Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.Comment: 14 pages, 13 figures, submitted to Optics Expres

Complementability of exponential systems

We prove that any incomplete system of complex exponentials $\{e^{i\lambda_n t}\}$ in $L^2(-\pi,\pi)$ is a subset of some complete and minimal system of exponentials. In addition, we prove analogous statement for systems of reproducing kernels in de Branges spaces.Comment: 6 page

Radio emission from Air Showers. Comparison of theoretical approaches

While the fluorescence and the ground counter techniques for the detection of ultra-high energy cosmic rays (UHECR) were being developed for decades, the interest in the radio detection diminished after the initial experiments in the 1960s. As a result, the fluorescence and the surface array techniques are more mature today, providing more reliable measurements of the primary cosmic particle energy, chemical composition and the inelastic cross-section. The advantages of the radio technique are 100 percent duty cycle and lower deployment and operational costs. Thus, the radio technique can greatly complement the fluorescence and the ground array detection and can also work independently. With the ANITA balloon detector observing UHECRs and the success of LOPES, CODALEMA and other surface radio detectors, the radio technique received a significant boost in recent years. Reliable Monte Carlo (MC) simulations are needed in order to obtain the energy and other parameters of the primary cosmic ray particle from the radio observations. Several MC techniques, like ZHairesS and the Endpoint Formalism, were proposed in recent years. While they seem to reproduce some of the observed data quite well, there is a divergence between the different approaches under certain conditions. In this work we derive these approaches from Maxwells equations and prove their identity under certain conditions as well as discuss their applicability to the UHECR air showers and to a proposed experiment at SLAC.Comment: Accepted to AIP Proc. Suppl. January 15, 201