Dispersive non-Hermitian optical heterostructures

O. V. Shramkova; K. G. Makris; D. N. Christodoulides; G. P. Tsironis

doi:10.1364/PRJ.6.0000A1

Journals >Photonics Research >Volume 6 >Issue 4 >Page A1 > Article

Photonics Research
Vol. 6, Issue 4, A1 (2018)

Dispersive non-Hermitian optical heterostructures

O. V. Shramkova^1、*, K. G. Makris², D. N. Christodoulides³, and G. P. Tsironis^2、4、5

Author Affiliations

¹Research & Innovation, Technicolor R&D France, 975 avenue des Champs Blancs, 35576 Cesson-Sévigné, France

²CCQCN, Department of Physics, University of Crete, P.O. Box 2208, 71003 Heraklion, Greece

³College of Optics & Photonics-CREOL, University of Central Florida, Orlando, Florida 32816, USA

⁴Institute of Electronic Structure and Laser, Foundation for Research and Technology–Hellas, P.O. Box 1527, 71110 Heraklion, Greece

⁵National University of Science and Technology MISiS, Leninsky prosp. 4, Moscow 119049, Russia

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DOI: 10.1364/PRJ.6.0000A1 Cite this Article Set citation alerts

O. V. Shramkova, K. G. Makris, D. N. Christodoulides, G. P. Tsironis. Dispersive non-Hermitian optical heterostructures[J]. Photonics Research, 2018, 6(4): A1 Copy Citation Text

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Abstract

The effect of material dispersion on the optical properties of one-dimensional non-Hermitian scattering systems is investigated in detail. In particular, multilayer heterostructures with gain and loss (parity-time symmetric or not) are examined by taking into account the dispersion of each layer. The exceptional points and phase transitions are characterized based on the spectrum of the corresponding scattering matrix. We demonstrate that an on-average lossy heterostructure can amplify an incident plane wave in the frequency range associated with the emission frequency of the layer with gain.

Keywords

Multilayers Photonic crystals

ϵ_{j} (ω) = ϵ_{0 j} - \frac{α_{j} ω_{0 j} γ_{j}}{ω^{2} - ω_{0 j}^{2} + i ω γ_{j}},

(1)

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Re ϵ_{1} (ω) = Re ϵ_{2} (ω), Im ϵ_{1} (ω) = - Im ϵ_{2} (ω) .

(2)

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| α_{1} | = α_{2} \frac{ω_{02} γ_{2}^{2} [{(ω^{2} - ω_{01}^{2})}^{2} + γ_{1}^{2} ω^{2}]}{ω_{01} γ_{1}^{2} [{(ω^{2} - ω_{02}^{2})}^{2} + γ_{2}^{2} ω^{2}]} .

(3)

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Δ ϵ = ϵ_{02} - ϵ_{01} = α_{2} \frac{ω_{02} γ_{2} [ω^{2} - ω_{02}^{2} + \frac{γ_{2}}{γ_{1}} (ω^{2} - ω_{01}^{2})]}{{(ω^{2} - ω_{02}^{2})}^{2} + γ_{2}^{2} ω^{2}} .

(4)

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(\begin{matrix} B \\ C \end{matrix}) = S̑ (\begin{matrix} A \\ D \end{matrix}) = (\begin{matrix} R^{(L)} (ω) & T (ω) \\ T (ω) & R^{(R)} (ω) \end{matrix}) (\begin{matrix} A \\ D \end{matrix}),

(5)

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λ_{1, 2} = \frac{R^{(L)} (ω) + R^{(R)} (ω) \pm \sqrt{{[R^{(L)} (ω) - R^{(R)} (ω)]}^{2} + 4 T {(ω)}^{2}}}{2} .

(6)

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O. V. Shramkova, K. G. Makris, D. N. Christodoulides, G. P. Tsironis. Dispersive non-Hermitian optical heterostructures[J]. Photonics Research, 2018, 6(4): A1

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