We consider a type of hypothetical compound materials in which its refractive
index in spatial distribution meet $n(-x)=-n^{*}(x)$, belonging to
anti-parity-time (APT) symmetric structures. Inoltre, we demand balanced
real positive- and negative- permeabilities with $\mu(-x)=-\mu(x)$. Di
introducing parametrization into APT symmetric transfer matrix, together with
reciprocity theorem, we propose a generic parametric space to display its
associated scattering results including symmetry phase, exceptional point, E
symmetry broken phase. The outcome is irrespective of any system complexity,
geometries, materials, and operating frequency. With the parametric space, Noi
find that APT symmetric system not only enables coherent perfect absorption or
lasing occurred at an exceptional point, but also realize a simultaneous
coherent perfect absorption-lasing. Since APT-symmetric system is constructed
by balanced positive and negative index materials, the phase accumulated from
optical path length is null, resulting in an assignment of mode order lost. To
verify our analysis, several designed heterostructures are demonstrated to
support our findings.

Questo articolo esplora i giri e le loro implicazioni.

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