High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Marie Touboul, Bruno Lombard, Raphael C. Assier, Sebastien Guenneau, Richard V. Craster
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引用次数: 0

Abstract

Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method of low-frequency homogenization, it was so far only possible to obtain non-reciprocal effective media when both material properties are modulated in time, in the form of a Willis-coupling (or bi-anisotropy in electromagnetism) model. If only one of the two properties is modulated in time, while the other is kept constant, it was thought impossible for the method of homogenization to recover the expected non-reciprocity since this Willis-coupling coefficient then vanishes. Contrary to this belief, we show that effective media with a single time-modulated parameter are non-reciprocal, provided homogenization is pushed to the second order. This is illustrated by numerical experiments (dispersion diagrams and time-domain simulations) for a bilayered modulated medium.

时间调制波方程的高阶同质化:单一变化参数的非互易性
众所周知,材料特性在空间和时间上以行波形式调制的层状介质长期以来一直表现出非互易性。然而,在使用低频均质化方法时,迄今为止只有当两种材料特性都在时间上受到调制时,才能以威利斯耦合(或电磁学中的双向各向异性)模型的形式获得非互易的有效介质。如果两个属性中只有一个随时间变化而变化,而另一个保持不变,则人们认为均质化方法不可能恢复预期的非互易性,因为威利斯耦合系数会消失。与这一观点相反,我们的研究表明,只要将均质化推至二阶,具有单一时间调制参数的有效介质是非互易的。我们通过对双层调制介质的数值实验(频散图和时域模拟)来说明这一点。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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