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Register a new userOn the inapplicability of a negative-phase-velocity condition as a negative-refraction condition for active materials
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A negative-phase-velocity condition derived by Depine and Lakhtakia [Microwave Opt Technol Lett 41 (2004) 315] for isotropic, homogeneous, passive, dielectric-magnetic materials is inapplicable as a negative-refraction condition for active materials.
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There are three widely-used conditions for characterizing negative refraction in isotropic dielectric-magnetic materials. Here we demonstrate that whilst all the different conditions are equivalent for purely passive media, they are distinct if active media are considered. Further, these criteria can also be applied to negative refraction in acoustic materials, where we might replace the dielectric permittivity $epsilon$ with a bulk modulus $kappa$, and the magnetic permeability $mu$ with the mass density $rho$.
Negative-index refraction is achieved in a lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials stacked alternatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the famous left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such an ENG-MNG lamellar composite. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.
In this paper we will show that the assumption on the negative Schwarzian derivative is redundant in the case of C^3 unimodal maps with a nonflat critical point. The following theorem will be proved: For any C^3 unimodal map of an interval with a nonflat critical point there exists an interval around the critical value such that the first entry map to this interval has negative Schwarzian derivative. Another theorem proved in the paper provides useful cross-ratio estimates. Thus, all theorems proved only for unimodal maps with negative Schwarzian derivative can be easily generalized.
By introducing a new mechanism based on purely imaginary conjugate metamaterials (PICMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PICMs, which is a breakthrough to the unidirectional limit in parity time (PT) symmetric systems. Compared with PT symmetric systems that require two different kinds of materials, the proposed negative refraction can be realized with only two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PICM system. Therefore, a new way to realize negative refraction is presented, with more properties than those in PT symmetric systems.
We analyze different factors which influence the negative refraction in solids and multi-atom molecules. We find that this negative refraction is significantly influenced by simultaneous multi-electron transitions with the same transition frequency and dipole redistribution over different eigenstates. We show that these simultaneous multi-electron transitions and enhanced transition dipole broaden the bandwidth of the negative refraction by at least one order of magnitude. This work provides additional connection between metamaterials and Mobius strips.
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