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Abstract The design and formation of van der Waals (vdW) heterostructures with different two-dimensional (2D) materials provide an opportunity to create materials with extraordinary physical properties tailored toward specific applications. Mechanical exfoliation of natural vdW materials has been recognized as an effective way for producing high-quality ultrathin vdW heterostructures. Abramovite is one of such naturally occurring vdW materials, where the superlattice is composed of alternating Pb 2 BiS 3 and SnInS 4 2D material lattices. The forced commensuration between the two incommensurate constituent 2D material lattices induces in-plane structural anisotropy in the formed vdW heterostructure of abramovite, even though the individual 2D material lattices are isotropic in nature. Here, we show that ultrathin layers of vdW heterostructures of abramovite can be achieved by mechanical exfoliation of the natural mineral. Furthermore, the structural anisotropy induced highly anisotropic vibrational and optical responses of abramovite thin flakes are demonstrated by angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent third-harmonic generation. Our results not only establish abramovite as a promising natural vdW material with tailored linear and nonlinear optical properties for building future anisotropic integrated photonic devices, but also provide a deeper understanding of the origin of structural, vibrational and optical anisotropy in vdWmore »heterostructures.« less

Many data applications have certain invariant constraints due to practical needs. Data curators who employ differential privacy need to respect such constraints on the sanitized data product as a primary utility requirement. Invariants challenge the formulation, implementation, and interpretation of privacy guarantees. We propose subspace differential privacy, to honestly characterize the dependence of the sanitized output on confidential aspects of the data. We discuss two design frameworks that convert well-known differentially private mechanisms, such as the Gaussian and the Laplace mechanisms, to subspace differentially private ones that respect the invariants specified by the curator. For linear queries, we discuss the design of near-optimal mechanisms that minimize the mean squared error. Subspace differentially private mechanisms rid the need for post-processing due to invariants, preserve transparency and statistical intelligibility of the output, and can be suitable for distributed implementation. We showcase the proposed mechanisms on the 2020 Census Disclosure Avoidance demonstration data, and a spatio-temporal dataset of mobile access point connections on a large university campus.

Cannizzarite is a naturally occurring mineral formed by van der Waals (vdW) stacking of alternating layers of PbS-like and Bi₂S₃-like two-dimensional (2D) materials. Although the PbS-type and Bi₂S₃-type 2D material layers are structurally isotropic individually, the forced commensuration between these two types of layers while forming the heterostructure of cannizzarite induces strong structural anisotropy. Here we demonstrate the mechanical exfoliation of natural cannizzarite mineral to obtain thin vdW heterostructures of PbS-type and Bi₂S₃-type atomic layers. The structural anisotropy induced anisotropic optical properties of thin cannizzarite flakes are explored through angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent anisotropic third-harmonic generation. Our study establishes cannizzarite as a new natural vdW heterostructure-based 2D material with highly anisotropic optical properties for realizing polarization-sensitive linear and nonlinear photonic devices for future on-chip optical computing and optical information processing.

Multi-element layered materials have gained substantial attention in the context of achieving the customized light-matter interactions at subwavelength scale via stoichiometric engineering, which is crucial for the realization of miniaturized polarization-sensitive optoelectronic and nanophotonic devices. Herein, naturally occurring hydrated sodium sulfosalt gerstleyite is introduced as one new multi-element van der Waals (vdW) layered material. The mechanically exfoliated thin gerstleyite flakes are demonstrated to exhibit polarization-sensitive anisotropic linear and nonlinear optical responses including angle-resolved Raman scattering, anomalous wavelength-dependent linear dichroism transition, birefringence effect, and polarization-dependent third-harmonic generation (THG). Furthermore, the third-order nonlinear susceptibility of gerstleyite crystal is estimated by the probed flake thickness-dependent THG response. We envisage that our findings in the context of polarization-sensitive light-matter interactions in the exfoliated hydrated sulfosalt layers will be a valuable addition to the vdW layered material family and will have many implications in compact waveplates, on-chip photodetectors, optical sensors and switches, integrated photonic circuits, and nonlinear signal processing applications.

Abstract Due to the highly nonlinear nature of the beam-loading, it is currently not possible to analytically determine the beam parameters needed in a two-bunch plasma wakefield accelerator for maintaining a low energy spread. Therefore in this paper, by using the Broyden–Fletcher–Goldfarb–Shanno algorithm for the parameter scanning with the code QuickPIC and the polynomial regression together with k -fold cross-validation method, we obtain two fitting formulas for calculating the parameters of tri-Gaussian electron beams when minimizing the energy spread based on the beam-loading effect in a nonlinear plasma wakefield accelerator. One formula allows the optimization of the normalized charge per unit length of a trailing beam to achieve the minimal energy spread, i.e. the optimal beam-loading. The other one directly gives the transformer ratio when the trailing beam achieves the optimal beam-loading. A simple scaling law for charges of drive beams and trailing beams is obtained from the fitting formula, which indicates that the optimal beam-loading is always achieved for a given charge ratio of the two beams when the length and separation of two beams and the plasma density are fixed. The formulas can also help obtain the optimal plasma densities for the maximum accelerated charge and the maximummore »acceleration efficiency under the optimal beam-loading respectively. These two fitting formulas will significantly enhance the efficiency for designing and optimizing a two-bunch plasma wakefield acceleration stage.« less

Naturally occurring layered mineral livingstonite is identified as a new type of van der Waals (vdW) heterostructure based 2D material, consisting of two commensurately modulated alternating layers of HgSb 2 S 4 and Sb 2 S 4 . The heterostructures of livingstonite crystal are prepared as thin flakes via mechanical exfoliation method. The prepared livingstonite crystals are further investigated in the context of vibrational, linear, and nonlinear optical properties, including anisotropic Raman scattering, wavelength-dependent linear dichroism (LD) transition effect, birefringence, and anisotropic third-harmonic generation (THG). Owing to the monoclinic crystal structure, livingstonite crystals exhibit strong anisotropic vibrational and optical responses. In contrast to conventional vdW heterostructures, the anomalous LD transition effect and the evolution of butterfly-shaped THG emission pattern in livingstonite crystals are demonstrated. Furthermore, the third-order nonlinear susceptibility is estimated for livingstonite crystal using the thickness-dependent THG emission response. Overall, the discussed outcomes establish livingstonite as a new type of naturally grown vdW heterostructure based 2D material and offer insights in tailoring linear and nonlinear light-matter interactions in such vdW heterostructures, which may find further relevance in polarized optical applications and on-chip integrated photonic circuits.

Van der Waals (vdW) materials have recently attracted significant interest in the context of orientation-dependent linear and nonlinear optical properties. Recently, arsenic trisulfide (As 2 S 3 ) or orpiment is identified as a new vdW layered material having anisotropic vibrational and optomechanical responses due to the reduced in-plane crystal symmetry, but its nonlinear optical response is still not well understood yet. Herein, the anisotropic third-harmonic generation (THG) response of mechanically exfoliated As 2 S 3 thin flakes is reported. The polarization-dependent evolution of THG emission from butterfly-shaped pattern to four-lobe pattern is comprehensively explored. Moreover, the third-order nonlinear susceptibility of As 2 S 3 crystal is extracted by analyzing the thickness-dependent THG emission. We anticipate that the discussed results will not only update the existing understanding on the nonlinear light-matter interaction in anisotropic vdW materials, but also promote future applications in integrated photonic circuits, on-chip nonlinear signal processing, and polarization-sensitive optical devices.