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\chapter{COMSOL Simulation Details} \label{Chapter:COMSOL}

COMSOL was used to model the zigzag metasurfaces. The model consisted of a single unit of the gold metasurface placed on top of fused quartz and with air above. The quartz and air extend 2um away from the gold with refractive indices of 1.45 and 1 respectively. An interpolated model of the real and imaginary refractive indices was used to define the properties of the gold. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/COMSOL/gold and glass.png}
  \caption{(a) Blue volume defined as gold for the zigzag wire samples. The inverse selection is made for the zigzag slits. (b) Blue volume defined as fused quartz}
  \label{Figure:goldglass}
\end{figure}

The parameters of the model were varied to create the different aspect ratio and different parts were selected to be gold to create the inverted and isolated structures.

\newpage

The 4 boundaries surrounding the metasurface were defined as periodic boundary conditions, effectively making the model an infinite plane. The top and bottom of the model were defined as ports to allow for waves to be created and collected. Scattering boundary conditions were used to eliminate any reflections from the ports. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/COMSOL/Boundaries.png}
  \caption{(a)\&(b) Periodic boundary conditions on the sides. (c) Ports with scattering boundary conditions at the top and bottom.}
  \label{Figure:Boundaries}
\end{figure}

Finer mesh elements were used in the metasurface plane. Larger mesh elements were used for the air and glass volumes. The mesh was defined for 2 perpendicular sides and then copied to the opposite sides to ensure the mesh matched for the periodic boundary conditions. The internal volume mesh was then generated after this.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/COMSOL/Mesh.png}
  \caption{The mesh.}
  \label{Figure:mesh}
\end{figure}