International Journal of

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In the present work, we investigate the tunability of the magnetic response of a new structure. A lattice of periodically arranged close-packed square conducting rings has been studied for this purpose. Here, instead of enhancing the magnetic activity via resonance, like in split-ring resonators, we concentrate on the analysis of the interactions between these rings. The core idea is to design an array with negligible capacity and to focus on inductive interactions between its building cells. In other words, in this structure, the enhancement of the microscopic process has been attained by the interaction of its building block, i.e. a collective feature has been considered. It is our goal to obtain a sizable magnetic response with this new approach. Our ultimate goal is to demonstrate that the relative magnetic permeability of this architecture could be less than one or even less than zero.

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In this paper, we have investigated the dependence of the spectral entanglement and indistinguishability of photon pairs produced by the spontaneous parametric down-conversion (SPDC) procedure on the bandwidth of spectral filters used in the detection setup. The SPDC is a three-wave mixing process which occurs in a nonlinear crystal and generates entangled photon pairs and utilizes as one of the most useful resources in a variety of fields such as quantum computation, quantum cryptography, and quantum communication. The amount of the spectral entanglement and the indistinguishability of photon pairs are the two critical characteristics of the photon pairs determining their potential applications. The degree of the spectral entanglement of a quantum system, i.e. photon pairs, is determined by the entanglement entropy which is a measure of the system disorder. First, we derive the eigenvalue equation of reduced density operator of the signal and the idler photons in terms of the bandwidth of spectral filters. Then, by numerically solving the eigenvalue equation, we calculate the Schmidt coefficients for different values of the bandwidth of spectral filters. Finally, by calculating the entropy operator one can obtain the dependence of spectral entanglement of the photon pairs on filter bandwidth. The amount of indistinguishability of the photon pairs is measured by the visibility of the HOM diagram. Since the whole spectral information of the photon pairs exists in their two-photon mode function, using this function and the presented model we calculate the amount of indistinguishability by obtaining the visibility of the HOM diagram for different values of the bandwidth of the spectral filters. In this way, the dependence of the indistinguishability of the photon pairs on this quantity is reported.