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The concept of lasers based on the frozen mode regime in active periodic optical waveguides with a 3rd-order exceptional point of degeneracy (EPD) is advanced. The frozen mode regime in a lossless and gainless waveguide is associated with a stationary inflection point (SIP) in the Bloch dispersion relation, where three Bloch eigenmodes coalesce forming the frozen mode. As a practical example, we consider an asymmetric serpentine optical waveguide (ASOW). An ASOW operating near the SIP frequency displays a large group delay of a non-resonant nature that scales as the cube of the waveguide length, leading to a strong gain enhancement when active material is included. Therefore, a laser operating in the close vicinity of an SIP has a gain threshold that scales as a negative cube of the waveguide length. We determine that this scaling law is maintained in the presence of small distributed losses, such as radiation associated with waveguide bends and roughness. In addition, we show that although gain causes a distortion in the modes coalescing at the SIP, the properties of the frozen mode are relatively resistant to such small perturbations and we still observe a large degree of exceptional degeneracy for gain values that bring the system above threshold. Finally, our study also reveals that lasing near an SIP is favored over lasing near a photonic band edge located in close proximity to the SIP. In particular, we observe that an SIP-induced lasing in an ASOW displays lower gain threshold compared to lasing near the photonic regular band edge (RBE), even though the SIP resonance has a lower quality factor than the RBE resonance.
The concept of lasers based on the frozen mode regime in active periodic optical waveguides with a 3rd-order exceptional point of degeneracy (EPD) is advanced. The frozen mode regime in a lossless and gainless waveguide is associated with a stationary inflection point (SIP) in the Bloch dispersion relation, where three Bloch eigenmodes coalesce forming the frozen mode. As a practical example, we consider an asymmetric serpentine optical waveguide (ASOW). An ASOW operating near the SIP frequency displays a large group delay of a non-resonant nature that scales as the cube of the waveguide length, leading to a strong gain enhancement when active material is included. Therefore, a laser operating in the close vicinity of an SIP has a gain threshold that scales as a negative cube of the waveguide length. We determine that this scaling law is maintained in the presence of small distributed losses, such as radiation associated with waveguide bends and roughness. In addition, we show that although gain causes a distortion in the modes coalescing at the SIP, the properties of the frozen mode are relatively resistant to such small perturbations and we still observe a large degree of exceptional degeneracy for gain values that bring the system above threshold. Finally, our study also reveals that lasing near an SIP is favored over lasing near a photonic band edge located in close proximity to the SIP. In particular, we observe that an SIP-induced lasing in an ASOW displays lower gain threshold compared to lasing near the photonic regular band edge (RBE), even though the SIP resonance has a lower quality factor than the RBE resonance.
The modern construction revolution throughout the past two decades has brought the need for ground vibration mitigation, and this has been one of the major study areas. These studies were mainly focused on the effect of forestation on vibration reduction as the available natural metamaterial. Physical methods such as the finite element method and the boundary conditions of 2D and 3D applications in ground vibration reduction have been developed. Many researchers, scientists, and organizations in this field have emphasized the importance of these methods theoretically and numerically. This paper presents the historical context of resonant metamaterials (MMs), the current progress of periodic 2D and 3D structures, and the possible future outcomes from the seismic metamaterials (SMs), and it relates them with their elastic counterparts to the natural metamaterial (NMs). The idea of bandgaps (FBGs) in the frequency range of interest is reviewed and discussed in some detail. Moreover, the attenuation associated with ground vibrations, noise, seismology, and the like is explained by managing the peculiar mechanisms of ground vibrations. However, a comprehensive computational review focuses on shielding MMs for ground vibration mitigation in urban areas. This phenomenon led to unique features for various techniques to control the bandgap width for various construction applications. Ecological solutions involve the creation of an economic, environmentally based seismic shield for both the Bragg scattering and the local resonance bandgaps. Reportedly, additive studies based on numerical simulation and experiments have improved the functionality of the 2D and 3D periodic structures. It was found that the mechanical properties differ (i.e., stiffness, Poisson’s ratio, and bulk density) and that the geometrical parameters (i.e., lattice, model dimensions, distance from vibration sources, and number of periodic structures) exhibited strong effects on the width and location of the derived FBGs. The geometrical properties of the used unit cell have a strong effect on the attenuation mechanism. Although deep analysis was created in much of the previous research, it was revealed, based on that research, that the attenuation mechanism is still unclear. However, this review article presents a detailed exposition of the recent research progress of the seismic metamaterials, including 2D, 3D, and the main mechanisms of the theoretical backgrounds of energy attenuation. It also summarizes the effects of the factors on the width and location of the bandgaps at a low frequency. In addition, the natural metamaterials and the study of the urban environment are surveyed. The major findings of this review involve the effectiveness of NMs for different functionalities in ground vibration attenuation, which leads to diverse purposes and applications and proposes a roadmap for developing natural materials for clean and quiet environments.
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