超材料准粒子时域弹性散射的模态近似
Modal approximation for time-domain elastic scattering from metamaterial quasiparticles
摘要：
本文的目的是定量地了解弹性波散射由于负的超材料结构下的宽带信号在时域。具体地，我们建立了弹性动力学中的超材料准粒子散射的含时场的模态展开。通过傅里叶变换，我们首先分析了时谐区的模态展开。随着准粒子的存在下，我们验证了这样的扩展在静态政权通过定量分析的Neumann-Poincaré算子与弹性静力系统的光谱特性。然后，我们近似的入射场与有限数量的模式和应用扰动理论，以获得这样的微扰制度的扩展。此外，我们给出了非零频率弹性系统的极化激元共振作为单极点。最后，我们表明，在时域中的散射场的低频部分，可以很好地近似使用尖锐的误差估计的谐振模态展开。
英文摘要：
This paper aims at quantitatively understanding the elastic wave scattering due to negative metamaterial structures under wide-band signals in the time domain. Specifically, we establish the modal expansion for the time-dependent field scattered by metamaterial quasiparticles in elastodynamics. By Fourier transform, we first analyze the modal expansion in the time-harmonic regime. With the presence of quasiparticles, we validate such an expansion in the static regime via quantitatively analyzing the spectral properties of the Neumann-Poincaré operator associated with the elastostatic system. We then approximate the incident field with a finite number of modes and apply perturbation theory to obtain such an expansion in the perturbative regime. In addition, we give polariton resonances as simple poles for the elastic system with non-zero frequency. Finally, we show that the low-frequency part of the scattered field in the time domain can be well approximated by using the resonant modal expansion with sharp error estimates.
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