A quantum graph approach to metamaterial design

When considering the interaction of a beam with a surface, it is essential to understand that the transmission pattern will shift with changes in the beam's angle, yet the fundamental characteristics remain constant. Transmission occurs only at specific angles; otherwise, the beam is reflected. This behavior distinguishes the phenomenon from traditional diffraction grating, as it is primarily a resonance effect.

We can visualize various configurations where we can tune the system to allow waves to pass through at designated angles. For instance, we might configure the system to permit transmission at zero degrees or at multiple specified angles. The design involves either a graph or a continuous material, interconnected through specific connectors. In this setup, we can connect to fourth neighbors and beyond, creating a network of resonant elements that influence the transmission properties of the surface.