Fig. 2: Elecric fields of band-edge modes A–D radiated into free-space by lattice points considered to function as nanoantennas.

a–d Electric-field distributions of band-edge modes A–D in a photonic crystal a without modulation and with b position modulation, c size modulation, and d dual modulation. a Far-field radiation is zero for all modes, due to the rotationally symmetric electric field of band-edge modes A and B with respect to the lattice points and the opposing electric-field vectors of band-edge modes C and D. b Far-field radiation is finite for band-edge modes A and B due to their finite electric-field vectors pointing in identical directions, and near-zero for band-edge modes C and D due to their finite electric-field vectors pointing in opposite directions. c Far-field radiation is zero for band-edge modes A and B, for the same reason as in a, and finite for band-edge modes C and D, due to the alleviation of destructive interference. d Far-field radiation is finite for all modes, due to the combined effects of position and size modulations. In each panel, the product of the size \(\bar S_{m,n}\) of each nanoantenna and the electric-field \({\mathbf{{\cal{E}}}}( {{\bar{\mathbf{r}}}_{m,n}} )\) at its center position \({\bar{\mathbf{r}}}_{m,n}\) is shown with blue and red arrows. When the product becomes zero, only dots are shown.