Abstract: Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens's radial phase gradient and locally approximate the phase profile by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method, and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite -difference time domain simulations at 632 nm, and we were able to simulate metalenses larger than 3000 wavelengths in diameter on a personal computer.

Abstract: The production of eta and eta' mesons is studied in proton -proton and proton -lead collisions collected with the LHCb detector. Proton -proton collisions are studied at center -of -mass energies of 5.02 and 13 TeV and proton -lead collisions are studied at a center -of -mass energy per nucleon of 8.16 TeV. The studies are performed in center -of -mass (c.m.) rapidity regions 2.5 < y(c.m.) < 3.5 (forward rapidity) and -4.0 < y(c.m.) < -3.0 (backward rapidity) defined relative to the proton beam direction. The eta and eta' production cross sections are measured differentially as a function of transverse momentum for 1.5 < p(T) < 10 GeV and 3 < p(T) < 10 GeV, respectively. The differential cross sections are used to calculate nuclear modification factors. The nuclear modification factors for eta and eta' mesons agree at both forward and backward rapidity, showing no significant evidence of mass dependence. The differential cross sections of eta mesons are also used to calculate eta/pi 0 cross-section ratios, which show evidence of a deviation from the world average. These studies offer new constraints on mass -dependent nuclear effects in heavy -ion collisions, as well as eta and eta' meson fragmentation.

Abstract: The N*(1535) can be dynamically generated in the chiral unitary approach with the coupled channels, K0E+; K+E0; K+A, and eta p. In this work, we evaluate the correlation functions for every channel and face the inverse problem. Assuming the correlation functions to correspond to real measurements, we conduct a fit to the data within a general framework in order to extract the information contained in these correlation functions. The bootstrap method is used to determine the uncertainties of the different observables, and we find that, assuming errors of the same order than in present measurements of correlation functions, one can determine the scattering length and effective range of all channels with a very good accuracy. Most remarkable is the fact that the method predicts the existence of a bound state of isospin 12 nature around the mass of the N*(1535) with an accuracy of 6 MeV. These results should encourage the actual measurement of these correlation functions (only the K+A one is measured so far), which can shed valuable light on the relationship of the N*(1535) state to these coupled channels, a subject of continuous debate.