Hasanli Shamkhal, Hasan Mehedi, Yoon Hyejin, Lee Seungyong, Kim Sangsik
School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea.
Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409, USA.
Nanophotonics. 2025 Mar 11;14(8):1301-1309. doi: 10.1515/nanoph-2024-0701. eCollection 2025 Apr.
Exceptional points (EPs) in non-Hermitian systems have attracted significant interest due to their unique behaviors, including novel wave propagation and radiation. While EPs have been explored in various photonic systems, their integration into standard photonic platforms can expand their applicability to broader technological domains. In this work, we propose and experimentally demonstrate EPs in an integrated photonic strip waveguide configuration, exhibiting unique deep wave penetration and uniform-intensity radiation profiles. By introducing the second-order grating on one side of the waveguide, forward and backward propagating modes are coupled both directly through second-order coupling and indirectly through first-order coupling via a radiative intermediate mode. To describe the EP behavior in a strip configuration, we introduce modified coupled-mode equations that account for both transverse and longitudinal components. These coupled-mode formulas reveal the formation of EPs in bandgap closure, achieved by numerically optimizing the grating's duty cycle to manipulate the first- and second-order couplings simultaneously. Experimental observations, consistent with simulations, confirm the EP behavior, with symmetric transmission spectra and constant radiation profiles at the EP wavelength, in contrast to conventional exponential decay observed at detuned wavelengths. These results demonstrate the realization of EPs in a widely applicable strip waveguide configuration, paving the way for advanced EP applications in nonlinear and ultrafast photonics, as well as advanced sensing technologies.
非厄米系统中的例外点(EPs)因其独特行为,包括新颖的波传播和辐射,而引起了广泛关注。虽然EPs已在各种光子系统中得到研究,但将它们集成到标准光子平台中可以将其适用性扩展到更广泛的技术领域。在这项工作中,我们提出并通过实验证明了集成光子条形波导结构中的EPs,其表现出独特的深波穿透和均匀强度辐射分布。通过在波导的一侧引入二阶光栅,正向和反向传播模式既通过二阶耦合直接耦合,又通过辐射中间模式通过一阶耦合间接耦合。为了描述条形结构中的EP行为,我们引入了修正的耦合模方程,该方程考虑了横向和纵向分量。这些耦合模公式揭示了在带隙闭合中EPs的形成,这是通过数值优化光栅的占空比以同时操纵一阶和二阶耦合来实现的。与模拟结果一致的实验观察结果证实了EP行为,在EP波长处具有对称的传输光谱和恒定的辐射分布,与在失谐波长处观察到的传统指数衰减形成对比。这些结果证明了在广泛适用的条形波导结构中实现了EPs,为非线性和超快光子学以及先进传感技术中的先进EP应用铺平了道路。