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The concept of supersymmetry originated in the fields of particle physics and enabled treatment for bosons and fermions on equal footing. Supersymmetry has rapidly expanded to other fields such as quantum mechanics, where it provided a way of generating pairs and families of potentials with similar properties, e.g. different reflection-less potentials; and optics where it can be used to design (de)multiplexing arrays of waveguides.
In the first part of the talk, we show that for parity-time symmetric structures supersymmetric transformation is isospectral only locally (at a specific amplitude of gain and loss). Moreover we show that depending on whether a passive mode (with real propagation constant) or an active mode (with gain or loss) is removed, the parity-time symmetry of the system is preserved or broken as a function of gain/loss amplitude.
In the second part of the talk we investigate the influence of supersymmetric transformation on the scattering spectrum of reflection-less structures and systems with epsilon-near-zero materials. We show that the transmission/reflection properties of a structure containing an epsilon-near-zero material can be mimicked using materials with refractive index values above unity, which are more easily accessible and introduce smaller losses to the system. The relation between these two systems is governed by supersymmetry. We conduct a quantitative performance analysis of realistic structure in which the continuous variation of the refractive index is replaced by the step-wise profile corresponding to a realistic layered structure.
Our studies pave the way towards achieving remarkable properties of the epsilon-near-zero materials with the use of much more accessible materials compatible with the state-of-the-art integrated optics fabrication.
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