Exception point induced flat-band and waveguide laser
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Exception point induced flat‑band and waveguide laser Xiao‑xue Li1 · Er‑pan Fan1 · Zhang‑xin Wang1 · Yun‑Tuan Fang1,2 Received: 3 March 2020 / Accepted: 15 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In order to study the exceptional point (EP) properties in the photonic crystal waveguide, we construct the two-dimensional photonic crystal waveguide with the parity–time symmetry configuration. With the calculation of the eigen frequencies, the evolution of the waveguide mode bands discloses two EP-induced flat bands. The transmittance and reflectance at the two flat bands show a huge amplification property and the structure become a waveguide laser. The waveguide lasing is due to the common properties of the EP and the flat band. The results have been demonstrated by the transmission spectra, Poynting vector distribution and simulations of field propagation. Keywords Waveguide · Exceptional point · Flat band · Lasing
1 Introduction Laser source and waveguide are the basic separated components in optical communication system. In future optical integrated circuit, the component with compound functionalities is extraordinary needed because it can decrease the number and volume of components in an optical integrated system. Thus if the laser source and waveguide are combined into one component, the compound structure will become a breakthrough in device design and play an important role in optical communication system. Such a goal is just what we pursue in this study. In recent years, the parity–time (PT)–symmetric systems have been introduced into optical structures (Guo et al. 2009; Rüter et al. 2010; Li et al. 2019; Lin et al. 2011; Zhen et al. 2015; Makris et al. 2008; Doppler et al. 2016; Xu et al. 2016; Hodaei et al. 2014; Feng et al. 2014; Ding and Wang 2015; Huang et al. 2017). In optics, the PT-symmetric system is defined by a distribution of complex refraction index with n(r) = n*(-r). The system will possess real eigenvalues with a small imaginary part of refraction index, and when the imaginary part is sufficiently large, the system undergoes a transition from real eigenvalues to complex ones. The phase transition point is called an exceptional point * Yun‑Tuan Fang [email protected] 1
School of Computer Science and Telecommunication Engineering, Jiangsu University, Zhenjiang 212013, China
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Jiangsu Key Laboratory of Security Technology for Industrial Cyberspace, Jiangsu University, Zhenjiang 212013, China
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(EP). The EP takes on unique phenomena (Li et al. 2019; Lin et al. 2011; Zhen et al. 2015; Makris et al. 2008; Doppler et al. 2016; Xu et al. 2016; Hodaei et al. 2014; Feng et al. 2014; Ding and Wang 2015). A detailed review is published in (Huang et al. 2017). The EP can been studied in various systems, such as the coupled resonators (Chang et al. 2014; Chen et al. 2018; Hodaei et al. 2017; Wong et al. 2016), waveguides (Li et al. 2019; Doppler et al. 2016), dielectric periodic sl
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