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7 May 2018 Exceptional points in the strong-coupling regime with active hyperbolic metamaterials
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In this work we analytically and numerically study the impact of dye infiltration in multilayer hyperbolic meta- materials. The dyes we use in our model are four-level dyes with an absorption and an emission line. Starting from the Maxwell-Bloch equations we derive a semi-analytical model for the coupling of an oscillator in a one- dimensional periodic structure. We compare our model with exact results obtained using the transfer-matrix method. In the weak coupling regime, both absorption and emission lines perturb the optical mode (in a finite multilayer) or the band (in an infinite multilayer) in similar ways, introducing positive and negative imaginary parts to the dispersion of Bloch vector within the bands without altering their shapes. In contrast, in the strong-coupling regime, the two lines are responsible for different phenomena: while coupling to the absorption line causes a severe distortion of the band due to classical Rabi splitting, coupling to the emission line causes fork-shaped bifurcations reminiscent of PT-symmetry breaking scenarios, with apparition of exceptional points at the loss-gain compensation frequencies.
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Fabio Vaianella, Joachim M. Hamm, Ortwin Hess, and Bjorn Maes "Exceptional points in the strong-coupling regime with active hyperbolic metamaterials", Proc. SPIE 10671, Metamaterials XI, 106712I (7 May 2018);

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