Diffraction grating parameter retrieval using non-paraxial structured beams in coherent Fourier scatterometry

In recent years, a lot of works have been published that use parameter retrieval using Orbital Angular Momentum (OAM) beams. Most make use of the OAM of different Laguerre-Gauss modes. However, those specific optical beams are paraxial beams and this limits the regime in which they can be used. In this paper, we report on the first results on retrieving the geometric parameters of a diffraction grating by analysing the corresponding complex-valued (i.e., amplitude and phase) Helmholtz Natural Modes (HNM) spectra containing both the azimuthal (i.e., n) and radial (i.e., m) indices. HNMs are a set of orthogonal, non-paraxial beams with finite energy carrying OAM. We use the coherent Fourier scatterometry (CFS) setup to calculate the field scattered from the diffraction grating. The amplitude and phase contributions of each HNM are then obtained by numerically calculating the overlap integral of the scattered field with the different modes. We show results on the sensitivity of the HNMs to several grating parameters.

Clutch may predict growth of hatchling Burmese pythons better than food availability or sex

ABSTRACT Identifying which environmental and genetic factors affect growth pattern phenotypes can help biologists predict how organisms distribute finite energy resources in response to varying environmental conditions and physiological states. This information may be useful for monitoring and managing populations of cryptic, endangered, and invasive species. Consequently, we assessed the effects of food availability, clutch, and sex on the growth of invasive Burmese pythons (Python bivittatus Kuhl) from the Greater Everglades Ecosystem in Florida, USA. Though little is known from the wild, Burmese pythons have been physiological model organisms for decades, with most experimental research sourcing individuals from the pet trade. Here, we used 60 hatchlings collected as eggs from the nests of two wild pythons, assigned them to High or Low feeding treatments, and monitored growth and meal consumption for 12 weeks, a period when pythons are thought to grow very rapidly. None of the 30 hatchlings that were offered food prior to their fourth week post-hatching consumed it, presumably because they were relying on internal yolk stores. Although only two clutches were used in the experiment, we found that nearly all phenotypic variation was explained by clutch rather than feeding treatment or sex. Hatchlings from clutch 1 (C1) grew faster and were longer, heavier, in better body condition, ate more frequently, and were bolder than hatchlings from clutch 2 (C2), regardless of food availability. On average, C1 and C2 hatchling snout-vent length (SVL) and weight grew 0.15 cm d−1 and 0.10 cm d−1, and 0.20 g d−1 and 0.03 g d−1, respectively. Additional research may be warranted to determine whether these effects remain with larger clutch sample sizes and to identify the underlying mechanisms and fitness implications of this variation to help inform risk assessments and management. This article has an associated First Person interview with the first author of the paper.

Discontinuous perturbations of nonhomogeneous strongly-singular Kirchhoff problems

In this paper, we are concerned with a Kirchhoff problem in the presence of a strongly-singular term perturbed by a discontinuous nonlinearity of the Heaviside type in the setting of Orlicz–Sobolev space. The presence of both strongly-singular and non-continuous terms brings up difficulties in associating a differentiable functional to the problem with finite energy in the whole space $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) . To overcome this obstacle, we establish an optimal condition for the existence of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) -solutions to a strongly-singular problem, which allows us to constrain the energy functional to a subset of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) in order to apply techniques of convex analysis and generalized gradient in the sense of Clarke.

Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $$\tau $$ τ -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $${\overline{\mathrm{MS}}}$$ MS ¯ coupling is $$\alpha _s(m_{\tau }^2) = 0.3116 \pm 0.0073$$ α s ( m τ 2 ) = 0.3116 ± 0.0073 [$$\alpha _s(M_Z^2)=0.1176 \pm 0.0010$$ α s ( M Z 2 ) = 0.1176 ± 0.0010 ] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $$\alpha _s(m_{\tau }^2) = 0.3194 \pm 0.0167$$ α s ( m τ 2 ) = 0.3194 ± 0.0167 [$$\alpha _s(M_Z^2)=0.1186 \pm 0.0021$$ α s ( M Z 2 ) = 0.1186 ± 0.0021 ].

Sparse Representations of Random Signals

Sparse (fast) representations of deterministic signals have been well studied. Among other types there exists one called adaptive Fourier decomposition (AFD) for functions in analytic Hardy spaces. Through the Hardy space decomposition of the $L^2$ space the AFD algorithm also gives rise to sparse representations of signals of finite energy. To deal with multivariate signals the general Hilbert space context comes into play. The multivariate counterpart of AFD in general Hilbert spaces with a dictionary has been named pre-orthogonal AFD (POAFD). In the present study we generalize AFD and POAFD to random analytic signals through formulating stochastic analytic Hardy spaces and stochastic Hilbert spaces. To analyze random analytic signals we work on two models, both being called stochastic AFD, or SAFD in brief. The two models are respectively made for (i) those expressible as the sum of a deterministic signal and an error term (SAFDI); and for (ii) those from different sources obeying certain distributive law (SAFDII). In the later part of the paper we drop off the analyticity assumption and generalize the SAFDI and SAFDII to what we call stochastic Hilbert spaces with a dictionary. The generalized methods are named as stochastic pre-orthogonal adaptive Fourier decompositions, SPOAFDI and SPOAFDII. Like AFDs and POAFDs for deterministic signals, the developed stochastic POAFD algorithms offer powerful tools to approximate and thus to analyze random signals.

Evidence of two-dimensional flat band at the surface of antiferromagnetic kagome metal FeSn

The kagome lattice has long been regarded as a theoretical framework that connects lattice geometry to unusual singularities in electronic structure. Transition metal kagome compounds have been recently identified as a promising material platform to investigate the long-sought electronic flat band. Here we report the signature of a two-dimensional flat band at the surface of antiferromagnetic kagome metal FeSn by means of planar tunneling spectroscopy. Employing a Schottky heterointerface of FeSn and an n-type semiconductor Nb-doped SrTiO3, we observe an anomalous enhancement in tunneling conductance within a finite energy range of FeSn. Our first-principles calculations show this is consistent with a spin-polarized flat band localized at the ferromagnetic kagome layer at the Schottky interface. The spectroscopic capability to characterize the electronic structure of a kagome compound at a thin film heterointerface will provide a unique opportunity to probe flat band induced phenomena in an energy-resolved fashion with simultaneous electrical tuning of its properties. Furthermore, the exotic surface state discussed herein is expected to manifest as peculiar spin-orbit torque signals in heterostructure-based spintronic devices.