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In this paper, dynamic effective parameters of mass-type and stiffness-type bilayer perforated thin-plate acoustic metamaterials (MBPM and SBPM) are investigated by simulations and experiments. Dynamic effective parameters are calculated by the retrieval method, and formation mechanisms of special effective parameters are analyzed by simulated fields. Divergent effective parameters are produced by anti-resonances of coupled perforations or coupled perforated thin-plates, zero effective parameters are produced by resonances of coupled perforated thin-plates. The impacts of perforation parameters on dynamic effective parameters for symmetric and asymmetric BPMs are systemically studied, the simulated and experimental results both show that variation trends of resonance and anti-resonance frequencies of mass-type bilayer perforated thin-plate acoustic metamaterial (MBPM) are different from stiffness-type bilayer perforated thin-plate acoustic metamaterial (SBPM), because perforations mainly change system mass in MBPM and system stiffness in SBPM, respectively. Dynamic effective parameters are bi-anisotropic in asymmetric BPM, and doubly negative effective parameters are achieved by coupled perforations when plan wave normal incident from the side with smaller perforation parameters. A modified retrieval method is proposed to calculate unified effective parameters for the asymmetric BPM, and the unified effective parameters equal to averaged effective parameters of two symmetric BPMs. This work systematically studies dynamic effective parameters of bilayer perforated structures, which has a great guiding significance in design of perforated acoustic devices.

Here, we propose a novel plasmonic structure, called asymmetric plasmonic nanocavity grating (APNCG), which is shown to dramatically enhance nonlinear optical process of second harmonic generation (SHG). The proposed structure consists of two different metals on both sides of lithium niobate and a thin layer of graphene. By using two different metals the nonlinear susceptibility of the waveguide would be increased noticeably causing to increase SHG. On the other hand, it consists of two identical gratings on one side. By two identical gratings, the pump beam is coupled to two opposing SPP waves, which interfere with each other and result in SPP standing wave in the region between the two gratings. The distance between two gratings will be optimized to reach the highest SHG. It will be shown that by optimizing the geometry of proposed structure and using different metals, field enhancement in APNCG waveguides can result in large enhancement of SHG.