. Some new and nontrivial results relating to properties of the scattered field which remains the second-order coherence of the incident field are presented. By assuming that the scattered field remains the second-order coherence, we can show that all of higher order correlation functions of Fourier component of the scattering potential can reduce to the like-factorization forms with a series of constant coefficients. These coefficients furnish an efficient and direct way to describe the higher order coherence property of the scattered field. We also show that the combination of the maintenance of second- and fourth-order coherence implies the scattered field coherence to all orders. Finally, the structure feature of the random medium is also discussed when the coherence of the incident field is retained up to 2nth order, in particular, in the case of the second-order coherence. Our theory is an important contribution for understanding of spatially fully coherent scattered fields, and also gives a general and new method to discuss the variation of the coherence of the scattered field.

Generalized partially coherent beams with nonseparable phases.

A new, to the best of our knowledge, family of partially coherent beams incorporating a set of nonseparable phases is introduced. Due to the nonnegative definiteness of the cross-spectral density function, these phases cannot survive in the limit of full coherence, which distinguishes them from conventional phase terms. An example of a nonuniform model beam with a quartic nonseparable phase is presented. It is shown that the presence of such a phase in effect stretches the beam in a specific direction upon propagation. In particular, the interplay between the magnitude and phase of the source coherence state endows the beam with a wing-like structure. The fundamental concept developed here brings into evidence the countless nonseparable phases differing from twist, and can be exploited to generate customized partially coherent beams for applications in optics.

Partially coherent dual and quad airy beams.

We investigate the partially coherent dual and quad Airy beams, which are the partially coherent version of multiple Airy beams, in the framework of cross-spectral density functions. They are constructed by the superposition of two and four partially coherent Airy beams without reduced acceleration properties (rate and range). In the case where the interference effect is not considered, the property of lacking side lobes in the partially coherent quad Airy beams leads to the performance of the optical frame during propagation. In the case with constructive interference, we find that the interference pattern produced by the partially coherent dual and quad Airy beams can remain stable and display a spot right in the center of the optical frame. The shape and peak intensity of this interference spot can be controlled by the transverse width of the beams. These results may provide new understanding for the partially coherent field of accelerating beams.

Generation and propagation of a new kind of power-exponent-phase vortex beam.

A general analytical formula for the propagation of the new kind of power-exponent-phase vortex beam through a paraxial ABCD optical system is derived. With two different calculation methods, the evolution of the intensity distribution and phase contour of such a beam in free space is investigated. Some experiments are carried out to verify the theoretical predictions. Both of the theoretical and experimental results show that the beam's profile can be modulated by the topological charge and the power order. In addition, the orbital angular momentum (OAM) density and the normalized OAM of such a beam are also studied.