A quantum graph approach to metamaterial design

We aimed to investigate the effectiveness of our approach in a continuum case. Gregory conducted an analysis by implementing a continuous waveguide, incorporating pipes and a spiral structure on top. By properly tuning the system, we observed that the incoming source primarily transmitted in specific directions, while other parameter regimes were filtered out by the interface.

The dispersion curves illustrate that transmission occurs only at certain angles. Although the system functions with a continuum beneath the spiral, its performance is somewhat diminished due to excessive flow occurring between the pillars connecting to the interface.

This phenomenon has practical applications. Tristan has advanced our understanding by exploring more complex 2D surfaces within 3D volumes, allowing for the imprinting of desired transmission and reflection characteristics in a two-dimensional format. One potential application is wave filtering, where specific waves are isolated. For instance, by identifying an interface that reflects vertically, we could enhance edge detection capabilities, effectively filtering out certain curvatures to delineate object boundaries.