A quantum graph approach to metamaterial design

In this section, we will discuss the experimental setup and results related to surface wave measurements. The process involves generating pulses and measuring the resulting surface waves. A Fourier transform is then applied to analyze these waves. We compare the dispersion curves obtained from our experiments, represented by dark and light yellow lines, with predictions from our finite element model, shown as dashed curves.

The experimental results reveal the presence of sound cones, indicating that certain information is lost as waves radiate from the surface. Notably, we observed a negative group velocity, which aligns with our theoretical predictions using the Graph Model.

Next, we will explore a concept that has intrigued us: the Angular or K filter. This concept can be applied to various materials, including graphene. The setup involves two plates separated by a medium, such as air, connected through pipes. These pipes are designed to resonate and facilitate interactions between non-nearest neighbors in the structure.

As we delve deeper, we will examine how incident plane waves interact with this surface. Depending on the tuning of the surface, only specific angles allow the waves to transmit, while others result in reflection. This behavior resembles diffraction grating, where interference patterns emerge from multiple slits, leading to distinct transmission peaks. However, our setup differs from traditional diffraction, as it does not require a complete grating to produce these effects. Instead, we observe narrow peaks that can extend infinitely, with the slope indicating the focused nature of the incident beam.