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Numerical and pseudo data for pion electroproduction from four reaction channels, p ( γ*, π 0 ) p , p ( γ*, π + ) n , n ( γ*, π − ) p , and n ( γ*, π 0 ) n , from threshold up to W = 1.575 GeV are used to perform a single energy partial wave analysis. As a constraint, higher partial waves are taken from the MAID07 model and lower partial waves are fitted. It is demonstrated that truncated partial wave analysis in a full isospin can be obtained with this procedure. The results for photon virtuality Q 2 = 0.5 GeV 2 are presented. Electromagnetic E ℓ± , M ℓ± , and longitudinal L ℓ± multipoles are presented and discussed. In the first step, numerical data are generated, and the optimal number of lower partial waves required for a good data fit is determined. In the second step, the same procedure is applied using generated pseudo data.

The role of multipolar expansion of the localized current is significant in a broad range of disciplines in the physics of nowadays. It is actively used in such problems as the design of nanoantennas in photonics or the description of exotic states of matter. The toroidal multipoles are the third group of multipoles which complements the electric and magnetic multipolar families. The investigation of toroidal multipoles is important because of their role in the formation of so-called anapole states, non-radiating sources. The further study showed that there are also exist the higher-order toroidal dipoles or mean-square radii, which are equivalent. Here we suggest the structure which consists of point magnetic dipoles and supports the toroidal anapole state, which is obtained with the destructive interference of electric toroidal dipole with the first mean-square radius of the electric toroidal dipole. We also present an analytical condition for toroidal anapole with this system of point magnetic dipoles placed in two circles.

Scattering of electromagnetic waves by an arbitrary nanoscale object can be characterized by a multipole decomposition of the electromagnetic field that allows one to describe the scattering intensity and radiation pattern through interferences of dominating multipole modes excited. In modern nanophotonics, both generation and interference of multipole modes start to play an indispensable role, and they enable nanoscale manipulation of light with many related applications. Here, we review the multipolar interference effects in metallic, metal-dielectric and dielectric nanostructures, and suggest a comprehensive view on many phenomena involving the interferences of electric, magnetic and toroidal multipoles, which drive a number of recently discussed effects in nanophotonics such as unidirectional scattering, effective optical antiferromagnetism, generalized Kerker scattering with controlled angular patterns, generalized Brewster angle, and non-radiating optical anapoles. We further discuss other types of possible multipolar interference effects not yet exploited in the literature and envisage the prospect of achieving more flexible and advanced nanoscale control of light relying on the concepts of multipolar interference through full phase and amplitude engineering. This article is part of the themed issue ‘New horizons for nanophotonics’.

The topological phases of matter are characterized using the Berry phase, a geometrical phase associated with the energy-momentum band structure. The quantization of the Berry phase and the associated wavefunction polarization manifest as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport1–5. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and quantized polarization, from dipole to multipole moments6–8. Here, we demonstrate photonic realization of the quantized quadrupole topological phase, using silicon photonics. In our two-dimensional second-order topological phase, we show that the quantization of the bulk quadrupole moment manifests as topologically robust zero-dimensional corner states. We contrast these topological states against topologically trivial corner states in a system without bulk quadrupole moment, where we observe no robustness. Our photonic platform could enable the development of robust on-chip classical and quantum optical devices with higher-order topological protection.

LiteBIRD is a candidate satellite for a strategic large mission of JAXA. With its expected launch in the middle of the 2020s with a H3 rocket, LiteBIRD plans to map the polarization of the cosmic microwave background radiation over the full sky with unprecedented precision. The full success of LiteBIRD is to achieve δ r < 0.001 , where δ r is the total error on the tensor-to-scalar ratio r . The required angular coverage corresponds to 2 ≤ ℓ ≤ 200 , where ℓ is the multipole moment. This allows us to test well-motivated cosmic inflation models. Full-sky surveys for 3 years at a Lagrangian point L2 will be carried out for 15 frequency bands between 34 and 448 GHz with two telescopes to achieve the total sensitivity of 2.5 μ K arcmin with a typical angular resolution of 0.5 ∘ at 150 GHz. Each telescope is equipped with a half-wave plate system for polarization signal modulation and a focal plane filled with polarization-sensitive TES bolometers. A cryogenic system provides a 100 mK base temperature for the focal planes and 2 K and 5 K stages for optical components.

We present a systematic study of the effect of higher-multipolar order plasmon modes on the spectral response and plasmonic coupling of silver nanoparticle dimers at nanojunction separation and introduce a coupling mechanism. The most prominent plasmonic band within the extinction spectra of coupled resonators is the dipolar coupling band. A detailed calculation of the plasmonic coupling between equivalent particles suggests that the coupling is not limited to the overlap between the main bands of individual particles but can also be affected by the contribution of the higher-order modes in the multipolar region. This requires an appropriate description of the mechanism that goes beyond the general coupling phenomenon introduced as the plasmonic ruler equation in 2007. In the present work, we found that the plasmonic coupling of nearby Ag nanocubes does not only depend on the plasmonic properties of the main band. The results suggest the decay length of the higher-order plasmon mode is more sensitive to changes in the magnitude of the interparticle axis and is a function of the gap size. For cubic particles, the contribution of the higher-order modes becomes significant due to the high density of oscillating dipoles localized on the corners. This gives rise to changes in the decay length of the plasmonic ruler equation. For spherical particles, as the size of the particle increases (i.e., ≥80 nm), the number of dipoles increases, which results in higher dipole– multipole interactions. This exhibits a strong impact on the plasmonic coupling, even at long separation distances (20 nm).

A bstract We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion.

Recently a D -dimensional regularization approach leading to the non-trivial ( 3 + 1 ) -dimensional Einstein–Gauss–Bonnet (EGB) effective description of gravity was formulated which was claimed to bypass the Lovelock’s theorem and avoid Ostrogradsky instability. Later it was shown that the regularization is possible only for some broad, but limited, class of metrics and Aoki et al. ( arXiv:2005.03859 ) formulated a well-defined four-dimensional EGB theory, which breaks the Lorentz invariance in a theoretically consistent and observationally viable way. The black-hole solution of the first naive approach proved out to be also the exact solution of the well-defined theory. Here we calculate quasinormal modes of scalar, electromagnetic and gravitational perturbations and find the radius of shadow for spherically symmetric and asymptotically flat black holes with Gauss–Bonnet corrections. We show that the black hole is gravitationally stable when ( - 16 M 2 < α ⪅ 0.6 M 2 ). The instability in the outer range is the eikonal one and it develops at high multipole numbers. The radius of the shadow R Sh obeys the linear law with a remarkable accuracy.

A bstract We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.

Topological photonics provides a fundamental framework for robust manipulation of light, including directional transport and localization with built-in immunity to disorder. Combined with an optical gain, active topological cavities hold special promise for a design of light-emitting devices. Most studies to date have focused on lasing at topological edges of finite systems or domain walls. Recently discovered higher-order topological phases enable strong high-quality confinement of light at the corners. Here, we demonstrate lasing action of corner states in nanophotonic topological structures. We identify several multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states. In addition, depending on the pump position in a large-size cavity, we generate selectively lasing from either edge or corner states within the topological bandgap. Our studies provide the direct observation of multipolar lasing and engineered collective resonances in active topological nanostructures. Higher-order photonic topological states, such as corner states, could enable robust and high-quality confinement of light to a small mode volume. Here, the authors demonstrate lasing from topological multipole corner states and investigate their emission profiles via hyperspectral imaging.