device, illustrating the splitting of the H and V modes due to fabrication imperfections. (d) FDTD simulated near-field amplitude components for the H dipole mode (top row) and the V dipole mode (bottom row). Plotted for each mode are Re($E_x$) and Re($E_y$). Scale bar in all plots: 250 nm. (e) FDTD simulated far-field radiation intensities of $E_x$ and $E_y$ components for the H dipole mode (top row) and the V dipole mode (bottom row). The white concentric circles correspond to NA $ = 0.2, 0.4, 0.6, 0.8,$ and $ 1.0.$[]{data-label="fignfff"}](fig1.eps){width="80.00000%"}

The H1 PhC cavity design is a candidate structure for polarization degenerate light emission, and by optimizing its structural properties, we are able to dramatically improve the coupling efficiency to the cavity modes. Figure \[fignfff\](a) gives a sketch of the H1 cavity, and an SEM image of a fabricated device in GaAs is shown in Fig. \[fignfff\](b). The H1 cavity, being a point-like defect on a triangular lattice, has a $C_{6v}$ symmetry, i.e. the geometry remains the same rotating the structure by $\pi/3$ around the center of the cavity. In such a geometry, if a mode is an eigenstate of the wave equation, then any rotation of the mode by 