The problem was recently reported that the far-zone electromagnetic momentum of light produced by scattering on a spatially anisotropic random medium can be the same at every azimuthal angle of scattering. Here, we extend the analysis to focus on the possibility of producing a rotationally symmetric spectral degree of coherence (SDOC) generated by scattering by an anisotropic process. The necessary and sufficient conditions for producing such a SDOC in the far zone are derived when a polychromatic electromagnetic plane wave is scattered by an anisotropic Gaussian Schell-model medium. We find that, unlike the generation of a rotationally symmetric momentum flow, it is not enough to simply restrict the structural characteristics of the medium and the incident light source to achieve a SDOC with rotational symmetry. An additional and essential requirement is that the azimuthal angles of scattering corresponding to the two observation points of the SDOC must be constrained to be equal. Only when all these constraints are satisfied simultaneously can a rotationally symmetric electromagnetic SDOC generated by scattering by an anisotropic process be realized. In addition, we find that although the medium parameter conditions for generating a rotationally symmetric SDOC and a rotationally symmetric momentum flow are completely different, it remains possible that the SDOC and the momentum flow produced by a spatially anisotropic medium can still simultaneously exhibit rotational symmetry, provided that the distribution of the correlation function of the scattering potential of the medium is isotropic in the plane perpendicular to the incident direction. Our results not only contribute to a deeper understanding of the far-field distribution of light scattering on an anisotropic scatterer, but also have potential applications in light-field manipulation and in the inverse scattering problem.

Although the equivalence theorem (ET) in the potential scattering theory has been proposed for a long time, its analysis is always confined to the idealized case where the incident field is a spatially coherent plane wave, which limits its practical applications. Here by exploiting Laplace's method for double integrals and the so-called beam condition, we generalize the ET in the potential scattering theory to partially coherent beams for the first time to the best of our knowledge. We present the analytical condition that two scattered fields, produced by Gaussian Schell-model beams on scattering from Gaussian Schell-model media, may have the same normalized spectral densities in the far zone. We find that the condition contains three implications, each corresponding to a statement of an ET for the spectral density in a scattering scenario, which exposes the concept of a previously unreported triad of ETs for the spectral density of partially coherent beams on scattering. Our results contribute to improving reconstruction accuracy when resolving the inverse scattering problem in practical situations, where the light field utilized to illuminate an unknown scatterer is a partially coherent beam rather than a plane wave.

By using Laplace's method for double integrals and the so-called beam condition obeyed by a partially coherent beamlike light field, we report the equivalence theory (ET) of partially coherent beams on scattering for the first time. We present the necessary and sufficient condition for the two scattered fields that have the same normalized radiant intensity distribution when Gaussian Schell-model beams whose effective beam widths are much greater than the effective transverse spectral coherence lengths are scattered by Gaussian Schell-model media. We find that the condition contain three implications, and each of them corresponds to a statement of an ET of radiant intensity in a scattering scenario, which exposes the concept of a previously unreported triad of ETs for the radiant intensity of partially coherent beams on scattering. We further find that the existing ET of plane waves on scattering, which only asserts that two scatterers with scattering potentials' correlations whose low-frequency antidiagonal spatial Fourier components are identical, essentially is merely the first member of our triad of ETs, while the other two hidden important members are completely ignored. Our findings are crucial for the inverse scattering problem since they contribute to avoid possible reconstruction errors in realistic situations, where the light field used to illuminate an unknown object is a partially coherent beam rather than an idealized plane wave.

