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Finite-sample bounds on the accuracy of Bhattacharya’s plug-in estimator for Fisher information are derived. These bounds are further improved by introducing a clipping step that allows for better control over the score function. This leads to superior upper bounds on the rates of convergence, albeit under slightly different regularity conditions. The performance bounds on both estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown’s identity, two corresponding estimators of the minimum mean-square error are proposed. 

Metamaterials are artificially engineered structures that have unique properties not usually found in natural materials, such as negative refractive index. Conventional interferometry or ellipsometry is generally used for characterizing the optical properties of metamaterials. Here, we report an alternative optical vortex based interferometric approach for the characterization of the effective parameters of optical metamaterials by directly measuring the transmission and reflection phase shifts from metamaterials according to the rotation of vortex spiral interference pattern. The fishnet metamaterials possessing positive, zero and negative refractive indices are characterized with the vortex based interferometry to precisely determine the complex values of effective permittivity, permeability, and refractive index. Our results will pave the way for the advancement of new spectroscopic and interferometric techniques to characterize optical metamaterials, metasurfaces, and nanostructured thin films in general. 

While recent experiments provided compelling evidence for an intricate dependence of attosecond photoemission-time delays on the solid’s electronic band structure, the extent to which electronic transport and dispersion in solids can be imaged in time-resolved photoelectron (PE) spectra remains poorly understood. Emphasizing the distinction between photoemission time delays measured with two-photon, two-color interferometric spectroscopy, and transport times, we demonstrate how the effect of energy dispersion in the solid on photoemission delays can, in principle, be observed in interferometric photoemission. We reveal analytically a scaling relation between the PE transport time in the solid and the observable photoemission delay and confirm this relation in numerical simulations for a model system. We trace photoemission delays to the phase difference the PE accumulates inside the solid and, in particular, predict negative photoemission delays. Based on these findings, we suggest a novel time-domain interferometric solid-state energy-momentum-dispersion imaging method.