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## Tunneling of Obliquely-Incident Waves through PT-Symmetric Epsilon-Near-Zero Bi-Layers

Silvio Savoia, Giuseppe Castaldi, Vincenzo Galdi, Andrea Alú, Nader Engheta

We show that obliquely-incident, transversely-magnetic-polarized plane waves can be totally transmitted (with zero reflection) through epsilon-near-zero (ENZ) bi-layers characterized by balanced loss and gain with parity-time (PT) symmetry. This tunneling phenomenon is mediated by the excitation of a surface-wave localized at the interface separating the loss and gain regions. We determine the parameter configurations for which the phenomenon may occur and, in particular, the relationship between the incidence direction and the electrical thickness. We show that, below a critical threshold of gain and loss, there always exists a tunneling angle which, for moderately thick (wavelength-sized) structures, approaches a critical value dictated by the surface-wave phase-matching condition. We also investigate the unidirectional character of the tunneling phenomenon, as well as the possible onset of spontaneous symmetry breaking, typical of PT-symmetric systems. Our results constitute an interesting example of a PT-symmetry-induced tunneling phenomenon, and may open up intriguing venues in the applications of ENZ materials featuring loss and gain.

http://arxiv.org/abs/1401.1619
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

## The large-g observability of the low-lying energies in the strongly singular potentials $$V(x)=x^2+g^2/x^6$$ after their PT-symmetric regularization

Miloslav Znojil

The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $$x=s−i\epsilon$$. The shift $$\epsilon>0$$ is fixed while the value of s is kept real and potentially observable, $$s∈(−\infty,\infty)$$. The low-lying energies of bound states are found in closed form for the large couplings g. Within the asymptotically vanishing $$\mathcal{O}(g^{−1/4})$$ error bars these energies are real so that the time-evolution of the system may be expected unitary in an {\em ad hoc} physical Hilbert space.

http://arxiv.org/abs/1401.1435
Quantum Physics (quant-ph)