The question is examined as to whether the far-zone distribution of the electromagnetic momentum of the light generated by scattering on a spatially anisotropic random medium can be the same in every azimuthal angle of scattering. We show that the rotationally symmetric distribution of the scattered momentum flow in the far zone may be realized, provided that the structural parameters of both the scattering medium and the incident light source are chosen appropriately, when a polychromatic electromagnetic plane wave is scattered by an anisotropic, Gaussian, Schell-model medium. We derive the necessary and sufficient conditions for producing such a distribution. It is found that the scatterers have the same effective widths (σx, σy) but different effective correlation widths (μx, μy), yet all of them have the ability to produce rotationally symmetric distributions of the scattered momentum flow in the far zone. The same is true of the media having the same (μx, μy) but different (σx, σy). It is also found that the realization of the rotationally symmetric scattered momentum flow is independent of the spectral degree of polarization of the incident light source-the rotationally symmetric distribution of the scattered momentum flow is always realizable regardless of whether the incident light field is fully polarized, partially polarized or completely unpolarized. Our results have potential practical applications in optical mircromanipulation such as optical trapping of particles, especially when the optical forces used to manipulate the particles are required to be rotationally symmetric.

As is well known that the distribution of the scattered radiation generated by an anisotropic scatterer usually lacks rotational symmetry about the direction of incidence due to the spatial anisotropy of the scatterer itself. Here we show that the rotationally symmetric distribution of the far-zone scattered momentum flow may be realized provided that the structural parameters of both the medium and the source are chosen suitably, when a polychromatic electromagnetic plane wave is scattered by an anisotropic Gaussian Schell-model medium. We derive necessary and sufficient conditions for producing such a symmetric distribution, and further elucidated the relationship between the spectral degree of polarization of the incident source and the rotationally symmetric momentum flow of the scattered field in the far zone. It is found that the realization of the rotationally symmetric scattered momentum flow is independent of the spectral degree of polarization of the source, i.e., the rotationally symmetric distribution of the far-zone scattered momentum flow is always realizable regardless of whether the incident source is fully polarized, partially polarized or completely unpolarized. Our results may find useful application in optical micromanipulation, especially when the optical force used to manipulate particles requires to be rotationally symmetric.

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.

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.

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.

A theoretical framework in the spherical polar coordinate system is developed to systematically treat the correlation between intensity fluctuations (CIF) of electromagnetic light waves on scattering from a collection of particles of ℒ types. Two ℒ×ℒ matrices called pair-potential matrix (PPM) and pair-structure matrix (PSM) are introduced to jointly formulate the normalized CIF of the scattered field for the first time. We build a closed-form relation that associates the normalized CIF with the PPM and the PSM as well as the spectral degree of polarization 𝒫 of the incident field, showing that the normalized CIF is closely related to the trace of the product of the PSM and the transpose of the PPM, and its dependence on 𝒫 is completely determined by the scattering polar angle and azimuth angle. For a special case where the spatial distributions of scattering potentials of particles of different types are similar and the same is true of their density distributions, 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 appears as a scaled factor to ensure the normalization of the CIF. The effects of the off-diagonal elements of the PPM and the PSM on the normalized CIF and its dependence on 𝒫 are illustrated by two numerical examples.

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.

Restriction to the one-excitation context allows two identical two-level atoms and their common one-mode cavity field to exhibit previously unreported features of three-party entanglement during fully coherent evolution. We find entanglement showing dynamical behavior in the form of nonanalytic slope discontinuities in the time record. Specifically, the entanglements of the system can become abruptly frozen in time, remaining at a constant value, and can subsequently suddenly begin thawing from this value. We calculate the onset timing of such sudden freezings and sudden thawings under several different initial conditions. The conditions producing permanent freezing of entanglement are found. We also identify a nontrivial upper limit for the sum of three individual bipartite entanglements, which exposes the concept of entanglement "volume" and the volume shrinkage that accompanies the entanglement sharing. Further analysis of these freezing and thawing processes reveals quantitative and qualitative constraints on entanglement sharing of three qubits.

The dynamical responses of two qubits jointly interacting with the same cavity mode are studied. New dynamical quantum phenomena labeled Entanglement Sudden Freezing and Entanglement Sudden Thawing are discovered by analyzing the normalized Schmidt weights.

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.

