Slow waves in locally resonant metamaterials line defect waveguides

In the past decades, many efforts have been devoted to the temporal manipulation of waves, especially focusing on slowing down their propagation. In electromagnetism, from microwave to optics, as well as in acoustics or for elastic waves, slow wave propagation indeed largely benefits both applied and fundamental physics. It is for instance essential in analog signal computing through the design of components such as delay lines and buffers, and it is one of the prerequisite for increased wave/matter interactions. Despite the interest of a broad community, researches have mostly been conducted in optics along with the development of wavelength scaled structured composite media, that appear promising candidates for compact slow light components. Yet their minimum structural scale prevents them from being transposed to lower frequencies where wavelengths range from sub-millimeter to meters. In this article, we propose to overcome this limitation thanks to the deep sub-wavelength scale of locally resonant metamaterials. In our approach, implemented here in the microwave regime, we show that introducing coupled resonant defects in such composite media allows the creation of deep sub-wavelength waveguides. We experimentally demonstrate that waves, while propagating in such waveguides, exhibit largely reduced group velocities. We qualitatively explain the mechanism underlying this slow wave propagation and first experimentally demonstrate, then numerically verify, how it can be taken advantage of to tune the velocity, achieving group indices ng as high as 227 over relatively large bandwidths. We conclude by highlighting the three beneficial consequences of our line defect slow wave waveguides in locally resonant metamaterials: the deep sub-wavelength scale, the very large group indices and the fact that slow wave propagation does not occur at the expense of drastic bandwidth reductions.