Floquet higher-order exceptional points and dynamics in PT-symmetric quadrimer waveguides
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Floquet higher-order exceptional points and dynamics in PT-symmetric quadrimer waveguides Jun Jia1 , Bo Zhu2 , Fuqiu Ye1,a , Honghua Zhong3,4,b , and Haiming Deng5 1 2 3 4 5
Department of Physics, Jishou University, Jishou 416000, P.R. China School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, P.R. China Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha 410004, P.R. China School of Materials Science and Energy Engineering, Foshan University, Foshan 528000, P.R. China School of Electronic Information and Electrical Engineering, Xiangnan University, Chenzhou 423000, P.R. China Received 10 January 2020 / Received in final form 10 April 2020 Published online 16 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We investigate the effect of periodic modulation on PT-symmetry recovery, higher-order exceptional points (EPs) and dynamics for a periodically modulated PT-symmetric quadrimer waveguide system. It is analytically and numerically revealed that the periodic modulation not only can restore the broken PT symmetry, but also can manipulate the PT symmetry by tuning modulation amplitude. Furthermore, we found that multiple EPs can emerge, and as the modulation amplitude vary, these EPs can collide and merge, leading to higher-order Floquet singularities. By defining average relative light intensity distribution, we explore the dynamical characteristics nearby these EPs. It is found that we can control the light tunneling direction of optical quadrimer waveguide via periodic modulation and proper choice of gain/loss parameters.
1 Introduction Parity-time (PT) symmetry, which is the invariance under simultaneous parity and time reversal transformation, plays a key role in determining the real energy spectrum, topological character and transport property of non-Hermitian system [1–15]. A characteristic property of PT-symmetric system is the existence of a phase transition (spontaneous PT-symmetry-breaking) from the unbroken to broken-PT-symmetric phase whenever the gain/loss parameter exceeds a certain threshold, separated by exceptional points (EPs) where two (or more) eigenstates become degenerate. There are many novel phenomena related to EPs, including single-mode lasers [16,17], loss-induced transparency [18], topological characteristics [19–23], coherent perfect absorption [24], nonHermiticity induced flatbands [25–27]. Therefore, an important issue in a PT-symmetric system is the ability to control and tune the PT symmetry and EPs. Optical waveguiding systems offer particularly convenient platforms for the realization of PT-symmetric potentials [5,28–31], because they allow the simultaneous modulation of the refractive index and the gain and losses. There is a considerable interest in the investigation of the physics of EPs and PT symmetry for some simple PT-symmetric photonic waveguide structures like
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