In the analysis of the correlation between intensity fluctuations (CIF) of light waves on scattering from a medium, it is implicitly assumed that the incident field is monochromatic. However, under usual circumstances, the field always has a certain frequency width. We examine the CIF of polychromatic electromagnetic light waves on scattering. It is found, in general, that the frequency components of the CIF may change on scattering from a medium whose dielectric susceptibility is a random function of position. The critical angle at which no frequency shift arises is introduced and the corresponding analytic expression is derived. The result shows that the critical angle is dominated by the physical properties of the medium and the source. Finally, we propose a scaling law for the normalized CIF for the scattering of polychromatic electromagnetic light waves. Our theory can be regarded as the vectorial extension of the scalar theory of Wolf et al.

Within the Markov approximation, we introduce a novel class of random media which can produce a scattered field with optical lattice patterns. It is shown that the array dimension, lobes intensity profile, and the periodicity of the optical lattice can be flexibly controlled by altering the correlation parameters of scattering potential of the random medium. In addition, a new method for designing random media is proposed. It is shown that the convolution of any two legitimate degrees of potential correlation can lead to a new degree of potential correlation corresponding to a new scattered intensity distribution. An example of a novel family of random media is cited to demonstrate the result.

Within the accuracy of the first-order Born approximation, the far-zone behaviors of light waves on scattering from a particulate medium with two different types of particles, i.e., deterministic particles and random particles, have been discussed. It is shown that both the location of the deterministic particles and the distribution of the random particles in the system play roles in the far-zone scattered spectral density. It is also shown that the distribution of the spectral degree of coherence of the scattered field oscillates with the increase of the scattering angle, and the amplitude of the oscillation is closely related to the location of the deterministic particles and the distribution of the random particles.

The spectral degree of coherence of light wave on scattering from a collection of particles is discussed. It is shown that both the characteristic of each particle and the distribution of particles in the collection play roles in the spectral degree of coherence of the far-zone scattered field. Two special cases, i.e. a collection of random particles with determinate distribution and a collection of determinate particles with random distribution, are discussed, and the particle-induced coherence change and the distribution-induced coherence change are found in the scattered field.

We present a condition for generating the same scattered spectral density by random and deterministic media. Examples of light waves on scattering from a Gaussian-centered deterministic medium and a Gaussian-correlated quasi-homogeneous random medium are discussed. It is shown that the normalized far-zone scattered spectral density produced by a Gaussian-centered deterministic medium and by a Gaussian-correlated quasi-homogeneous random medium will be identical provided that the square of the effective width of normalized correlation coefficient of the quasi-homogeneous random medium is twice the square of the effective width of scattering potential of the determinate medium.

The far-zone scattered spectral density of a light wave on the scattering from a collection of particles is investigated, and the relationship between the character of the collection and the distribution of the scattered spectral density is discussed. It is shown that both the number of particles and their locations in the collection play roles in the distribution of the far-zone scattered spectral density. This phenomenon may provide a potential method to reconstruct the structure character of a collection of particles from measurements of the far-zone scattered spectral density.

In order to improve the energy efficiency and image contrast of liquid crystal display(LCD) projector,a wide-angle and broadband optical thin-film polarizing beam splitter(PBS) was designed.Several thin-film materials was adopted to achieve multi-kinds of Brewster's angles.The number and thickness of the films were optimized to obtain the wide-angle and broadband PBS.Using SF57 and SF2 glasses as prism materials,and TiO 2,Ta 2O 5,Al 2O 3,SiO 2 as film materials,four typical PBS multi-layer designs were given based on the above principle and the automatic Needle design method.The layer number of the optimized thin-film is 50～60,and the incident angle in air for the PBS reaches ±10.5°.The measured results showed that the integrated transmittance of P-polarization was 88.0% and 93.4% respectively at wavelength of 420—460 nm and 460—680 nm as well as that of S-polarization was 0.095% at wavelength of 420—680 nm.The PBS can be applied to F/2.8 optical systems to improve their performance obviously.