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Register a new userHigher order multipoles in metamaterial homogenization
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The higher order multipoles above the electric quadrupole are commonly neglected in metamaterial homogenization. We show that they nevertheless can be significant when second order spatial dispersive effects, such as the magnetic response, are considered. In this respect, they can be equally important as the magnetization and quadrupole terms, and should not automatically be neglected.
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We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments are measured after the light has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific values of the angles of the waveplates. For more general two-mode problems, equivalent measurements can be performed.
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate otherwise time-consuming computations. By means of an asymptotic expansion, a hierarchy of linear problems is derived, whose solutions are looked at in detail. It is highlighted how these generalized homogenization problems depend on each other. We extend the Basic Scheme to fit this new problem class and give some numerical results for the first two problem orders.
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher moments of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.
Estimates of the source parameters of gravitational-wave (GW) events produced by compact binary mergers rely on theoretical models for the GW signal. We present the first frequency-domain model for inspiral, merger and ringdown of the GW signal from precessing binary-black-hole systems that also includes multipoles beyond the leading-order quadrupole. Our model, {tt PhenomPv3HM}, is a combination of the higher-multipole non-precessing model {tt PhenomHM} and the spin-precessing model {tt PhenomPv3} that includes two-spin precession via a dynamical rotation of the GW multipoles. We validate the new model by comparing to a large set of precessing numerical-relativity simulations and find excellent agreement across the majority of the parameter space they cover. For mass ratios $<5$ the mismatch improves, on average, from $sim6%$ to $sim 2%$ compared to {tt PhenomPv3} when we include higher multipoles in the model. However, we find mismatches $sim8%$ for the mass-ratio $6$ and highly spinning simulation. As a first application of the new model we have analysed the binary black hole event GW170729. We find larger values for the primary black hole mass of $58.25^{+11.73}_{-12.53} , M_odot$ (90% credible interval). The lower limit ($sim 46 , M_odot$) is comparable to the proposed maximum black hole mass predicted by different stellar evolution models due to the pulsation pair-instability supernova (PPISN) mechanism. If we assume that the primary ac{BH} in GW170729 formed through a PPISN then out of the four PPISN models we considered only the model of Woosley (2017) is consistent with our mass measurements at the 90% level.
Gradient metasurfaces have been extensively applied in recent years for enabling an unprecedented control of light beam over thin optical components. However, these metasurfaces suffer from low efficiency when it comes to bending light with large angle and high fabrication demand when it requires fine discretion. In this work, we investigate the all-dielectric metagrating based on mie-type resonances interference, allowing extraordinary optical diffraction for beam steering with ultralarge angle. It is found that the coupling inside and among lattice of metagrating can tune the exciting state of electric and magnetic resonances including both fundamental dipoles and high-order multipoles, leading to ideal asymmetrical scattering pattern for redistributing the energy between the diffraction channels at will. The participation of quadrupole and hexapole not only significantly enhance the working efficiency, but also bring distinctive possibilities for wave manipulation which cannot be reached by dipoles. Utilizing a thin array of silicon rods, large-angle negative refraction and reflection are demonstrated with almost unity efficiency under both polarizations. Compared with conventional metasurfaces, such an all-dielectric mategrating has the merits of high flexibility, high efficiency and low fabrication demand. The strong coupling and prosperous interactions among multipoles may behave as a cornerstone for broad range of wavefront control and offer an effective solution for various on-chip optical wave control such as bending, focusing, filtering and sensing.
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