Abstract The parameter retrieval method based on scattering data is used to derive dynamic constitutive parameters of solids with periodic structure. There are inherent ambiguities in the real part of the retrieved wavenumber and the sign of impedance, though the latter has a one-to-one correspondence with the direction of energy flux. Moreover, for lossless structures there can be multiple solution branches that satisfy passivity and continuity of the wavenumber as a function of frequency, leading to potentially double positive or double negative (in terms of density and modulus) overall descriptions of the micro-structured medium. The continuity of wavenumber for lossy unit cells is used to unambiguously determine their constitutive parameters and by taking the limit when loss approaches zero, one can determine the stable solution branches of lossless micro-structures. The two loss models of nonzero damping and complex modulus are compared in terms of their energy loss characteristics and retrieved parameters. These models are employed in both time and frequency domain calculations. The lossy solutions demonstrate that from double-negative and double-positive solutions, only the latter is the stable solution branch in a pass-band of a lossless 1D unit cell. A 2D photonic crystal example is used to demonstrate that the wavenumber appears to jump, discontinuously, at the transition point between two consecutive stop-bands, hence rendering the existing methods based on continuity of wavenumber ineffective. In contrast, the proposed approach based on taking limit of lossy solutions can successfully be used to determine stable overall properties of such media. Finally, certain features of half- and full-cycle stop-bands are discussed.

中文翻译：

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在弹性微结构介质的基于散射的参数检索中使用损失限制方法为零

摘要 采用基于散射数据的参数反演方法，推导出周期结构固体的动态本构参数。检索到的波数的实部和阻抗的符号存在固有的模糊性，尽管后者与能量通量的方向一一对应。此外，对于无损结构，可以有多个解分支满足作为频率函数的波数的无源性和连续性，从而导致微结构介质的潜在双正或双负（在密度和模量方面）整体描述。有损单位单元的波数连续性用于明确确定它们的本构参数，并在损失接近零时取极限，可以确定无损微结构的稳定解分支。比较非零阻尼和复模量这两种损耗模型的能量损耗特性和检索参数。这些模型用于时域和频域计算。有损解表明，从双负解和双正解中，只有后者是无损一维晶胞通带中的稳定解支路。一个二维光子晶体的例子被用来证明波数在两个连续阻带之间的过渡点出现不连续的跳跃，从而使现有的基于波数连续性的方法无效。相比之下，所提出的基于有损解极限的方法可以成功地用于确定此类介质的稳定整体属性。最后，讨论了半周期和全周期阻带的某些特征。