Topological Waveguiding near an Exceptional Point: Defect-Immune, Slow-Light, and Loss-Immune Propagation

S. Ali Hassani Gangaraj and Francesco Monticone

Phys. Rev. Lett. 121, 093901 – Published 28 August 2018

Abstract

Electromagnetic waves propagating in conventional wave-guiding structures are reflected by discontinuities and decay in lossy regions. In this Letter, we drastically modify this typical guided-wave behavior by combining concepts from non-Hermitian physics and topological photonics. To this aim, we theoretically study, for the first time, the possibility of realizing an exceptional point between coupled topological modes in a non-Hermitian nonreciprocal waveguide. Our proposed system is composed of oppositely biased gyrotropic materials (e.g., biased plasmas or graphene layers) with a balanced distribution of loss and gain. To study this complex wave-guiding problem, we put forward an exact analysis based on classical Green’s function theory, and we elucidate the behavior of coupled topological modes and the nature of their non-Hermitian degeneracies. We find that, by operating near an exceptional point, we can realize anomalous topological wave propagation with, at the same time, low group velocity, inherent immunity to backscattering at discontinuities, and immunity to losses. These theoretical findings may open exciting research directions and stimulate further investigations of non-Hermitian topological waveguides to realize robust wave propagation in practical scenarios.

Received 11 March 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.093901

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Topological effects in photonic systems

Hydrodynamic waves Metamaterials

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalPlasma Physics

Authors & Affiliations

S. Ali Hassani Gangaraj^* and Francesco Monticone^†

School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

^*ali.gangaraj@gmail.com
^†francesco.monticone@cornell.edu

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Vol. 121, Iss. 9 — 31 August 2018

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Images

Figure 1
(a) Topological wave-guiding structure composed of two oppositely biased gyrotropic media separated by an isotropic layer ( $J_{m}$ indicates a current source). (b) Example of magnetic field distribution (time snapshot) propagating in a lossless (Hermitian) topological waveguide as in (a), excited by a dipolar source (black arrow). The magnetic field is normalized to its maximum value. Two unidirectional surface waves propagate along the interfaces and couple through the isotropic layer. For this example, we assumed $ω_{p, 1} = ω_{p, 2} = 0.9 ω_{0}$ , $ε_{r} = - 1$ , and $ω_{c, 1} = - ω_{c, 2} = 0.28 ω_{0}$ , where $ω_{0}$ is the source frequency. The width of the isotropic layer is $0.55 λ_{0}$ , where $λ_{0}$ is the free-space wavelength at $ω_{0}$ . Throughout the Letter, we have purposely normalized all parameters in the figures by wavelength and plasma frequency; our designs can, therefore, be scaled to any size and frequency range of interest.
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Figure 2
(a) Evolution of the guided-wave poles in the complex wave number plane for the topological waveguide in Fig. 1, as a function of the level of loss and gain in the system (with $ω_{p} / ω_{0} = 0.904$ , $ω_{c} / ω_{0} = 0.287$ , and $h = 0.35 λ_{0}$ ). Black dots indicate the roots of the dispersion equation. (b) Dispersion curves of the bulk modes (blue) and topological surface modes (red) for a TNT waveguide with $ω_{p} / ω_{c} = 3.16$ , $δ = - δ^{'} = δ_{EP}$ , $ω_{p}$ , $h = 0.63 π c / ω_{p}$ , and $ε_{r} = - 1$ . (c) Comparison between the dispersion curves of the topological surface modes in a Hermitian system (dashed green) and a non-Hermitian system (blue). (d) Similar to (a) but varying the isotropic spacer thickness (with $δ = - δ^{'} = δ_{EP}$ ).
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Figure 3
Magnetic field distribution at the center of the topological waveguide considered in Fig. 2 excited by a dipolar source at $x = 0$ as its frequency $ω_{0}$ approaches $ω_{EP} = ω_{p} / 0.904$ (exact Green’s function calculations): (a) $ω_{0} / ω_{EP} = 1.047$ , (b) $ω_{0} / ω_{EP} = 1.004$ and (c) $ω_{0} / ω_{EP} = 1.00004$ .
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Figure 4
Magnetic field distributions (time snapshots) in topological non-Hermitian wave-guiding structures excited by a dipolar source (black arrow). Different configurations are considered: (a) no gap between the gyrotropic layers (poles on the real axis); (b) a gap of thickness $h = 0.35 λ_{0}$ is introduced (poles merge at an EP); (c) same as (b) but with a large defect along the waveguide; (d) gap of thickness $h > 0.35 λ_{0}$ (complex-conjugate poles). The material parameters are the same as in Fig. 2 with level of loss and gain $δ = - δ^{'} = δ_{EP} = 0.021 73 ω_{p}$ .
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